LIBRARY 

OF    THE 

UNIVERSITY  OF  CALIFORNIA. 


Class 


GENERAL 


^9^ 


< 


SYSTEM  AND  TABLES 


OP 


Life  Insurance. 


A    TREATISE    DEVELOPED    FROM    THE    EXPERIENCE    AND    RECORDS    OF 

THIRTY   AMERICAN    LIFE    OFFICES,    UNDER    THE    DIRECTION 

OF    A    COMMITTEE    OF    ACTUARIES. 


BY 

LEVI    W.    MEECH, 

ACTUARY    IN    CHARGE. 


REVISED    EDITION    OF   1898, 

WITH    AMERICAN    LIFE    TABLES,    INCLUDINa    VALUATION     OF 
ANNUITIES    OR    PENSIONS,    REVERSIONS    AND    DOWER. 


THE  SPECTATOR  COMPANY, 

NEW  YORK. 


wy\^ 


rx^\\i^^^ 


100.000 


98,000 


90.000 


85.000 


AMERICAN    LIFE    TABLE 

CMALES) 

FROM  COMBINATIONS  OF  THE  CENSUS. 


f 


SCALE  OF  AGES 


Copyright,  1881,  by  Levi  W.  Meech. 


NEPAL     S>i'^<^^^ 


PREFACE. 


THE  origin  of  the  present  collection  of  statistics,  dates  from  the  re-organization  of 
the  Chamber  of  Life  Insurance  in  1873.  Among  the  leading  objects,  it  was 
provided  that,  "there  shall  be  a  standing  Committee  on  Mortality  Experience, 
appointed  by  the  Executive  Committee,  immediately  after  the  Annual  Election 
of  the  Chamber,  in  each  year,  and  consisting  of  five  members,  to  whom  shall  be 
referred  the  work  of  collecting  the  statistics  of  Mortality  Experience,  classifying, 
arranging,  and  tabulating  them  for  practical  use,  with  power  to  employ  skilled 
assistance." 

In  entering  upon  the  duties  assigned  them,  this  Committee,  after  some  prelimi- 
nary consultation,  decided  to  invite  a  more  full  expression  of  opinions  in  a  general 
meeting  of  Actuaries,  which  was  held  in  New  York,  Nov.  19,  1874.  Among  those 
present  and  participating  in  the  deliberations,  besides  the  Committee,  were  S.  Co 
Chandler  Jr.,  D.  Parks  Fackler,  C.  M.  Hibbard,  Sheppard  Homans,  Jas.  Weir  Mason. 
Prof.  C.  F.  McCay,  Emory  McClintock,  George  W.  Phillips,  William  D.  Whiting,  and 
Charlton  T.  Lewis,  Secretary  of  the  Chamber.  Besides  these,  a  considerable  number 
communicated  their  views  by  letter.  An  enlarged  plan  of  operations  having  been 
generally  called  for,  the  Committee,  in  concurrence,  subsequently  issued  the  following 
Circular,  under  date  of  March  16,  1875  ;  copies  of  which  were  addressed  to  all  Life 
Insurance  Companies  in  the  United  States : 

Sir: 

The  Chamber  of  Life  Insurance  has,  through  its  Executive  Committee,  appointed  the  under- 
signed a  Committee  upon  Mortality  Experience,  with  instructions  to  procure  from  every  American 
Company  willing  to  furnish  it,  their  experience  in  full  up  to  a  recent  period.  In  accordance  therewith, 
we  respectfully  and  most  earnestly  request  you  to  favor  us  with  the  data  of  your  company  to  Decem- 
ber 31,  1874,  as  indicated  below.  While  the  amount  of  labor  to  be  performed  both  by  the  companies 
and  the  Committee  mil  be  considerable,  the  importance  of  this  work,  if  well  done,  to  American 
companies,  cannot  be  over  estimated.  Tables  made  from  such  experience  can  justly  be  regarded  as  of 
higher  authority,  and  will  probably  more  nearly  approximate  the  true  average  of  mortality  among 
insured  American  lives  than  any  now  in  use.  And  should  similar  examinations  be  made  hereafter,  as 
we  trust  may  be  the  case,  in  which  the  results  of  the  work  now  in  hand  may  be  merged,  by  such 
periodic  examinations,  and  the  aggregation  of  experience,  we  shall  be  able  measurably  to  trace  any 
general  improvement  in  longevity,  the  effect  of  causes  operating  specially  within  the  period  under 
consideration,  the  effect  of  public  sanitary  measures,  and  probably  many  other  points  of  interest 
incident  to  the  development  and  improvement  of  a  new  and  growing  country.  We  hope  that  the 
present  undertaking  is  but  the  beginning  of  a  systematic  and  profound  study  of  the  mortality  among 
insured  American  lives. 

In  settling  the  details  of  this  work,  we  have  had  in  view  certain  important  classifications,  leaving 
many  minor  though  interesting  ones  to  be  wrought  out  by  the  companies  themselves ;  and  the  saving 
of  all  but  indispensable  labor  to  the  companies  contributing  their  data. 

The  points  agreed  upon  by  this  Committee  for  consideration  are : 

First,  The  general  mortality  among  insured  lives ; 
Second,  The  mortality  by  sexes  ; 

Third,  The  mortality  by  localities,  taking  the  State  as  a  basis,  except  in  certain  States  where 
the  County  is  to  be  designated ; 


115492 


4  PREFACE. 

Fourth,  The  mortality  by  years  of  insurance,  in  order  to  sbow  the  eflfect  and  duration  of 

medical  selection  ; 
Fifth,  The  ratio  of  financial  loss  to  sums  exposed  to  risk  ; 
Sixth,  A  classification  of  the  causes  of  death,  in  general,  by  locality,  and  such  other  special 

relations  as  may  be  deemed  advisable  hereafter. 

For  these  purposes  the  Committee  have  adopted  the  enclosed  card,  as  enabling  the  companies  to 
furnish  the  necessary  data  vfith  the  least  possible  labor.  The  instructions  upon  another  page  will 
enable  a  clerk  to  make  correct  and  rapid  use  of  it. 

Companies  which  have  already  arranged  their  data  for  their  own  examination  in  a  manner  to 
supply  the  Committee  what  is  called  for  by  the  card,  need  only  furnish  their  cards  or  sheets  already 
prepared  or  their  classifications  if  these  correspond  to  those  above  stated,  and  any  such  material  will 
be  returned  after  use ;  and,  if  desired,  all  cards  will  be  returned.  No  tabulation  or  exhibit  will  be 
made  in  any  manner  of  the  separate  mortality  of  any  company,  and  the  data  will  be  held  as  confiden- 
tially given.  It  is  our  desire  that  the  data  may  be  given  with  all  reasonable  speed,  and  in  view  of  the 
great  interest  and  importance  attaching  to  the  work,  we  trust  all  will  make  this  matter  one  of  special 
care  and  attention,  and  employ  in  it  sufficiently  skilled  labor  to  insure  neat  and  accurate  execution. 
The  cards  should  be  carefully  verified  t)efore  being  sent  to  the  Committee,  which  will  have  no  means 
of  correcting  errors  made  at  the  offices  of  the  companies. 

The  results  of  this  labor  will  be  reported  to  the  Chamber  at  the  earliest  practicable  moment,  and 
by  it  published  so  as  to  be  accessible  to  all  desiring  it. 

We  believe  it  to  be  the  general  conviction  among  American  and  foreign  Insurance  officials  and 
actuaries  that  the  material  now  capable  of  being  supplied  here  will  give  results  of  peculiar  value  and 
importance,  and  that  American  companies  owe  it  to  the  business  at  large  and  to  their  own  interests 
that  these  should  be  collated  and  properly  classified ;  and  that  it  would  be  a  cause  of  regret  should 
any  Company  fail  to  join  in  this  work,  which  is  not  undertaken  for  the  benefit  of  the  Chamber  alone, 
or  of  the  companies  belonging  to  it,  but  for  that  of  all  companies  doing  business  in  this  country.  We 
promise  our  best  endeavors  to  make  the  character  of  the  work  worthy  of  its  importance. 

Please  indicate  at  once  to  the  Chairman  at  Hartford,  Conn.,  the  number  of  cards  you  may  need, 
and  the  probable  time  at  which  they  can  be  completed. 

Respectfully,  Jacob  L.  Gkeene,  Chairman. 

Edwin  W.  Bryant, 
Robert  A.  Granniss, 
i  Levi  W.  Meech, 

Howell  W.  St.  John. 

The  way  had  been  opened  for  this  investigation,  by  the  London  Institute  of 
Actuaries,  which  had  collected  the  records  of  twenty  Life  Offices  in  England  and 
Scotland.  But  the  strongest  incentive,  lay  in  the  recent  remarkable  increase  of  Life 
Insurance  in  the  United  States,  creating  a  demand  for  a  more  systematic  exposition  of 
insured  experience.  The  following  summary  from  the  current  Massachusetts  and  New 
York  State  Reports,  comprising  the  greater  part  of  the  Companies  in  the  Union,  may 
serve  to  illustrate  the  magnitude  of  the  business  at  this  epoch. 

In  a  general  statement,  the  fifty  thousand  policies  of  1859  had,  in  four  years  or 
in  1863,  increased  to  a  hundred  thousand.  Then  the  rate  of  increase  was  temporarily 
doubled,  and  within  two  years  more,  at  the  end  of  the  year  1865,  the  number  exceeded 
two  hundred  thousand.  In  another  two  years,  or  in  1867,  it  exceeded  four  hundred 
thousand.  And  in  1872,  the  number  of  policies  had  risen  to  eight  hundred  thousand. 
By  this  time,  the  annual  discontinuances  began  to  balance  the  diminished  number  of 
entrants ;  and  at  the  epoch  of  the  experience,  Dec.  31,  1874,  the  total  number  exposed 
to  risk  had  been  nearly  stationary  for  five  or  six  years,  with  about  eight  hundred 
thousand  policies  in  force. 

The  preceding  Circular, was  accompanied  by  the  adopted  form  of  policy  cards,  and 
instructions,  which  are  given  hereafter.  In  the  final  result,  twenty- three  Companies 
returned  the  cards,  filled  out  from  their  office  records  ;  and  seven  gave  the  results  of 
their  own  investigations,  brought  down  to  the  beginning  of  the  year  1874.  The  latter 
returns  were  accompanied  by  collateral  explanations  and  results  sufficient  for  verifying 


PREFACE.  5 

and  resolving  them  into  the  original  elements,  in  uniformity  with  the  card  reductions. 
In  this  manner  the  entire  returns  were  united  ;  and  it  was  found  that,  of  all  the  valid 
experience,  recorded  upon  the  office  registers  in  the  United  States,  so  favorable  had 
the  enterprise  been  regarded,  fully  three-fourths  had  been  contributed  for  this  collection. 

The  following  are  the  names  of  the  Companies  whose  combined  experience  is  given 
in  the  succeeding  pages,  with  the  year  of  organization  and  aggregate  number  of  policies: 


COSIPANIES.  OBGANIZATION. 

1.  Aetna  Life,  Connecticut,    .    .    .    .    .  1850 

2.  American  Mutual,  Connecticut,      .    .  1848 

3.  Brooklyn,  New  York, 1864 

4.  Charter  Oak,  Connecticut,      ....  1850 

5.  Connecticut  General,  Connecticut,  .  1865 

6.  Connecticut  Mutual,  Connecticut,     .  1846 

7.  Continental,  New  York, 1866 

8.  Covenant,  Missouri, 1853 

9.  Equitable,  Iowa, ' .    .    .  1867 

10.  Equitable,  New  York, 1859 

11.  Germania,  New  York, I860 

12.  Globe,  New  York,  ........  1864 


Companies.  OBOANizATtoN. 

16.  Massachusetts  Mutual,  Massachusetts,  1851 

17.  Metropolitan,  New  York,     ....  1867 

18.  Mutual  Life,  New  York, 1843 

19.  Mutual  Benefit,  New  Jersey,    .    .    .  1845 

20.  National  of  United  States,  Illinois,  1868 

21.  New  England  Mutual,  Massachusetts,  1844 

22.  Northwestern,  Wisconsin,    ....  1858 

23.  Penn  Mutual,  Pennsylvania,  ....  1847 

24.  St.  Louis  Mutual,  Missouri,  ....  1858 

25.  Travelers,  Connecticut, 1866 

26.  Union  Central.  Ohio,    ......  1867 

27.  Union  Mutual,  Maine, 1849 


13.  John  Hancock,  Massachusetts,     ,    .    .    1862  1  28.  United  States,  New  York,     ....    1850 

14.  Life  Association,  Missouri,    ....    1868  |  29.  Washington,  New  York 1860 

15.  Massachusetts  Hospital,  Mass.,    .    .    1823  i  30.  Western  New  York.    ......    1868 

Summary  in  1874.           Net  Number  op  Policies  or  Lives.  Amount  Insured. 

Existing  or  not  terminated,         .        .        549,418  $1,367,217,000 

Discontinued, 431,568  1,159,867,000 

Died, 46,543  130,224,000 

Whole  Number,  .        .        .        .     1,027,529  $2,657,308.000 

Exposed  tc  Risk  one  Year,       .     4,504,797  $11,839,005,500 

These  figures  represent  the  net  numbers  after  more  than  a  hundred  thousand 
secondary  and  other  policies  have  been  omitted  or  transferred  according  to  the  rules  of 
reduction.  Thus  the  total  Experience  of  the  Thirty  Life  Offices  has  a  net  basis  of 
more  than  a  million  of  policies,  or  lives,  insured  for  more  than  twenty-six  hundred 
millions  of  dollars. 

The  arrangement  of  so  extensive  a  serjes  of  tables  has  been  guided,  as  far  as  possi- 
ble, by  the  best  established  precedents,  and,  mere  innovation  has  been  carefully  avoided. 
In  several  particulars,  however,  the  system  of  Life  Tables  as  described  in  that  great 
repository,  the  Journal  of  the  Institute  of  Actuaries,  was  found  to  be  still  in  a  state  of 
progress.  Different  courses  were  indicated  for  determining  the  proper  resultant  between 
the  effects  of  the  medical  selection  and  the  counter  selection  of  the  insured,  such  as  the 
omission  of  the  first  three  or  five  years  experience.  Also  shorter  methods  were  demand- 
ed for  changing  the  standard  life  table  to  higher  or  lower  grades  of  mortality.  And 
another  desideratum  was  the  condensation  within  a  convenient  compass  of  the  vcflunii- 
nous  tables  for  term  policies,  endowments,  and  joint  lives,  to  give  monthly  as  well  as 
annual  values.  It  has  been  much  easier  to  describe,  than  to  supply  what  is  needed. 
That  an  advance  might  be  made  to  meet  these  difficulties,  the  actuary  in  charge  has 
given  them  all  the  consideration  which  other  duties  have  permitted  ;  Avith  what  success 
the  examination  of  the  following  pages  prepared  by  him,  must  determine.  Among  the 
improvements  to  meet  the  necessities  of  the  work,  may  be  named,  the  principles  of 
transformation  of  Office  data,  the  system  of  final  series,  the  life  table  graded  for  different 


6  PREFACE. 

climates,  the  proof  of  the  logarithmic  law  of  mortality,  the  general  yaluation  tables,  the 
arrangement  of  joint  lives  and  survivorships,  with  new  investigations  described  hereafter. 

The  first  reductions  of  the  Mortality  Experience,  were  commenced  in  November, 
1875  ;  but  the  principal  part  of  the  returns  arrived  in  the  following  summer,  when  the 
number  of  clerks  engaged  in  their  reduction,  was  augmented  from  three  to  ten.  Other 
returns  came  in  at  later  dates ;  and  the  last  was  received  at  the  close  of  the  year  4877. 
With  an  adequate  clerical  force,  the  reductions  were  pressed  forward  as  fast  as  the 
returns  arrived ;  and  in  March  1878,  the  first  fruits  appeared  in  the  issue  of  copies  of 
the  Climatic  Tables  for  examination. 

It  may  here  be  mentioned,  that  after  the  preliminary  arrangements  had  been 
initiated  and  were  fairly  in  progress,  two  of  the  Committee  withdrew  from  membership 
though  not  from  interest  in  the  work,  and  their  places  were  supplied  in  succession  by 
the  election  of  Emory  McClintock  and  George  W.  Phillips.  The  former  actuary  had 
especially  advocated  the  importance  of  the  returns  of  losses  and  amounts  insured ;  while 
the  latter  actuary,  by  elaborate  office  reductions,  had  prepared  the  way  for  the  present 
climatic  statistics.  For  the  position  of  chairman  of  the  committee,  Levi  W.  Meech  was 
chosen,  who  had  at  an  early  stage  been  designated  to  take  charge  of  the  returns,  and  to 
make  the  proper  reductions  at  the  expense  of  the  Chamber.  And  in  May,  1878,  after 
the  dissolution  of  the  Chamber,  John  M.  Taylor,  Secretary  of  the  Connecticut  Mutual 
Life  Office,  accepted  the  position  of  Treasurer. 

In  the  medical  department,  the  classification  of  diseases  given  by  the  cards,  required 
the  services  of  a  physician  long  conversant  with  office  examinations,  and  the  current 
applications  from  different  parts  of  the  United  States.  Such  an  examiner  Avas  found  in 
J.  C.  Jackson,  M.D.,  of  Hartford,  by  whom  the  numerous  returns  of  diseases  were  faith- 
fully examined  during  several  months,  till  the  medical  statistics  were  classified  under 
the  most  favorable  conditions  of  accuracy  and  authority.  It  should  also  be  mentioned 
that  the  returns  from  two  Western  Life  Companies,  were  generously  furnished  by  the 
late  William  E.  Harvey,  Actuary,  after  his  own  reductions.  And  in  this  connection, 
for  maintaining  the  highest  attainable  accuracy,  thanks  and  commendation  are  due  to 
our  clerical  force,  especially  to  M.  C.  Spring,  S.  E.  Warner,  and  S.  M.  Hayward,  assist- 
ants. From  the  amateur  collection  courteously  furnished  by  Mr.  J.  Downes,  of  Wash- 
ington, D.  C,  we  have  copied  the  accurate  table  of  anti-logarithms,  reduced  from  the 
eleven  place  values  of  Dodson,  compared  with  Vega ;  and  have  added  proportional  parts 
for  the  middle  of  each  division,  computed  with  three  extra  decimals. 

To  give  confidence  in  employing  the  vital  statistics,  it  may  be  proper  to  state,  that 
all  the  original  returns  had  been  copied  under  responsible  direction,  from  regular  Office 
records,  alike  free  from  objection.  The  subsequent  reductions  by  the  Committee,  have 
been  verified  by  two  independent  operations ;  and  a  further  check  was  obtained  by 
comparison  of  the  parallel  columns  of  Lives  and  Amounts.  The  work  has  been  nearly 
six  years  in  progress,  under  a  single  direction  of  large  experience;  and  with  favorable 
conditions,  has  thus  resulted  in  an  authentic  standard  for  reference. 

Levi  W.  Meech,  in  Charge. 
'  EDWijf  W.  Bryant, 

Emory  McClintock, 
George  W.  Phillips, 
Howell  W.  St,  John. 


CONTENTS. 


ELEMENTARY  OBSERVATIONS  AND  TABLES. 


DIVISION    FIRST.    Mortality  and  Loss  Experience. 

SECTION  PA«B 

I.    Instbuctions  and  Sample  Cakds 13 

II.    Adjustments  op  Cards.    Dtjkation 31 

Method  for  Joint  Lives,  Transfers,  Original  Death  Claims 32 

III.  Classifications  op  Data 33 

IV.  Calendar  Years  and  Policy  Years 34 

V.    Notation  and  Annual  Equations - 35 

VI.    Transformation  op  Data 36 

VII.    Exposed  to  Risk , 38 

VIII.    Comparative  Results.    Ratios  op  Mortality  and  of  Loss  to  1874 39 

Influence  of  Medical  Examinations  and  the  Amounts  at  Risk 30 

Insured  Females 34 

IX.    Continuation  of  the  Experience  op^  1874  to  Final  Series 35 

X.    Notes  on  Graduation.     Short  Method  for  the  Expectation  of  Life 38 

Graduation  by  Formula  and  by  Divided  Differences 40 

Loss  relative  to  Term  and  other  Species  of  Insurances 43 


DIVISION    SECOND.    Climatic  Tables. 

I.    Computation  op  Probable  Loss,  with  Tabular  Factors 43 

Change  of  Probable  Loss  from  the  standard  of  one  Life  Table  to  another 46 

II.    Classification  op  Counties.    Miscellaneous  Statistics 46 

Climate  Extra 48 

III.    The  Life  Table  Graded  for  Different  Climates 49 

Climatic  Formulas  and  Special  Ratios  for  Tables 50 


CONTENTS. 


DIVISION    THIRD.    Medical  Statistics. 

SECTION  FAeS 

I.    Desckiption  of  the  Tables 52 

II.    Statistics  of  Consumption  Compabed 54 

Sanitary  Survey  of  the  United  States 56 

Table  of  the  Relation  of  Height  and  Weight 57 

III.    The  Germ  Theory  op  Malarial  Diseases 57 

Table  of  Sickness  and  Recovery  in  Adult  Life 58 


DIVISION    FOURTH.    Time  and  Monetary  Tables. 

I.    The  System  of  Interest  and  Annuities 59 

II.    Time  and  Interest  Tables  for  Days 60 

Copy  Multiplication 61 

III.    Compound  Interest  and  Discount  Tables.    For  Twelve  Rates  of  Interest 

continued  to  100  Years 64 

Connection  of  the  Tables 65 

IV".    To  FIND  THE  Rate  of  Interest  of  an  Annuity 41,  65 

V.    To  FIND  THE  Rate  of  Interest  on  the  Price  of  Funded  Stocks  or  Bonds 67 

Table  of  the  Auxiliary  Factor 68 

VI,    Interest  Compounded  oftener  than  Once  a  Year 69 

Correction  of  the  Present  Value  of  Half- Yearly  and  Quarterly  Annuities 70 

Illustrations  of  Compound  Interest 71 


F^PtT      SEOOISTD. 

LIFE     ANNUITIES*  AND     INSURANCES. 

I.    First  Principles  op  Probability  for  Reference 233 

Mathematical  and  Moral  Expectation 235 

II.    The  Life  Table.    Law  op  Mortality  Established 237 

Construction  of  Life  Tables  from  the  Final  Series  of  Tables  III  and  IV 237 

Formula  and  Constants  of  the  Life  Table  for  Males 237 

Fluctuating  periods  of  health  or  Climacterics 238 

Expressions  for  the  relative  Force  and  the  Rate  of  Mortality 239 

III.  Present  Value  op  Life  Annuities 240 

Temporary  and  Deferred  Annuities.     Joint  Lives ...  241 

Simpson's  Rule.    Half- Yearly  and  Quarterly  Annuities 242 

Annuities  payable  to  the  day  of  Death 242 

IV.  Expectation  of  Life  and  Probable  Life 242 

The  Curtate  and  the  Even  Expectation 243 

Probable  Life  in  Europe. 244 


CONTENTS.  9 

SECTION  PAGE 

V.    Commutation  Tables 244 

Methods  of  Construction 246 

VI,    Single  and  Annual  Premiums  of  Insurance - 248 

1.  Formulas  for  Single  Premium 249 

2.  Annual  Premium 249 

3.  Five,  Ten,  or  Limited  Annual  Premiums 250 

4.  Temporary  Insurances 250 

5.  Pure  Endowments ...  251 

6.  Endowment  Insurances, 251 

7.  Deferred  Insurances 252 

8.  Return  Premiums 252 

9.  Increasing  and  Decreasing  Scales  of  Premium 253 

10.  Increasing  and  Decreasing  Insurances 254 

11.  Price  of  Annuities  secured  by  Life  Insurance 355 

12.  Insurance  on  Female  Life 256 

13.  Insurance  on  Joint  Lives 256 

Method  for  Three  or  Four  Joint  Lives 258 

Equalization  of  Annuities.     Tables  for  Simpson's  Rule 259 

14.  Survivorship  Insurances.     Makeham's  General  Solution 260 

15.  Insurances  payable  at  Death.     16.  Semi- Annual  and  Quarterly  Premiums 264 

VII.    Reserve  or  Valuation  of  Policies 264 

Months  and  Days.     Reserve  on  Paid-up  Policies 265 

Valuation  of  Annual  Premium  Policies.    Prospective  Formulas 265 

Valuation  of  Gross  Premiums 266 

Valuation  of  Annual  Premium  Policies.     Retrospective  Formulas 267 

Elementary  Formula  of  Valuation 268 

Application  to  Return  Premium  and  other  Species  of  Policy 268 

General  Valuation  Table.     Adjustment  for  Months 269 

Valuation  Table  for  Joint  Lives  by  Single  Entry 270 

Reserve  on  Survivorship  Insurances,  new  process 271 

Short  Method  for  the  equivalent  Sum  Insured  by  Paid-up  Policy 271 

Non-Forfeiture.     Annual  Valuation  of  an  Insurance  Office 272 

Reference  to  Methods  for  the  Distribution  of  Surplus 273 

Illustrations  of  the  Contribution  Formula 274 

Tontine  Dividends 295 

VIII.    Life  Annuities.    Survivorshlp  and  Reversionary  Annuities.    Successive  Lives,  275 

Present  Value  of  Single  Life  Annuities  of  different  Species „ . .  275 

Reserve  or  Valuation  of  Annuity  Policies 276 

Annuity  extended  to  an  extra  payment ;  also  to  the  day  of  Death 277 

Present  Value  of  an  Annuity  on  the  longest  Life  or  last  Survivor 277 

Annuity  on  the  last  n  Survivors  of  m  Lives 278 

Reversionary  Annuities.     Verification 279 

Partition  of  Annuities.     Conditional  Periods 281 

Survivorship  Problems.     Successive  Lives 283 

IX.    Derivative  Formulas.     The  Continuous  Method 285 

Annual  Derivation.     Tables  of  Addition  and  Cubtraction  Logarithms 283 

Summation  Formula  applied  to  Annuities  and  Instalments 288 

Change  from  Ordinary  to  Continuous  Annuities  and  Premiums 290 

Applications  of  the  Differential  and  Integral  Calculus 291 

Total  Probability  of  Survivorship  between  Two  Lives 294 

Remarkable  Simplification  of  the  Survivorship  Problems 295 

X.    Insurance  on  Lives  according  to  the  Order  of  Survivorship 296 

Notation 302 Interpolation.    CoNSTANTf 304 


Tumbles    iint    p^^rt    p^irst. 


DIVISION    FIRST.    Mortality  and  Loss  Experience. 

TABLE  PAGE 

I.    Observations  on  Insured  Male  Life 77-123 

Summary  (A).    According  to  Ages  of  Exposure 74- 

Summary  (B).    According  to  Years  of  Insurance 76 

II.    Observations  on  Insured  Female  Life 127-158 

Summary  (A).     According  to  Ages  of  Exposure 124 

Summary  (B).    According  to  Years  of  Insurance  126 

III.  Male  Life  (A).     Mortality  and  Death.  Claims  per  cent,  by  Ages 159 

Male  Life  (B).     Mortality  and  Discontinued  per  cent,  by  Durations jl61 

Male  Life  (C).     Logarithm  of  Multiplier  for  Final  Series. 162 

Average  Sum  Insured 159-161 

IV.  Female  Life  (A).     Mortality  and  Death  Claims  per  cent,  by  Ages 164 

Female  Life  (B).     Mortality"  and  Discontinued  per  cent,  by  Durations 166 

Female  Life  (C).     Logarithm  of  Multiplier  for  Final  Series 166 

Average  Sum  Insured 164-166 

Mean  Percentage  of  Mortality  by  the  Year  of  Insurance 30 

Male  Life.     Deaths  and  Claims  per  cent,  to  1874 31 

Female  Life.     Death  and  Claims  per  cent,  to  1874 32 

Comparison  from  several  Tables  of  Mortality 34 

Comparisons  of  Experience  to  1874  with  Final  Scries 36-38 

Short  Method  for  Expectation  of  Life 39 

Loss  relative  to  Species  and  to  Amount  of  Policy 42 


DIVISION    SECOND.    Climatic  Tables. 

V.    Probable  Loss  and  Actual  Loss  by  States  and  Territories 167 

VI.     Order  and  Variability  of  Climatic  Ratios  in  thirty-five  States 168 

VII.    Probable  Loss  and  Actual  Loss  by  Counties  in  twelve  States 169-179 

VIII.     Climatic  Commutation  Table.     Interest  4  per  cent 180 

Multiplier  to  give  the  Probable  Loss 44 

Classification  of  Counties 46 

Age  of  Mean  Rate  of  Probable  Loss 47 

Comparison  of  Northampton  and  Carlisle  Annuities 49 

DIVISION    THIRD.    Medical  Statistics. 

IX.    General  Table  of  Diseases  and  Deaths  with  Variability 182-185 

X.    (A)  Males.    (B)  Females.     Diseases  and  Durations  of  Policy  at  Death 186 

XL    (A),  (B).     Diseases  and  Ages  at  Death 188 

XII.     (A),  (B).     Diseases  and  Deaths  by  States  and  Territories 190 

Xm.    (A),  (B).     Ratio  of  Deaths  to  Exposed,  by  Duration  of  Policy 192 

XIV.    (A),  (B).    Ratio  of  Deaths  to  Living  by  Ages  of  Exposure 194 

XV.    (A),  (B).     Percentage  Distribution  of  Disease  by  Duration  of  Policy. 196 

XVI.     (B),  (A).     Percentage  Distribution  of  Diseases  by  Ages  of  Exposure 197 


Note.— The  Formola  of  Computation  is  generally  given  ou  the  first  Page  of  each  Table. 


TABLES.  .11 

TABLE  PAGE 

XVII.     (A),  (B).  Climatic  Distribution  of  Diseases  among  100  Deaths.   Results  of  the  Census  199 

(C).     Diseases  and  Deaths  among  10,000  Exposed  in  each  Group  of  States 201 

A  Sanitary  Survey  of  the  United  States 56 

Table  of  Relative  Height  and  Weight 57 

Table  of  Sickness  and  Recovery  in  adult  Life 58 


DIVISION    FOURTH.    Time  and  Monetary  Tables. 

XVIII,    Calendar  and  Decimal  Parts  of  a  Year 202 

XIX.    Simple  Interest  for  Days  at  5  per  cent.  Omitted 204-207 

Copy  Multiplication 62 

XX.     Amount  of  $1  at  the  End  of  any  Number  of  Years 208-211 

XXI.    Present  Value  of  $1  due  at  the  End  of  any  Number  of  Years 212-215 

XXII,    Amount  of  $1  per  annum  at  the  End  of  any  Number  of  Years 216-219 

XXIII.  Present  Value  of  $1  per  annum  for  any  Number  of  Years 220-223 

XXIV.  Annuity  which  $1  will  purchase  for  any  Number  of  Years 224-227 

XXV.    Logarithm  of  the  Present  Value  of  $1  due  at  the  End  of  any  Number  of  Years. . .  228-231 

Table  of  the  Auxiliary  Factor. . .    ^ 68 

Illustrations  of  Compound  Interest 71 


TABLES     IlSr     F.^I^T     SEOOISTID. 

THIRTY    AMERICAN    OFFICES'    EXPERIENCE. 

XXVL  Male  Life  Table.     Expectation  of  Life  and  Probable  Life *3 

XXVII.  Common  Logarithms  of  the  preceding  Life  Table *4 

XXVm.  Life  Annuities.     Present  Value  (a) *6 

XXIX.  Animal  Premium  to  insure  $1000  for  Life *8 

XXX.  Single  Premium  to  insure  $1000  for  Life *10 

XXXI.  Reversion  or  Life  Insurance  equivalent  to  Single  Premium  of  $1 *12 

XXXn.  Life  Annuity  which  $1000  will  purchase *13 

XXXIII.  Commutation  Table  and  Logarithms,  3  per  cent *14 

XXXIV.  Commutation  Table  and  Logarithms,  3^  per  cent *18 

XXXV.  Commutation  Table  and  Logarithms,  4  per  cent *22 

XXXVI.  Commutation  Table  and  Logarithms,  4^  per  cent *26 

XXXVII.  Commutation  Table  and  Logarithms,  5  per  cent *30 

XXXVIII.  Commutation  Table  and  Logarithms,  6  per  cent *34 

XXXIX.  Commutation  Table  and  Logarithms,  7  per  cent *38 

XL.  Commutation  Table,  8  per  cent ''42 

XLI.  Commutation  Table,  9  per  cent *44 

XLII.  Commutation  Table,  10  per  cent ,  *46 

XLIII.  Common  Logarithms  for  Special  Formulas *48 

.^L.JV.  Life  and  Temporary  Annuities,  or  Log  (1  +  «"~*),  4  per  cent *50 

XLV.  Life  and  Temporary  Annuities,  or  Log  (1  +  a"~^),  4^  per  cent *61 

^VI.  Life  and  Temporary  Annuities,  or  Log  (1  +  «""■'),  5  per  cent *72 


12  TABLES. 

TABLE  TAGE 

XLVII,  Life  and  Temporary  Annuities,  or  Log  (1  +  a^  ),  6  per  cent *83 

XLVIIL  Conversion  Table  from  Annuities  to  Annual  Premiums *94 

XLIX.  Conversion  Table  from  Annuities  to  Single  Premiums *99 

ju.  Single  Premium  for  Life  or  Reserve  on  1000  by  Months *104 

LL  Logarithm  of  Single  Premium  by  Months  on  $1  Insured *108 

LIL  Single  Premium  or  Reserve  for  Term  Insurance  of  1000 *112 

LIII.  Annual  Premium  for  Term  Insurance  with  Valuation  Factor *118 

LIV.  Single  Premium  or  Reserve  for  Endowment  Insurance *123 

LV.  Continued  Annual  Premium  for  Endowment  Insurance  of  1000  payable  at  Death 

or  Age  30,  35,  .... ,  75.     Also  X  (P-n;) *135 

LVI.  Five  Annual  Premium  for  Endowment  Insurance  as  above *138 

LVII.  Ten  Annual  Premium  for  Endowment  Insurance  as  above *141 

LVIII.  Continued  Annual  Premium  for  Endowment  Insurance  of  1000,  payable  at  Death, 

or  at  the  end  of  5,  10, ,40  Years *144 

LIX.  Five  Annual  Premium  for  Endowment  Insurance  as  above *146 

LX.  Ten  Annual  Premium  for  Endowment  Insurance  as  above *148 

LXI.  Limited  Annual  Premiums  for  Life  Policies *150 

LXII.  Net  Value  or  Reserve  on  Ten  Payment  Life  Policies *151 

LXIII.  General  Valuation  Table  for  Annual  Premium  Policies *154 

LXIV.  Value  of  /  and  /'  for  every  Year  and  Month  of  Age *200 

JOINT     LIVES     MALE. 

LXV.  Correction  for  reducing  Two  Lives  or  Three  to  the  case  of  Two  Equal  Ages *204 

LXVI.  D  and  N  Columns  for  Two  Equal  Ages,  3  per  cent *206 

LXVII.  D  and  N  Columns  for  Two  Equal  Ages,  3^  per  cent *207 

LXVIII.  D  and  N  Columns  for  Two  Equal  Ages,  4  per  cent ^ *208 

LXIX.  D  and  N  Columns  for  Two  Equal  Ages,  4^  per  cent »209 

LXX.  D  and  N  Columns  for  Two  Equal  Ages,  5  per  cent ^  *210 

LXXL  D  and  N  Columns  for  Two  Equal  Ages,  6  per  cent *211 

LXXII.  Annuitieis  on  the  Joint  Continuance  of  Two  Lives  . .  .Page  301.    New  Table. . . .  *212 

LXXIII.  Annual  Premium  for  Insurance  on  Two  Joint  Lives *213 

LXXIV.  Single  Premium  or  Reserve  on  Two  Joint  Lives *214 

LXXV.  Ten  Payment  Premiums  with  Valuation  Factors  *215 

LXX VI.  General  Valuation  of  Annual  Premium  Policies  on  Joint  Lives *216 

LXXVII.  Female  Life  Table.    Expectation  of  Life *224 

LXXVIII.  Female  Life.     D,  N,  a,  and  Correction  of  Age.     4  per  cent *226 

MISCELLANEOUS. 

LXXIX.  Comparison  of  different  Life  Tables *228 

LXXX.  Expectation  of  Life  by  various  Tables *230 

Probable  Life  in  Europe Text,  244 

LXXXI.  Percentage  of  Mortality  by  different  Life  Tables *232 

LXXXII.  Anti- Logarithms,  or  Numbers  to  Logarithms *234 


TABLES.  12a 

PAGE 

Amkricajst  Life  Tables.     From  Combinations  of  the  Census. — Introduction *255-*259 

The  Mathematical  Law  of  Mortality Tontines.  Method  of  Least  Squp-res,  *254 *257 

Tables  of  D  and  N  for  Males  and  for  Females.     Interest  3,  4,  5  and  6  per  cent *360-*263 

Present  Value  of  Life  Annuities.     Interest  3,  4,  5,  6  and  7  per  cent *264 

Single  Premiums  and  Reversions *266,  *267 

Present  Value  of  Joint  Life  Annuities,  Parts  I  and  II *268,  *269 

Present  Value  of  the  Right  of  Dower *370 


NOTES    AND    ADDITIONS. 

The  additions  made  to  the  present  Revised  Edition  will  be  found  on  the  four  pages 
inserted  after  page  12,  and  those  which  follow  page  *254,  comprising  American  Life 
Tables  and  their  mode  of  analysis.  Some  slight  corrections  have  been  made,  and  the 
separate  paging  of  the  Insurance  Tables  denoted  by  stars,  after  page  298  of  the  original 
treatise,  is  still  retained. 

Or  Ages  in  the  Tables. — To  facilitate  a  correct  and  ready  reference  to  tabular 
values,  the  letter  x  everywhere  denotes  the  Office  Age  at  Entry,  in  entire  years.  After 
Entry,  x-\-n  denotes  the  Age  ai  the  begitming  of  each  Policy  Year.  And  h  denotes  the 
Months  ov  fraction  of  a  year  elapsed  since  the  last  regular  payment  of  Annual  Pre- 
mium. Thus,  a; +  w  always  denotes  "the  Office  Age  last  birth-day"  \n  integer  years, 
and  x4-n-\-h  denotes  the  exact  age  of  the  insured  at  any  date,  in  years  and  months. 
Instead  of  n  years,  the  proper  side  column  can  also  be  entered  with  one  less  than  the 
number  of  premiums  paid. 

The  above  system  is  applied  uniformly  in  all  the  Tables,  except  the  Life  and  Tem- 
porary Annuities,  Tables  XLIV  to  XLVII.  In  these  four  Tables,  pages  *50-*93,  the 
Age  of  Entry  x  at  the  head  of  the  columns  is  the  same  as  in  the  other  Tables.  But 
the  n  "  Payments  "  at  the  side  denote  the  number  of  Policy  years  at  next  birth-day,  or 
the  number  of  annual  premiums  already  paid,  in  the  case  of  life  policies,  or  w  =:  w  +  1. 

It  may  also  be  noted  that  •'  4  Per  Cent."  or  any  other  rate  given  at  the  head  of  a 
column  or  Table,  signifies  the  rate  of  Interest  employed  in  its  construction. 

Reductions  of  Mortality  Experience. — Commencing  with  the  original  obser- 
vations on  Lives  and  Amounts,  the  relation  which  has  been  conventionally  adopted 
between  Calendar  and  Policy  Years,  and  the  mode  of  averaging  fractional  parts  of 
Years,  are  described  with  "sample  cards"  on  pages  17,  23,  and  24.  Page  24  also 
sketches  the  extended  classifications  given  in  Table  I.  by  double  entry,  that  is,  "Age 
of  Entry"  above,  and  "Years  of  Insurance"  at  the  side,  shown  on  pages  77-123. 

These  double-entry  elements  are  next  classified  in  groups  to  become  the  single- 
entry — Summary  (A),  page  74.  Here  on  the  line  of  age  25,  for  example,  is  given  the 
sum  of  Death  Claims  1,002,  and  of  Exposed  to  Risk  152^867*5.  How  these  results 
were  found  for  each  separate  age  is  shown  by  the  grouping  on  page  38.  Observing  that 
25  scattering  were  omitted  from  this  illustration,  but  included  in  Summary  (A),  all 
the  other  elements  in  the  central  Columns  under  (1874)  can  be  readily  traced  to  theiy 
original  places  on  pages  88,  87,  etc. 

The  next  reduction  gives  the  Mortality  Per  Cent.  (1874),  page  159,  third  column. 
On  the  line  of  age  25,  for  example,  the  Tabular  per  Cent,  is  0.657.     This,  like  th© 


123  NOTES  AND    ADDITIONS. 

other  values,  is  derived  from  two  adjacent  ages  of  Summary  (A),  as  follows : — Taking 
the  sum  of  death  claims  opposite  ages  25  and  26,  or  2,231  as  numerator  and  the  sum  of 
the  exposed  339,592-5  as  denominator,  the  value  of  the  fraction  is  0-657,  as  before 
quoted.  One  more  simple  process,  described  on  page  237,  would  change  these  per- 
centages to  the  relative  numbers  in  Table  XXVI,  which  completes  the  whole  of  the 
former  course  of  reduction  from  the  original  registry  of  Policies  to  the  Life  Tables. 

The  Method  of  Final  Series. — By  this  extension  of  the  former  method,  the 
experience  of  the  Existing  was  carried  forward,  so  that  the  general  experience  was 
determined  in  the  final  Table  with  superior  accuracy.  To  aid  in  the  explanations  of 
the  text,  the  specimen  columns  of  page  38  may  here  be  translated  into  general 
formulas :  ^ 

Let  D  denote  the  Death  Claims,  E  the  Exposed  to  Eisk,  and  1  the  relative  weight 
for  the  first  combination  of  ages  0-25.  Let  Di,  Ei,  ii\,  v  denote  the  like  numbers  for 
the  next  combination  1-24,  and  so  on ;  where  v  denotes  the  present  value  of  $1  dis- 
counted for  1  year.     By  the  Former  Method  of  reduction  :  Death  Claims  per  Cent. 

_  (D  +  Dx-f-D,  +  D3  +  D4+.  -QlOO 

-       E  +  E,  +  E,  +  E3-rE.-h... 

By  the  Method  of  Final  Serieg :  Death  Claims  per  Cent. 

_  (D  +  DiWiz;  +  'D^iv^v^+  ^zW^i^-\- .  . . )  100 

~  E  +"EiWiV  +  E2W2V2  +  E3?t'3t73  +   .  :  . 

The  weights  w  were  at  first  computed  by  direct  solution,  as  described  on  page  37. 
A  parallel  Example  may  be  found  in  De  Morgan!s  Essay  on  Probabilities,  page  137. 
It  may  further  be  noted  that  as  w  increases  from  year  to  year,  the  discount  factors 
V,  v^,  't^.  .  .continually  diminish. 

On  page  36,  the  question  may  arise  why  are  two  ages  of  entry  united  ?  and  why  is 
the  process  of  Final' Series  stopped  with  the  27th  year?  In  reply,  the  derivation  of 
the  fundamental  Formula  for  jp"  on  page  25,  pre-supposes  the  Observations  to  be  suffi- 
ciently numerous  to  change  uniformly  (or  approximately  so)  from  the  beginning  to  the 
end  of  each  year,  as  illustrated  by  the  trapezoid.  After  the  27th  year,  the  Claims  were 
so  few  and  irregular  that  the  Formula  for  p",  thus  derived  conditionally,  could  not  be 
applied;  and  so  46,413— 215— 2,361,  that  is,  43,837  Existing  still  remain  at  the  28th 
year.  The  real  errors  of  their  omission  from  the  Preceding  Formula  of  Final  Series 
are  deemed  insensible.  For,  were  the  43,837  distributed  to  older  ages  and  then  dis- 
counted by  1^,  v^. .  .the  whole  present  values  would  be  less  than  13,000.  Whereas  in 
the  former  Method  of  constructing  Life  Tables,  the  future  experience  of  a  much 
greater  number,  or  102,484  Existing,  would  be  left  undetermined  and  omitted. 

The  factors  v,  1?,  ifi.  .  .introduced  on  page  37,  may  be  further  illustrated.  A 
careful  inspection  of  Commutation  columns  and  formulas  for  premiums  discloses  the 
fact  that  the  Commutation  factors  v,  v^,  1^^  . .  after  the  manner  of  Weights,  are 
effective  only  as  they  commence  with  the  "age  of  entry;"  thus  practically  attenuating 
the  more  distant  data,  they  make  the  Value  of  Premiums  and  Annuities  depend  chiefly 
on  the  ages  nearest  to  the  "age  of  entry."  Therefore,  it  appeared  important  to  recog- 
nize this  inevitable  attenuation,  before  as  well  as  after  the  construction  of  the  Life 
Table,  by  discountijig  the  original  data  to  Present  Value  at  the  respective  ages 
of  entry. 

A  majority  of  the  Committee  held  that  an  Experience  Table  based  on  the  Amounts 
would  represent  the  actual  business  of  a  Life  Office  more  closely  than  one  based  upon 


N0TE8   AND    ADDITIONS.  12c 

Lives.  And  the  different  sums  insured  found  on  pages  159,  160  sustained  this  view; 
while  the  method  of  Lives  virtually  assumes  the  sum  insured  to  be  uniform  at  every 
age.  In  separate  offices,  'however,  the  ratios  of  Death  Claims  by  ages,  although  more 
correct,  were  more  fluctuating,  than  the  ratios  from  Lives.  This  difficulty  was  obviated 
by  resorting  to  the  larger  numbers  of  the  Thirty  Offices  united,  which  give  a  very 
regular  curve  from  the  Amounts,  as  shown  in  the  fundamental  Table  XXVI. 

The  inquiry  has  arisen,  what  is  the  relation  of  Table  XXVI  to  the  Actuaries 
jjM(5)  Table  which  omitted  the  experience  of  the  first  4.5  years,  and  to  the  earlier  plan 
of  a  series  of  separate  Life  Tables  for  every  Age  of  Entry?  Without  attempting  a  full 
answer,  we  note  from  page  30  that  the  mean  duration  of  the  Thirty  Offices  Policies 
was  4.36  years,  and  for  equal  ages  of  exposure  the  average  rate  of  mortality  was 
attained  in  2.5  years  after  Entry.  The  corresponding  numbers  for  the  Twenty  British 
Offices  were  9.12  years  and  4.5  years.  Hence  the  inference  that  the  latter  terms  2.5 
and  4.5  being  half  the  former  nearly,  are  not  fixed  periods,  but  vary  with  the  mean 
age  of  Policies  in  each  Office. 

Therefore  returning  to  the  earlier  plan,  so  perfect  in  theory,  suppose  one  Life 
Table  constructed  from  the  Amounts  under  Age-at-Entry  37,  another  for  38,  and  so 
for  every  other  Age  of  Entry, — taking  not  the  usual  10,000,  but  the  entrant  amounts, 
as  94,029,  etc.,  for  their  initial  numbers.  This  secures  to  the  0  and  D  Commutation 
elements  their  proper  weights  in  one  general  Life  Table  which  might  be  constructed 
from  all  of  them.  Were  the  distribution  of  insured  ages  very  dissimilar  in  different 
Life  Offices,  the  many  single  Tables  might  be  required ;  but  the  researches  of  King, 
Chandler,  and  other  actuaries  prove  the  ages  to  be  so  nearly  similar,  that  one  general 
Life  Table  has  appeared  sufficient.  The  method  of  Final  Series  might  ha^■e  been 
derived  as  an  improvement  on  this  earlier  plan. 

Climate  Extra,  Page  48. — In  the  case  of  extra  premium  on  a  life  long  resident 
in  India,  returning  after  many  years  to  reside  permanently  in  Europe,  Mr.  Makeham 
proposed  to  determine  the  future  reduced  premium  P,  by  the  following  equation  of 
Eeserves  : 

l_l±^^  =  l-(l-t;)  (l  +  «^+«)-P(l+«x-H.). 
i.-\-a  X 

Here  the  Eeserve  on  the  left  by  the  Bengal  or*  other  foreign  Table  is  equated  to 
the  Reserve  by  the  home  Office  Table  ;  whence  is  determined 

P  = l±^tlt (1  —  v). 

(l  +  a'a,)(l  +  aa;  +  n)      ^  ^ 

Besides  this  method,  the  two  letters  of  Mr.  Makeham  in  the  14th  volume  of  the 
Assurance  Magazine,  also  contain  the  first  extension  of  the  commutation  principle  or 
factor  fc^  to  climatic  mortality,  here  revived  as  described  in  Section  III. 

Pages  62,  63. — The  Copy  Multiplication  Table  is  now  entirely  correct.  In  the 
first  edition  were  two  errata,  the  one  requiring  the  first  9X  in  column  100  to  be 
changed  to  8X  ;  the  other  in  column  0  opposite  70  at  the  side,  requiring  the  first 
4556  to  be  changed  to  4456. 

Page  270,  line  38. — The  Valuation  of  Ordinary  Joint  Life  Policies  may  be  effected 
with  great  facility,  as  shown  by  the  Example  at  the  foot  of  Page  270.  Since  in  these 
Policies  F  =  n,  the  general  formula  becomes 

V  —  f'"  —  V"  h' 


nd  NOTES   AND    ADDITIONS. 

Price  of  Stocks  and  Bonds,  Page  67. — To  find  the  Price  (not  the  interest) 
at  which  a  specified  Bond  should  he  bought  or  sold,  to  yield  an  assigned  rate 
of  Interest  on  the  purchase.  In  the  notation  of  the  text,  i — i'  can  be  regarded  as 
the  temporary  annuity,  which  p — 1  will  purchase  with  i'  as  the  rate  of  interest,  till 
maturity. 

Example. — Required  the  equivalent  Price  p  to  yield  4  per  cent,  interest,  which 
should  be  paid  for  a  6  per  cent.  Bond,  that  will  mature  in  18  years. 

Answer,  p  =  $1.25318  on  each  II  of  par  value. 
Formula,    p  =  l-^{i—i')  V'„.     Table  XXIII,  Page  220,  .... 

Valuation  of  Ordinary  Endowments,  Page  266,  lines  2  and  32. — Both  of 
these  Formulas,  like  the  general  Table  LXIII,  have  the  usual  simple  cases.  When 
w  =  0,  before  the  first  premium  was  paid,  Va;  =  0.  Also  comparison  with  page  251 
proves  that,  one  year  before  maturity,  when  n^m  —  1,  Va;+n  =  v — Pa;.  And  at 
maturity,  when  n  ■=  m,  Yx+m  =  1>  the  sum  insured.  To  interpolate  for  Months, 
besides  the  use  of  Table  LXIII,  we  may  substitute  the  preceding  value  of  V  into  line 
7,  page  270 ;  and  thus,  \in  =:  n-\-l, 

1         I     'y^^~^ 

J   '~J\    ,     m-l 
!  +  «« 

Example.  — Required  the  4  per  cent.  Reserve  V  on  each  $1  insured,  at  the  end  of 
7^  years,  for  an  Endowment  Insurance  by  annual  premium,  beginning  at  the  age  x  = 
26  years,  to  mature  in  m  =:  15  years, 

solution." 

(1)  By  the  General  Table  LXIII: 

Page  *144.     x  =  26,  m  =  15,  1.581343  =  A  (P— tt). 

''     *163.     x,n  +  h  =  7  yrs.  6  m.      70.79       0.986978  =  A  (B/). 
"     *245.  •  .,.+370. 10  ...2.568321 

V  =  440.89  =  Reserve  on  $1000. 

(2)  By  the  above  Formula : 

Page  *201.     x  +  n  =  Sd,h  =  6"',f' —  0.98077,      T. 989888  =  A/. 
"      *53,     x-^n  =  S4:,m—n  =  7,  0.785055 

"       *52.  X  =  26,         7n  =  15,  1.042648  sub. 

''    *248.     n=zn-{-l,  /— 0.53988...  1. 732295 

V  =  0.44089  =  Reserve  on  $1. 

Commutation  Formulas,  Page  293,  237. — Instead  of  integration,  we  may  develop 
T)x  in  series,  and  take  the  sum  of  the  geometrical  progressions  between  x  and  the  end  a> 
of  the  life-table,  by  the  common  rule.     If  Xh  =  5.028254: 

(1  u  w^  ?/  ) 

N^  =  -C.-^rTc{vsY  -j  ^— -^+  — _^-  J  2  (^,^2_-I)  +  1.2.3  {vsq^-1)  -•'•]' 

With  interest  4  per  cent.,     A  {vs)  =  T.9802201  ;     Xu  =  4.837557  +  0.041279507a; ; 

Na;  =  — 121,828 -tk{vs)^  {22.46015  + 19. 70403W- 3.214919^2 

+  0.6155736w3— 0.1048335^4 +  0.0155241  w5_  .  _  |, 


PART    FIRST. 
ELEMENTARY   OBSERVATIONS   AND   TABLES. 


The  Elementary  Observations  and  Tables  of  Part   First   are  classed  into  four 
Divisions,  as  follows : 


First.    Mortality  and  Loss  Experience,    - 
Second.    Climatic  Tables,       ------ 

Third.    Medical  Statistics, 

Fourth.    Time  and  Monetary  Tables     -    - 


Tables 


I-IV. 
V-VIII. 
IX-XVI. 
XVII-XXV. 


DIVISION    FIRST. 


ORTALITY    AND    LOSS     EXPERIENCE. 


The  received  method  of  reduction  presupposes  the  new  business  of  different 
calendar  years  to  be  superimposed  or  brought  together,  as  if  the  entrant  insurances 
were  all  effected  in  one  calendar  year.  Thus  the  entrants  at  the  age  of  thirty,  for 
example,  are  all  classified  together,  as  entering  in  the  same  initial  year.  From  this 
origin,  the  annual  deaths  and  discontinuances  are  traced  forward  and  noted  year  by 
year,  through  the  whole  course  of  insured  experience.  Such  are  the  elementary 
observations  given  in  Tables  I-IV,  for  male,  and  for  female  life.  Let  us  first  glance 
at  the  methods  from  the  beginning. 

SECTION    I. 
Instructions  and  Cards. 

The  following  Instructions  of  the  Committee  in  March,  1875,  were  published 
and  attached  to  folio  card-boards,  for  constant  reference  in  filling  out  the  blank  cards, 
from  the  Office  records. 

INSTRUCTIONS. 

Let  each  figure  and  word  be  plainly  written  with  a  pointed 
pencil  of  medium  hardness. 

The  first  blank,  in  the  left  hand  upper  corner,  is  for  the  con- 
venience of  the  Committee  in  separating  the  cards,  and  will  contain 
their  private  mark  for  the  several  companies,  and  need  not  be 
regarded  by  you, — nor  the  second,  which  contains  the  policy-num- 
ber,— inserted  consecutively  by  the  printer's  numbering  machine. 


Private  mark  and 
number  of  fotictf. 


14 


MORTALITY  AND    LOSS   EXPERIENCE. 


Mesidenee. 


Amount  and  Kind. 


Tears  of  JEntry  and 
Exit. 


The  third  blank,  "residence,"  is  to  be  filled  with  the  name  of 
the  State  only,  except  that  in  the  following  States  the  County  is 
also  to  be  inserted,  viz.:  Virginia,  North  Carolina,  South  Caro- 
lina, Georgia,  Florida,  Alabama.  Tennessee,  Arkansas,  Mississippi, 
Louisiana  and  Texas. 

In  case  the  residence  be  in  any  foreign  country,  draw  a  line 
through  the  word  "  State  "  and  write  the  name  of  the  country  in 
the  same  space. 

The  series  of  blanks  relating  to  the  amount,  kind,  and  duration 
of  the  policy  are  to  be  treated  as  follows : 

In  the  top  space,  under  "  Amount,"  write  the  amount  insured, 
thousands  at  the  left  hand,  and  hundreds  at  the  right  hand  of  the 
light  perpendicular  line,  using  no  ciphers,  where  even  hundreds  or 
thousands  are  entered. 

On  the  same  horizontal  line  under  "  Kind,"  indicate  the  kind 
of  policy  by  L  for  Life,  E  for  Endowment,  and  T  for  Term 
Policies. 

On  the  same  horizontal  line,  under  "  Cal.  Year  of  Entry," 
enter  the  calendar  year  in  which  the  policy  was  issued. 

If  the  policy  be  still  in  force,  make  a  dash  after  the  -figures 
"  18"  in  the  same  horizontal  line,  under  the  "  Cal.  Year  of  Exit." 

If  it  has  ceased  to  be  in  force  for  any  reason  except  death,  enter 
upon  that  line  and  under  the  '•  Cal.  Year  of  Exit,"  the  calendar 
year  in  which  it  ceased,  and  make  a  dash  in  the  blank  "  Cause  of 
Death." 

If  it  ceased  by  death,  make  the  same  entries,  but  carefully  write 
D  after  the  year  of  exit. 

If  any  changes  have  occurred  in  the  amount  or  kind,  the 
original  number,  age  and  date  being  retained,  other  entries  must 
be  made  as  follows : 

The  original  amount,  kind  and  year  of  entry  having  been 
entered  as  above,  the  calendar  year  in  which  the  change  was  made 
is  to  be  taken  as  the  year  of  exit  of  the  original  policy,  and  entered 
in  the  top  line  under  that  head. 

Then  an  entry  of  the  changed  amount  or  kind,  as  the  case  may 
be,  is  to  be  made  under  the  proper  head  on  the  second  line,  and 
the  date  of  the  change  is  to  be  taken  as  the  calendar  year  of  entry 
of  the  changed  policy,  which  will  of  course  correspond  with  the 
calendar  year  of  exit  of  the  original  policy. 

xiKit  by  Death  under         The  termination  by  death  or  otherwise  of  the  second  or  changed 
CHANGED  Policies,  policy  is  to  be  treated  in  the  same  manner  as  has  been  pointed  out 
for  the  original 

Should  the  changed  poHcy  have  been  still  further  changed,  the 
proper  entries  are  to  be  made  upon  the  third  line,  under  the  several 
heads,  in  the  same  manner  as  required  for  the  changes  from  the 
original. 

If  more  than  two  changes  have  taken  place,  the  subsequent 
ones  may  be  entered  in  the  bottom  blank  for  memoranda. 


Exit  by  Death. 


Changes  in  Amount 
and  Kind. 


Second  Changes, 


Third   and   subse- 
quent Changes, 


MORTALITY  AND    LOSS   EXPERIENCE. 


15 


Wlien  changed  Pol- 
icy is  in  force- 


Revival  of   lapsed 
Policies, 


Revival  or  change 
triTHO  UT  new  med- 
ical examination. 


Policies  lapsed  and 
good  for  ''PRO  RA- 
TA "  amounts. 


Revival    of    "  PRO 
RATA  "   Policies. 


Aye  of  Entry. 

"Rated  Age^^ 
"  True  Age." 


Sew, 

Cause  of  Death. 

"Xot  Taken"  Pol's. 
"  JRe-insur,"  Pol's. 

Joint  Life  Policies, 


If  the  policy  in  which  change  has  been  made,  be  in  force,  make 
a  dash  after  the  figures  "  18  "  under  the  "  Oal.  Year  of  Exit,"  in 
the  horizontal  line  occupied  by  that  policy. 

If  a  policy  has  lapsed  and  has  subsequently  been  revived  under 
the  same  number,  date,  age,  etc.,  and  the  ;"evival  has  taken  place 
in  the  calendar  year  in  which  the  lapse  occurred  no  entry  of  these 
facts  need  be  made. 

If  the  revival  has  taken  place  in  a  later  calendar  year  than 
that  in  which  the  lapse  occurred,  then  the  calendar  year  of  lapse  is 
to  be  entered  as  the  year  of  exit  of  the  original  policy,  and  the 
revival  is  to  be  treated  as  a  change,  and  the  proper  entries  are  to 
be  made  upon  the  second  line,  the  calendar  year  of  revival  being 
taken  as  the  year  of  entry  of  the  changed  policy,  and  write  the 
letter  K.  in  the  memorandum  blank  at  the  bottom. 

If  revival  or  change  has  been  made  by  a  policy  under  a  new 
number,  without  a  new  medical  examination,  let  the  card  for  the 
new  policy  contain  in  the  memorandum  blank  the  number  of  the 
original  policy  also,  with  an  0  written  before  it. 

In  case  policies  after  lapse  remain  good  by  their  own  terms  for 
a  fixed  or  ^^ pro  rata^^  amount  of  the  original  sum  insured,  the 
year  of  lapse  is  to  be  taken  as  the  year  of  exit  of  the  original,  and 
also  as  the  year  of  entry  of  the  changed  or  ^'pro  rata"  amount. 

In  case  such  policies,  after  continuing  for  a  time  for  the  '^ pro 
rata  "  amount,  are  revived  under  the  same  number,  date,  etc.,  such 
revival  is  to  be  treated  as  a  second  change  and  entered  accordingly. 

The  blank  "  Age  at  Entry,"  is  to  be  filled  with  the  office  age,  or 
that  upon  which  the  premium  is  written. 

When  for  any  special  reason,  the  age  has  been  rated  higher  or 
lower  than  the  true  age,  the  true  age  at  nearest  birthday  should 
be  stated  in  the  memorandum  blank  with  the  words  "  true  age  " 
before  it. 

The  blank  following  "Age  of  Entry,"  upon  the  same  line,  may 
be  disregarded,  being  for  the  use  of  the  Committee  only. 

The  blank  "  Sex  "  is  to  be  marked  with  a  dash  for  a  male  life, 
and  with  a  capital  F  for  a  female  life. 

In  the  blank  "  Cause  of  Death  "  write  the  cause  stated  upon  the 
Company's  register. 

The  following  special  cases  must  be  carefully  noted : 
Omit  all  policies  "  not  taken  "  or  not  actually  put  in  force. 

Omit  all  policies  of  re-insurance,  or  for  the  benefit  of  other 
companies. 

In  case  of  a  "joint  life  policy"  mahe  a  card  in  full  for  each 
life,  using  a  separate  card  for  the  second,  but  writing  in  the 
number. 


16 


MORTALITY  AND    LOSS   EXPERIENCE. 


J'oitU  lAfe  Policies. 


Ziimited  premium 
Policies. 


Mark  each  card  in  the  memorandum  blank  with  a  capital  J, 
and  place  them  both  in  an  envelope  also  marked  J. 

It  may  sometimes  happen  that  a  "  joint  life  policy "  is  discon- 
tinued as  to  one  of  the  lives,  and  so  adjusted  as  to  continue  upon 
the  other  life  singly. 

The  card  representing  the  life  upon  which  the  insurance  is  dis- 
contiyiued  will  show  the  amount,  kind,  calendar  year  of  entry  and 
calendar  year  of  exit,  in  the  usual  manner  of  a  terminated  policy. 

The  card  representing  the  life  upon  which  the  insurance  is 
continued  will  show  the  change  in  the  same  manner  as  other 
changes  are  indicated,  with  the  addition  of  the  letter  S  in  the 
memorandum  blank,  signifying  "  Single  Life." 

No  special  designation  need  be  made  of  policies  with  a  limited 
number  of  premium  payments,  whether  completed  or  otherwise. 


Policies  terminated        "When  a  policy  has  terminated  for  any  cause  other  than  death, 
by  causes  other  than  j-j^g  causc  need  uot  be  Stated,  but  be  careful  to  make  a  dash  in  the 

Death, 

blank  "  Cause  of  Death." 


SAMPLE     CARDS. 


A. 

\ 

RESIDENCE. 

State.    Ci>4%tz-c^'e. 

County. 

Amount. 

Kind. 

Cal.  Year 
of  Entry. 

Cal.  Year 
of  Exit. 

/^ 

--^ 

18^¥ 

18 — 

18 

18 

18 

18 

Age  at  Entry. 

SO 

/O 

Sex. 

1 

Cause  of  Death. 

..... 

AA. 

\ 

RESIDENCE. 

State.    O^^zWte. 

County. 

Amount. 

Kind. 

Cal.  Year 
of  Entry. 

Cal.  Year 
of  Exit. 

/O 

.?' 

18^-^ 

18 

18 

18 

18 

18 

Kge:  at  Entry. 

SO 

/O 

Sex. 

(^ 

Cause  of  Death. 

1 

MORTALITY  AND    LOSS  EXPERIENCE. 


17 


B. 

\ 

RESIDENCE. 

State.    ^l^u-aM^t-a. 

County.     ^i{?e'^^€.co . 

Amount. 

Kind. 

Cal.  Year 
of  Entry. 

Cal.  Year 
of  Exit. 

/ 

S 

# 

18<^^ 

18^^ 

S 

^ 

IS^J* 

18 

18 

18 

Age  at  Entry. 

sr 

Sex. 

Cause  of  Death. 

. 

o. 

\ 

RESIDENCE. 

State.    C/iMad-l. 

County. 

Amount. 

Kind. 

Cal.  Year 
of  Entry. 

Cal.  Year 
of  Exit. 

S 

s^ 

18^^ 

18<^-^ 

S 

18^^ 

\%e^ 

/ 

S 

18^^ 

18 — 

Age  at  Entry. 

SS 

Sex. 

Cause  of  Death. 

X). 

\ 

RESIDENCE. 

State.    C/!utdd. 

County.    C/J  a-Ct-vtZ't. 

Amount. 

Kind. 

Cal.  Year 
of  Entry. 

Cal.  Year 
of  Exit. 

^0 

18^^ 

187^  jf^ 

18 

18 

1 

18               18 

Age  at  Entry. 

^i» 

Sex. 

Cause  of  Death. 

Cyy,^-n-a'i.c/  C/e^e^. 

E. 

\ 

RESIDENCE. 

State.    J^iQ,<i-n.dfz<!. 

County. 

Amount. 

Kind. 

Cal.  Year 
of  Entry. 

Cal.  Year 
of  Exit. 

JT 

<§ 

\^eo 

18(^^ 

^ 

i? 

is(fdr 

187^  .#' 

18 

18 

Age  at  Entry. 

S4 

Sex. 

Cause  of  Death. 

18 


MORTALITY   AND    LOSS   EXPERIENCE. 


F 

■     \ 

RESIDENCE. 

State.    GrnQtz-i^-Ui^^i/. 

County. 

Amount. 

Kind. 

Cal.  Year 
of  Entry. 

Cal.  Year  I 
of  Exit. 

S 

St 

18(^^ 

18  ^<^ 

2 

S 

€ 

\%ee 

\%e^ 

<f 

1 

Age  at  Entry. 

sp 

Sex. 

Cause  of  Death. 

C^ei^^,t//e^/  Cye^ue-i. 

<3r. 

■'    \ 

RESIDENCE. 

State,     ^l^€^^^■a4^^. 

County. 

Amount. 

Kind. 

Cal.  Year 
of  Entry. 

Cal.  Year 
of  Exit. 

/O 

£l 

18/^ 

187J> 

18 

18 

18 

18 

Age  at  Entry. 

JS' 

Sex. 

Cause  of  Death. 

H. 

-/-/JS^S                  \ 

RESIDENCE. 

State.    Cy!/(Qit-cAe-ry.€i'n, 

County. 

Amount. 

Kind. 

Cal.  Year 
of  Entry. 

Cal.  Year  1 
of  Exit.      ] 

S 

S 

^ 

"^18^^ 

18 

18 

18 

18 

18 

Age  at  Entry. 

M 

Sex. 

Cause  of  Death. 

/ 

HH. 

^</J2^3              \ 

RESIDENCE. 

State.    Cyi/%l■■cA■c■-a,€^■7^. 

County. 

Amount. 

Kind. 

Cal.  Year 
of  Entry. 

Cal.  Year 
of  Exit. 

J       JT 

y: 

18J^ 

18 — 

18 

18 

18                  18 

Age  at  Entry. 

J2 

Sex. 

J^ 

Cause  of  Death. 

/ 

MORTALITY  AND    LOSS   EXPERIENCE. 


19 


I. 

\ 

RESIDENCE. 

State.    Ofeu^ 

County. 

Amount. 

Kind. 

Cal.  Year 
of  Entry. 

Cal.  Year 
of  Exit. 

/ 

S 

^^ 

18-^^ 

187^ 

1 

18 

18 

18 

18 

i 

Age  at  Entry. 

si 

Sex. 

Cause  of  Death. 

/ 

II. 

\ 

RESIDENCE. 

State.    cJ^et-ti    ^^i-iA. 

County. 

Amount. 

Kind. 

Cal.  Year 
of  Entry. 

Cal.  Year 
of  Exit. 

/ 

S 

^^. 

18-^^ 

\%7o£if 

18 

18 

18 

18 

Age  at  Entry. 

SO 

Sex. 

cF 

Cause  of  Death. 

Wele'Uio     QT/itna-t    ,yfCetnna.t^tJ. 

/ 

^37^                \ 

RESIDENCE. 

State.    C/e-i-t^. 

1 
County.                                      1 

Amount. 

Kind. 

Cal.  Year 
of  Entry. 

Cal.  Year  1 
of  Exit.      1 

J 

SC 

18(^(^ 

18/^ 

1 

^ 

187^ 

,s          [ 

18 

:s        1 

Age  at  Entry. 

ss 

Sex. 

n 

Cause  of  Death. 

/^ 

KK. 

^^7^               \ 

RESIDENCE. 

State.    Lye^-f^i. 

County. 

Amount. 

Kind. 

Cal.  Year 
of  Entry. 

Cal.  Year 
of  Exit. 

J 

^ 

\S6'(P 

187^ 

18 

18 

18 

18 

Age  at  Entry. 

so 

Sex. 

cF 

Cause  of  Death. 

- 

/ 

20 


MORTALITY  AND    LOSS  EXPERIENCE. 


M. 

\ 

RESIDENCE. 

State.    Ci    M 

County. 

Amount. 

^-^-      'of^.Z 

Cal.  Year 
of  Exit. 

S  j 

^ 

\%&o 

\%e^ 

S 

S 

Si 

18(^^ 

\%es 

J 

^. 

18(^^ 

18 

Age  at  Entry. 

so 

<?f>Y 

Cause  of  Death. 

N. 

\ 

RESIDENCE. 

State.    <o4^^idd-tkdt^/zt.'. 

County.     ^■ac'/td-O'i^. 

Amount. 

Kind. 

Cal.  Year 
of  Entry. 

Cal.  Year 
of  Exit. 

3 

•$f        18/J* 

18 — 

18 

18 

1 

18 

18 

K^e  at  Entry. 

=// 

Sex. 

Cause  of  Death. 

Q-^g2e3 

DESCRIPTION    OF    SAMPLE    CARDS. 

Each  of  the  sample  cards  is  marked  with  a  letter  of  the  alphabet — a  single  letter 
for  male  lives  and  a  double  letter  for  female  lives — the  single  and  double  letter  cards 
each  showing  the  same  data. 

Thus,  A  shows  a  policy  on  the  life  of  a  resident  of  Maine,  insured  at  age  30  for 
$10,000;  Life  Policy;  year  1864;  still  in  force;  male  life.  AA  shows  precisely  the 
same  data  for  a  female  life. 

B  shows  a  policy  on  the  life  of  a  resident  of  Virginia,  Henrico  County,  for 
17,500;  Endowment;  issued  1860;  changed  in  1863  to  a  $3,000  Life  Policy;  still  in 
force ;  age  at  entry  37. 

C  shows  a  policy  on  the  life  of  a  resident  of  Massachusetts  for  $500 ;  Life ;  issued 
in  1855;  changed  in  1864  to  $3,000  Life;  changed  in  1869  to  $7,500  Life;  still  in 
force ;  age  at  entry  35. 

D  shows  a  policy  on  a  resident  of  Bolivar  County,  Mississippi,  for  $10,000 ; 
Endowment ;  issued  in  1865  ;  terminated  by  death  in  1870 ;  age  at  entry  42 ;  cause  of 
death,  Typhoid  Fever. 

E  shows  a  pohcy  upon  a  resident  of  Kansas  for  $5,000 ;  Endowment ;  issued  in 
1860 ;  changed  in  1865  to  a  Life  policy  for  the  same  amount ;  terminated  in  1872  by 
death  from  Pneumonia ;  age  at  entry  34. 

F  shows  a  policy  upon  a  resident  of  Maryland  for  $3,000;  Life;  issued  in  1860; 
changed  in  1866  to  $2,500 ;  Endowment ;  and  changed  again  in  1868  to  $800  Endow- 
ment ;  terminated  in  1873  by  death  from  Eemittent  Fever ;  age  at  entry  29. 


MORTALITY  AND    LOSS   EXPERIENCE.  %1 

G  shows  a  policy  upon  a  resident  of  Vermont;  issued  for  $10,000  ;  Life  ;  m  18.70; 
terminated  in  1872  for  any  cause  other  than  death ;  age  at  entry  38. 

H  and  HH  are  the  proper  cards  for  a  Joint  Life  Policy  upon  residents  of  Michigan ; 
male  and  female  ;  for  $3,500  Life  ;  issued  in  1859  ;  still  in  force  ;  age  of  the  male  34 ; 
age  of  the  female  32. 

I  and  II  are  the  cards  of  a  Joint  Life  Policy  upon  residents  of  New  York,  issued 
for  $7,500  ;  Life ;  in  1849 ;  terminated  by  death  of  female  in  1870,  from  Cerebro  Spinal 
Meningitis;  age  at  entry  of  male  36;  age  of  female  30. 

K  and  KK  are  cards  representing  Joint  Lives ;  insured  for  $5,000  in  1860  ;  and 
from  which  the  female  life  was  dropped  in  1870;  the  policy  adjusted  to  continue  as  a 
single  insurance  upon  the  male  from  that  dat#i 

L  shows  a  policy  upon  the  life  of  a  resident  of  New  Jersey  for  $5,000;  Life; 
issued  in  1860 ;  at  age  25  ;  lapsed  in  1865 ;  revived  in  1866,  and  still  in  force. 

M  shows  a  policy  upon  the  life  of  a  resident  of  New  Hampshire  for  $5,000 ;  Life ; 
issued  in  1860;  at  age  30:  lapsed  in  1865;  continuing  good  by  its  own  terms  for 
$2,500,  and  revived  for  the  original  amount  in  1868 ;  still  in  force. 

N  shows  a  life  Policy  still  in  force,  upon  the  life  of  a  resident  of  Jackson  County, 
Mississippi,  issued  for  $5,000,  in  1872,  at  age  37,  without  medical  examination,  to  revive 
or  take  the  place  of  Policy  No.  19,263,  upon  the  same  life,  lapsed. 


SECTION     II. 
Adjiistment  of  Cards.    Durations.    Joint  Lives.    Transfers. 

After  an  interval  of  four  years,  during  which  these  Instructions  have  been  followed 
to  their  proper  completion,  the  following  additional  remarks  and  specifications  may  be 
noted. 

The  general  plan  has  been  guided  by  the  adoption  of  two  important  precepts. 
First,  that  every  insurance  must  commence  with  a  Medical  Examination.  Second, 
that  after  the  Medical  Examination  at  the  beginning,  the  method  of  reduction  must 
correctly  trace  the  counter  selections  of  the  insured,  which  are  continued  from  year  to 
year,  by  changes  of  the  Amount  Insured,  that  is,  by  increase  or  by  decrease,  by  taking 
out  additional  policies,  or  by  total  lapse,  surrender,  or  decease.  In  this  aspect,  the 
investigation  might  not  inappropriately  be  termed  the  Problem  of  the  Selections. 

To  accord  with  the  latter  precept,  the  English  method  of  Lives,  on  the  i>lan  of 
a  census  of  living  and  deaths  only,  without  the  sums  insured,  has  been  supplemented 
by  parallel  columns  of  the  Amounts,  treating  dollars  as  lives.  The  present  statistics, 
therefore,  are  two-fold ;  and  have  required  more  than  double  the  usual  labor  in  their 
preparation. 

The  cards,  on  reception,  were  first  examined  from  beginning  to  end,  to  select  out 
all  the  secondary  insurances,  such  as  the  preceding  sample  card  N,  marked  0  under- 
neath. This  particular  entry  0 — 19,263  simply  refers  from  the  secondary  to  the 
original  insurance  noted  on  card  No.  19,263.  The  secondary  or  "  0-cards  "  so  called, 
were  next  copied  on  the  middle  line  of  the  originals,  which  were  sought  out  for  this  pur- 
pose, before  the  regular  order  of  the  cards  by  number  was  broken  up.  The  0-cards, 
being  about  one-tenth  of  the  whole,  together  with  Reversionary  Dividends,  were  laid 
aside  as  supernumerary. 


23  MORTALITY   AND    LOSS   EXPERIENCE. 

After  this  and  other  preparations,  presently  described,  the  next  step  was  to  note 
the  Duration  on  each  card  of  single  insurance,  which  was  found  by  subtracting  the 
first  "Cal.  Year  of  Entry"  from  the  last  "Cal.  Year  of  Exit,"  or  (in  case  of  Non- 
terminated  or  Existing  policies)  from  the  Epoch  1874,  when  the  experience  was  inven- 
toried. Thus  on  the  preceding  cards  A,  and  AA,  the  difference  of  1864  and  1874,  that 
is,  Duration  10,  is  noted  opposite  the  age.  We  may  observe  that  the  sum  of  the  age 
and  duration,  or  30  and  10  on  the  card  A,  gives  the  advanced  age  of  the  insured, 
40  years,  in  1874.  A  more  full  account  of  the  connection  of  Age  and  Duration  will  be 
given  hereafter. 

With  respect  to  cards  having  two  or  more  successive  insurances,  the  Durations  are 
noted,  after  preparation,  in  the  following  manner.  To  refer  to  a  few  instances : — Where 
the  amounts  are  alike  as  on  the  preceding  card  E,  the  entries  may  be  regarded  as  two 
parts  of  one  experience,  or  $5,000  exposed  to  risk  through  a  duration  of  12  years,  like 
a  single  policy.  Where  the  amounts  are  different,  as  shown  on  the  preceding  card  F, 
the  above  rules  require  its  resolution  into  three  new  separately  written  cards,  all 
commencing  with  the  medical  examination  of  1860;  that  is,  (1)  a  Death  card  of  the 
last  amount  $800  for  the  whole  Duration  13  years ;  (2)  a  Discontinued  card  of  the 
difference  2,500-800,  or  $1,700  from  1860  to  1868  or  Duration  8  years  ;  and  (3)  another 
Discontinued  card  of  the  difference  3,000-2,500,  or  $500  from  1860  to  1866  or  Duration 
6  years. 

All  the  other  similar  cards  B,  0,  M,  can  be  superseded  by  single  cards  on  the  same 
principle.  Indeed,  experience  seems  to  indicate  that  separate  cards  are  more  convenient 
in  practice,  than  the  three  ruled  lines  of  the  present  arrangement.  Thus  the  card  B  is 
to  be  resolved  (1)  into  an  Existing  card  of  the  last  amount  $3,000  for  Duration 
14  years,  and  (2)  a  Discontinued  card  of  the  difference  7,500-3,000  or  $4,500  for 
3  years. 

On  cards  0,  M,  the  lower  amount  always  subtracted  from  the  next  preceding 
amount  over  it,  will  give  a  negative  difference.  The  corresponding  cards  of  this 
species  are  to  be  reserved  for  future  subtraction  from  positive  results  of  the  same  age 
and  duration.  Thus,  card  C  is  to  be  superseded  by  (1)  an  Existing  card  of  the  last 
amount  $7,500  from  1855  to  1874  or  19  years ;  (2)  a  Discontinued  card  for  the  negative 
difference — $4,500  from  1855  to  1869  or  Duration  14  years;  and  (3)  another  Discon- 
tinued card  for  the  negative  difference — $2,500  from  1855  to  1864  or  Duration  9  years. 
These  cards  (2),  (3)  are  to  be  reserved  for  future  subtraction  as  above  mentioned. 
These  reductions  will  be  best  understood  by  clerks  who  are  familiar  with  algebraic 
operations. 

Heretofore,  the  cards  of  Joint  Lives  have  usually  been  reduced  as  single  lives.  But 
the  death  of  the  first  of  a  couple,  is  occasionally  followed  by  the  death  of  the  second  in 
the  same  year;  and  such  second  deaths,  although  noted  on  the  single  life  plan,  escape 
the  record  Of  joint  lives.  To  correct  for  this  omission,  let  q,  q'  or  1  —p,  1  —p  denote 
the  probabilities  that  two  persons  insured  for  %a  each  will  die  within  one  year.  As 
single  livQS,  the  Expectation  of  Loss  in  one  year  will  be  a{q-{-q').  As  joint  lives,  the 
Expectation  of  Loss  will  be  a{l—pp'),  or  a—a{l—q){l—q'),th2it  is,  a{q  +  q'—qq')'y 
which  may  evidently  take  the  form 

The  last  expression  of  Probable  Loss  may  also  represent  the  Actual  Loss  on  Joint 
Lives.  Hence  if  each  Actual  Loss  is  divided  by  the  six  months  probability  (1— i^')  of 
the  survivor,  the  results  will  correspond  to  the  experience  of  single  lives.  Since  the 
average  value  of  \q'  is  about  \  oi  1  per  cent,  we  may  for  every  200  Death  cards  of 
Joint  Lives,  select  and  change  into  a  Death  card  one  Discontinued  card  of  the  same 


MORTALITY   AND    LOSS   EXPERIENCE.  23 

sex,  and  of  similar  age,  duration  and  amount.  After  this  simple  correction,  first 
devised  in  the  present  investigation,  the  pairs  of  cards  of  joint  lives  can  be  separated, 
and  the  whole  series  united  with,  the  other  cards  for  single  lives. 

Another  practical  artifice  was  employed  to  change  a  few  thousand  policies  from 
the  })lan  of  next  birthday  to  the  American  custom  of  nearest  birthday.  Instead  of 
dating  back  each  card  of  the  whole  series  half  a  year,  each  alternate  card  was  dated 
back  a  whole  year ;  since  all  the  policies  were  for  ordinary  amounts,  and  opposite  errors 
would  compensate  each  other.  Another  large  collection  of  data  with  ages  according  to 
lad  birthday,  was  dated  forward  on  the  same  convenient  principle. 

There  were  also  several  thousand  Transferred  Policies,  or  policies  which  on  the 
winding-up  of  the  Company  that  issued  them,  had  been  transferred  to  another  Com- 
pany. The  transfer  was  accompanied  with  the  original  ages  or  years  of  Entry  of  the 
Existing  policies,  but  the  corresponding  Discontinuances  and  Deaths  up  to  the  time  of 
transfer,  were  not  stated.  Thus,  suppose  ]00  or  more  persons  to  have  entered  the 
Cadmus  Life  Company  at  the  age  of  30  years.  Five  years  after,  the  Cadmus  is  closed 
up,  and  the  survivors  at  the  age  of  35,  are  transferred  to  a  second  Company.  The  valid 
experiences  commencing  at  age  35,  or  five  years  after  the  medical  examination,  should 
enter  Tables  I  and  II,  not  on  the  first  line,  but  on  the  fifth  line  below,  at  Duration  5. 

This  object  can  be  accomplished  by  writing  two  cards  for  each  transfer;  the  card 
(1)  beginning  with  the  medical  examination  at  the  age  of  30,  and  extending  forward 
into  the  returns  of  the  second  Company,  as  usual ;  and  the  card  (2)  beginning  at  the 
same  age  of  30,  to  be  discontinued  after  a  Duration  of  5  years.  The  latter  is  to  be 
reserved  for  future  subtraction  from  positive  Discontinuances  of  the  same  age  and 
duration.  In  this  way,  the  first  five  years  exposure  of  the  card  (1)  will  finally  be  can- 
celled by  the  card  (2),  as  was  proposed. 

In  relation  to  Endowment  Insurances,  composed  of  two  parts ;  that  is,  of  a 
Temporary  Insurance,  and  a  Pure  Endowment  for  the  same  amount;  since  the 
maturity  of  the  Endowments  was  not  specified  on  our  cards,  their  effect  on  the  whole 
experience  is  that  of  Temporary  Insurance  only. 

Death  Claims  reduced  by  compromise  or  by  litigation  have  been  restored  to  the 
original  amount,  as  the  uniform  standard  of  this  investigation.  In  the  case  of  a  single 
Company  where  the  amount  actually  paid,  had  been  given  in  lieu  of  the  normal  Death 
Claims,  a  small  correction  of  about  2|  per  cent,  was  applied  for  compromised  and 
litigated  claims,  taken  together. 

Having  thus  represented  the  whole  series  by  single  cards,  each  commencing  with  a 
medical  examination,  and  having  noted  on  each  of  them  its  proper  Duration,  we  apply 
the  advantages  of  the  card  system  as  follows. 

SECTION     III. 
Classifications  of  Data. 

The  next  operation  was  to  separate  the  cards  of  Male  Life  from  those  of  Female 
Life.  Each  of  these  groups  was  then  divided  into  the  three  classes  of  Existing, 
Discontinued,  and  Died. 

Each  of  these  classes  was  then  sub-classified  according  to  the  Durations  of  Policy, 

0,  1,  2,  3,  4, And  these  were  next  sub-divided  into  smaller  packages  of  cards 

corresponding  to  the  Age  of  Entry.  The  counting  of  cards  in  these  packages,  gave 
the  Existing,  Discontinued,  and  Died,  of  Lives  in  Table  I  and  II.  And  the  addition 
of  the  corresponding  Amounts,  by  the  same  packages,  gave  the  parallel  columns  of 


24 


MORTALITY  AND    LOSS   EXPERIENCE. 


ExistiDg,  Discontinued  and  Death  Claims.    The  latter  were  first  added  in  full,  and  then 
changed  to  the  nearest  TJwusands  of  Dollars,  omitting  the  last  three  residual  figures. 

For  every  Age  of  Entry,  the  sum  of  the  Existing,  Discontinued,  and  Died,  expresses 
the  total  Number  of  Entrants  at  the  head  of  the  columns.  For  example,  at  the  age 
of  27  years,  on  Page  90;  36,221  had  entered,  and  were  insured  for  the  initial  amount  of 
$87,030,000.  Of  these  policies,  18,328  were  still  in  force,  or  existing  at  the  epoch  in 
1874;  also  16,790  had  been  discontinued;  and  1,103  had  died,  as  noted  at  the  foot  of 
the  columns.  Of  the  Deaths,  the  largest  number  in  any  one  year,  and  more  than 
one-third  of  the  Discontinuances  had  occurred  in  the  second  year,  shown  opposite 
Duration  1.  This  feature  is  common  to  all  the  Companies.  Tlie  first  ten  or  fifteen 
years  Duration  comprise  the  greatest  part  of  the  business;  and  the  whole  is  practically 
limited  to  thirty  years ;  although  a  few  cases  are  of  older  date. 


SECTION     IV. 
Calendar  Years  and  Policy  Years. 

For  greater  convenience,  as  before  mentioned,  the  new  business  of  different  cal- 
endar years  is  superimposed,  for  this  investigation,  as  if  all  the  insured  entered  the 
Company  uniformly  during  one  initial  year.  On  the  average  they  enter  at  the  middle 
of  this  year ;  and  so  the  average  are  exposed  for  only  the  latter  half  of  the  first  calendar 
year.  The  Exits  as  well  as  the  Entrances  of  subsequent  years,  are  likewise  assumed 
to  occur  uniformly  during  each  separate  calendar  year.  Average  Policy  Years  thus 
begin  and  end  loith  the  middle  of  Calendar  Years  ;  and  the  average  birthday  is  taken  at 
the  middle  of  the  initial  year. 

The  ratio  of  mortality  for  the  first  year  has  been  a  subject  of  discussion  in  the 
Journal  of  the  Institute  ;  but,  as  there  stated,  "  it  is  difficult  to  devise  a  better  plan  ; " 
and  m  practice,  the  regular  formula  for  subsequent  years  has  been  generally  applied 
to  the  first  year,  as  will  be  presently  exhibited. 

Throughout  the  Tables  I  and  11,  the  first  column  headed  "  Years  of  Insurance," 
0,  1,  2,  3,  etc.  expresses  the  Durations  found  by  subtracting  the  Year  of  Entry  on  the 
cards  from  the  Year  of  Exit  or  termination.  For  future  reference,  the  more  definite 
scale,  0 — ^,  ^ — 1^,  \\ — 2^,  etc.  is  also  given  in  the  right  hand  columns  of  Summary 
A  and  B,  at  the  beginning  of  Tables  I  and  II.  As  before  described,  assuming  the 
entrances  to  occur  uniformly  during  the  twelve  months  of  the  initial  calendar  year, 
the  average  date  of  insurance  or  entry  is  taken  at  the  middle  of  the  year,  when  the 
"  Years  of  Insurance  "  begin,  as  follows.  The  title  "  Years  of  Insurance "  is  synony- 
mous with  "  Durations"  and  with  "Policy  Years." 


Calendar 
Teabs. 

Years  of 
Insurance. 

Existing,  Discontinued,  Died. 

i  Beginning 

]  Middle 

(  End 

f  Middle 

]  Middle 

(  End 

r  Middle 

]  Middle 

(Etc 

0 

1 
1 

H 

2 
2 

3i 

Insurances  commence. 
Average  date  of  Entrance. 
First  Year's  "  Existing "  record  closes. 
Average  date  of  Deaths  and  Discontinued. 
Survivors  enter  on  second  Policy  Year. 
Second  Year's  "Existing"  record  closes. 
Average  date  of  Deaths  and  Discontinued. 
Survivors  enter  on  third  Policy  Year. 
Third  Year's  "  Existing  "  record  closes. 

Beginning 

Middle 

End 

Beginning 

Middle 

End 

Beginning 

Etc 

MORTALITY  AND   LOSS  EXPERIENCE.  25 

SECTION    V. 
Notation  and  Annual  Equations. 

Let  N  =  number  of  admissions  during  any  year  of  Age. 
J)  _       a         it   Deaths  during  any  year  of  Age. 
r    =       "         "   Discontinuances  during  any  year  of  Age. 
e    =        "         "   survivors  entering  on  any  year  of  Age. 
R  =       "         "   Existing  at  the  end  of  the  year. 

Ni,  Di,  r,,  e„  Ri  =  the  like  numbers  for  the  next  higher  year  of  age,  etc.  These 
are  here  adopted  from  the  short  method  of  W.  S.  B.  Woolhouse  in  the  Journal  of  the 
Institute,  Vol.  13,  page  10. 

M  =  e+^N— ^(r  +  D)  =  number  exposed  at  the  middle  of  the  year,  if  the  changes 
occur  uniformly.  M  can  also  denote  the  middle  altitude  of  a  trapezoid,  whose  base  is 
unity  or  one  year,  and  whose  area  represents  the  total  exposure  of  the  year.  Assuming 
half  the  annual  decrement  to  occur  before,  and  the  other  half  to  occur  after,  the 
middle  of  the  year,  we  have, 

p  =  ^ — jjT  =  the  proportion  that  survive  one  year's  exposure  to  Death. 

M— ir 
p'  =  ^ — J-  =  the  proportion  that  survive  one  year's  exposure  to  Discontinuance. 

f>      M— ^(r+D)      e,  +  R       ,,  ^'       ..x.  t  -  _, 

p  =  ^  .u    ,j){  = =  the  proportion  that  survive  one  years  exposure  to 

^^         '^  both  Death  and  Discontinuance. 

q  =  rr= — -r=-  =  1  —  p  =  proportion  that  die  in  one  year. 

j3  =  M+|D=£+^N—^r=  Exposed  to  Risk  [of  Death].    The  last  denominator 

M  +  ^D  or  i3  has  been  named  the  "  Exposed  to  Risk," 
although  it  differs  from  the  mean  exposure  M  shown 
above. 

q  =  -p^ r,  for  the  initial  year  of  Entry  or  Duration  0. 

T  T 

1  —  p'  =  ^ — --  =:  -p^ — T^pr  =  proportion  that  discontinue  in  one  year. 

^       M  +  ^r      i3  +  |r— ^D       ^    ^  ^ 

r-i-J)  r  +  D 

1  —  »"  =  ST? — TT =Frr  =  73 — r-  =  proportion  of  both  deaths  and  discontinuances 

''^  '  r         m  one  year. 

For  Duration  0,  Co  =  N=  Sum  of  (R  +  D+r),  j3o  =  ^(N— ro), 

1,  e,  =  N-(R„+Do  +  ro),  /3,  =  e,-^r„ 

2,  e,  =  e,-(R,  +  D,  +  r,),  jS,  =  e,-^r,, 
"          "         3,  E,  =  E,-(R,  +  D,  +  r,),  Pz  =  e,-lrs, 

etc.  etc.  etc. 

By  eliminating  e,  and  by  transposition,  or  substitution, 

3,  =  2/3o-Ro-Do-K 
/3,  =  /3.-R,-D,-ir,-ir„ 
Pa  =  /J2— Rq— Dj— ^rj— |r3, 
etc.  etc. 


26 


MORTALITY  AND    LOSS   EXPERIENCE. 


etc. 


etc. 


M,  =  2Mo-E.-i(r,  +  D,), 
M,  =  M,-E,-i(D,+n)-i(D,+r,), 
M3  =  M2-E,-i(D,  +  r,)-i(D3  +  r3). 
etc.  etc. 

A  method  for  carrying  forward  the  Existing  to  their  proportional  terminations  in 
the  columns  of  Discontinued  and  Died,  will  be  described  hereafter  in  Section  IX. 


SECTION     VI. 
Transformation  of  Data. 

The  foregoing  equations  have  been  particularly  serviceable  in  transforming  the 
results,  which  had  been  wrought  out  by  different  Actuaries  and  Companies,  to  a 
uniform  system.  A  brief  memorandum  of  some  of  the  operations  may  be  useful  for 
future  reference.  The  Experience  of  one,  designated  as  Company  A,  gave  the  values 
of  N,  /J,  and  D  for  Lives  at  every  age,  with  but  an  abstract  of  the  values  of  r.  After 
the  latter  had  been  interpolated  for  all  ages,  the  Existing  were  then  found  from  the 
above  equations  of  R. 

Having  now  obtained  the  elementary  data  for  Lives,  the  omitted  Amounts  were 
next  supplied  by  proportions  wrought  out  for  the  Existing,  Discontinued,  and  Died, 
separately  at  each  age.  Thus,  taking  the  first  two  terms  from  the  general  experience 
of  the  other  similar  Companies,  we  have  the  simple  statement,  as  R  of  the  Lives  is  to 
R  of  the  Amounts,  so  is  R  of  the  Lives  in  Company  A,  to  the  corresponding  Amount 
at  the  same  age. 

The  returns  from  another,  which  may  be  designated  as  Company  B,  gave  the 
Deaths  and  Exposed  to  Risk  by  Policy  years,  accompanied  by  the  following  explanation. 
"  The  classification  is  by  Calendar  Years  of  Issue  and  Policy  Years  after  Issue.  In 
regard  to  fractions  of  years,  a  policy  for  $10,000  lapsed  or  discontinued  at  the  end  of 
3^  years  stands  pro  rata  in  the  fourth  year  as  $5,000,  etc.  If  a  policy  was  terminated 
by  Death,  it  was  entered  as  at  risk  for  the  whole  year,  and  entered  as  a  death  for  the 
whole  amount."  In  order  to  change  to  the  forms  of  the  card  system,  the  data  P,  D 
in  thousands  of  dollars  were  first  added  as  follows.  Here  P  denotes  the  Amount 
Exposed  to  risk  in  one  Policy  year,  and  D  the  corresponding  Death  Claims. 


Age 

OF 

Entbt. 

Values  of  P.  Ist  Pouct  Yeab. 

Age 

OF 

Entbt. 

P.  2d  Pouct  Yeab. 

1869 

'70 

'71 

•72 

'73 

'74A 

P. 

1869 

'70 

'71 

'72 

'73A 

P. 

7 

8 

1 

14 

8 

14 
IS 
16 
17 
18 
19 

5 

5 
6 
S 

1 

1 

8 
8 
3 

6 
1 

1 
1 
7 

7 
6 

12 
18 
18 

14 
18 
16 
17 
18 
19 

8 
8 

1 

1 

8 

8 
3 

6 
1 

MORTALITY  AND    LOSS   EXPERIENCE. 


27 


For  any  one  Age  of  Entry,  as  18  years,  let  D\,  P„  denote  the  Deaths  and  the 
Exposure  of  the  1st  Policy  Year;  D'a,  Pa,  the  like  quantities  for  the  2d  Policy  Year; 
and  go  on.  Let  us  assume  the  entrants  to  begin,  on  an  average,  in  the  middle  of  the 
initial  calendar  year.  Then  if  the  deaths  occur  uniformly  in  each  year,  and  Do,  D,, 
D.J,  . . .  denote  the  Deaths  on  the  card  system,  we  have 

Do  =  iD\;      Di  =  iD\  +  iD'a;      D,  =  iD',  +  ^J)',;      etc. 

In  like  manner  if  Eo,  Ej,  etc.  denote  the  Existing  on  the  card  system,  at  the  end  of 
Calendar  years  or  the  middle  of  Policy  years,  and  Deaths  were  included  as  above 
described,  we  shall  have  by  the  middle  ordinate  of  the  trapezoid  denoting  the  exposure 
of  the  pohcy  year,  restricted  to  the  last  columns  denoted  by  '74A,  '73  A,  '72A,  . . . 

E«=Px-iD\;      E,  =  P,-p'a;      Ea  =  P3-iD'3;      etc. 

Lastly  if  ro,  Ti,  r^,  —  denote  the  Discontinued  on  the  card  system,  Tq  only  is  to 
be  estimated,  being  about  one-half,  or  rather  0.45  of  rj.  It  is  evident  that  discontin- 
uances and  lapses  will  occur  mostly  at  the  end  of  policy  years,  that  is,  at  the  middle  of 
calendar  years,  on  the  average.  We  also  note  that  by  adding  and  subtracting  |D'„  the 
middle  ordinate  Pi — ^D',  becomes  P,,  at  the  beginning,  and  P,— D',  at  the  end  of  the 
policy  year.  Consequently  Pa  is  the  value  at  the  beginning  of  the  next  year;  and  the 
Existing  Eo  were  withdrawn  (at  the  end  of  the  calendar  year)  six  moiiths  previous, 
Taking  the  difference,  we  have 

ri  =  P,— D',— Eo— Pa;      r^  =  Pa— D'a— E,— P3 ;      etc. 

After  transformation  of  the  Amounts  given  by  Company  B,  in  accordance  with 
these  three  series  of  equations,  investigated  for  the  purpose,  the  corresponding  normal 
number  of  Lives  or  Policies  was  then  obtained  conversely  from  the  principle  of  pro 
portions  employed  for  Company  A. 

The  records  of  a  third  Company,  denoted  as  Company  C,  gave  the  Deaths  and 
Exposed  for  both  Lives  and  Amounts,  according  to  Calendar  years  of  exposure,  with 
correction  for  fractional  parts  of  the  year.  The  age  nearest  to  Jan.  1st  had  been  taken 
as  the  Age  of  Entry.  After  tlie  first  Policy  on  any  life,  the  subsequent  policies  or 
surrenders,  had  been  regarded  merely  as  increase  or  decrease  of  the  first  Policy.  By 
aid  of  further  statistics,  the  stated  Loss  actually  paid,  was  corrected  to  the  Loss  as 
insured.  The  lives  were  assumed  to  enter  the  Company  at  the  middle  of  the  initial 
calendar  year,  on  an  average,  and  in  this  sense,  at  their  real  ages.  The  results  annually 
wrought  out  by  the  Office,  had  been  given  in  the  form  of  summation  tables  of  the 
quantities  N,  M,  D,  E,  which,  besides  determining  the  final  ratios  of  mortality,  were 
sufficiently  extensive  for  other  purposes.  In  order  to  unite  with  the  returns  of  other 
Companies,  as  here  presented,  it  became  necessary  to  resolve  the  results  into  their 
original  or  annual  elements.  A  single  example  will  illustrate  the  special  process 
devised  for  this  object. 


Years  of 
Insurance. 

Probpble 
Deaths 

Ages. 

34 

35 

36 

37 

38 

0 
1 
2 
8 

4 
6 

136.33 

258.86 
2  3  0.55 
212.97 
198.11 
179.33 

Probable  Deaths. 

2,283.48 

53.56 

55.37 

57.83 

60.04 

61.33 

28  MORTALITY   AND    LOSS   EXPERIENCE. 

The  horizontal  and  vertical  sums  were  thus  given,  and  it  was  required  to  fill  out 
the  series  of  squares,  with  such  compatible  numbers  as  should  make  up  these  sums. 
Instead  of  resorting  to  equations  of  condition  for  five  year  periods,  the  squares  were 
first  filled  out  approximately,  from  the  Experience  of  another  similar  Company.  Their 
vertical  sums,  when  compared  with  the  true  sums,  gave  a  multiplier  for  each  column, 
such  that  the  vertical  sums  of  products  agreed  with  the  true  sums,  shown  at  the  foot  of 
the  columns.  Next,  the  same  products  were  added  horizontally ;  their  sums  when 
compared  with  the  actual  sums  in  the  left  hand  column,  gave  a  new  set  of  multipliers, 
such  that  the  horizontal  sums  of  the  new  products  agreed  with  those  stated  in  the  left- 
hand  column  respectively.  The  same  products  were  next  added  vertically,  to  get  new 
multipliers  and  products  as  first  described,  and  so  on.  It  proved  to  be  a  converging 
process,  which  terminated  when  the  last  multipliers  became  virtually  1 ;  and  the  joint 
conditions  of  horizontal  and  of  vertical  summation  were  satisfactorily  fulfilled.  The 
resulting  Probable  Losses  when  divided  by  the  same  tabular  probabilities  previously 
used  as  multipliers  to  determine  the  Probable  Loss,  gave  the  corresponding  values  of 
M  as  required. 

After  this  leading  determination,  different  courses  were  suggested.  Approximate 
values  of  D  could  readily  be  found  by  applying  the  known  ratios  of  mortality  to  the 
values  of  M ;  and  approximate  values  of  E  and  r  could  then  be  derived  from  the 
foregoing  Equations  for  M  (page  26),  by  assuming  the  ratio  of  E  to  r  to  be  the  same 
as  in  the  general  experience  of  other  similar  Companies,  at  the  same  age  and  duration. 
Each  equation  would  then  have  only  one  unknown  quantity.  And  these  approximate 
values  could  lastly  be  made  to  accord  with  the  given  sums  by  slight  percentage 
corrections.  But  the  work  being  already  performed,  the  present  sketch  sufficiently 
indicates  the  methods  of  interpolation.  The  new  converging  process,  which  opened 
the  way  as  above  described,  could  be  applied  more  extensively,  as  where  the  sums  of  the 
columns  had  been  taken  in  the  two  directions  vertically  and  diagonally. 


SECTION     VII. 
Exposed   to   Risk. 

After  the  original  data  had  been  reduced  to  the  three  %rms  of  Existing,  Discon- 
tinued, and  Died,  shown  in  Tables  I  and  II,  the  next  process  was  to  fill  out  the 
columns  of  Exposed  to  Eisk  [of  Death].  This  peculiar  term  has  already  been  defined 
under  Notation,  by  the  quantnty  i3,  or  M  +  ^D. 

To  explain  the  application, — in  Table  I  Male  Life,  Age  at  Entry  33  years,  for 
example,  the  Number  of  Entrants  40,498  at  the  head  of  the  first  columns,  was  found 
by  adding  the  first  three  sums  at  the  foot  of  the  columns.  And  the  Entrant  Amount 
Insured  $104,474,000  was  found  in  like  manner.  Then  by  the  preceding  equations 
/or  i3  (page  ^5),  half  the  number  of  entrants  less  half  of  1,872  the  discontinuances  of 
the  year  0,  gives  19,313  years  of  exposure  in  the  year  0.  And  the  number  of  entrants 
N  diminished  by  the  sum  of  Existing,  Discontinued,  and  Died  of  the  Year  0,  gave  the 
surviving  entrants  ei,  on  the  year  1.  And  f,  diminished  by  half  the  discontinued 
6,484  of  the  year  1,  gave  (i,  or  32,927  Exposed  to  risk  during  the  year  1.  After 
the  first  year,  the  process  is  uniform,  as  follows. 


MORTALITY  AND    LOSS   EXPERIENCE. 


29 


FROM  TABLE  I.  AGE  AT  ENTEY  33  YEARS. 


Year  of 

Insukance. 

Entrants  less  Existing, 
Discontinued,  and  Died. 

Surviving 
Entrants. 

Subtract 
^  Disc'd. 

Exposed 
TO  Risk. 

0 

1 

2 
3 

40,498-(2,349  +  1,872  + 108) 
36,169-(2,181 +  6,484  +  219) 

27,285-(l,776  +  2,845  +  218) 

1(40,498) 
36,169 
27,285 
22,446 

1(1.872) 
1(6,484) 
1(2,845) 
K1.856) 

19,313 
32,927 
25,862| 
21,518 

In  the  columns  of  Amounts,  the  Exposed  to  Kisk  [of  Death]  are  found  in  the 
same  manner.  Thence,  the  ratios  of  mortality,  and  of  discontinuance,  or  of  both 
combined,  can  be  determined  by  the  preceding  formulas.  The  collective  data  will  be 
found  unusually  complete  for  these,  as  well  as  other  inquiries. 

The  preceding  principles  require  that,  after  passing  from  Deaths  to  the  Ratios  of 
mortality,  or  to  the  life  table,  the  current  Ages  on  the  plan  of  "  nearest  birthday  "  are 
to  be  diminished  by  \  year,  as  if  changing  the  Ages  from  the  middle  to  the  beginning 
of  the  year  of  the  ratio.  Thus  29^  current  is  change^  to  29  years.  The  English 
custom  of  age  "next  birthday"  would  require  a  similar,  final  change  of  one  year, 
reducing  the  current  age  30  to  29,  for  example,  as  noted  in  the  first  volume  of  the 
Institute  Experience,  page  18. 


SECTION     VIII. 

Comparative  Results.     Ratios  of  Mortality  and  of  Loss 

to  the  Year   1874. 

The  collection  of  the  Thirty  Life  Offices  represents  an  aggregate  of  about  1,177,000 
original  policies.  But  under  the  rules  of  reduction,  before  described,  these  were  adjusted 
to  the  net  number  stated  below,  comprising  above  a  million  of  regular  observations.  It 
will  be  seen  that  the  number  of  female  entrants  was  relatively  small ;  the  total  propor- 
tion being  twenty-two  males  to  one  female  insured.  The  ages  of  entry  group  themselves 
above  and  below  the  mean  age  of  thirty-five,  the  half  of  "  three-score  years  and  ten." 


Numbers. 

Males. 

Females. 

Total. 

Number  of  Entrants 

Whole  number  of  Deaths 

982,734 

44,485 

35.23 

36.27 

44,795 

2,058 
34.46 

34.87 

1,027,529 

46,543 

35.20 

36.23 

Average  Age  of  Entry  for  Lives,  years 

"           "              "        "    Amounts,  years 

'                            Proportions  : 

Existing. 

Discon- 
tinued. 

Died. 

Total. 

Of    982,734  Male  Entrants 

53.7 
49.7 
53.5 

41.8 

4.5 
4  (^ 

100.0 
100.0 
100.0 

"       44,795  Female  Entrants 

"  1,027,529  Male  and  Female  Entrants 

42.0 

4. 

5 

30 


MORTALITY  AND    LOSS  EXPERIENCE. 


Dividing  now  the  corrected  number  "  Exposed  to  Eisk  "  by  the  whole  number  of 
Entrants,  we  find  at  the  epoch  of  the  Experience  in  1874,  the  Mean  Duration  of 
Policies  was  4.36  years.  Adding  this  to  the  Average  Age  of  Entry  35.23  years,  we  find 
that  the  Lives  Insured  had  attained  the  Average  Age  of  39.6  years  at  the  epoch.  In 
the  older  Experience  of  the  Twenty  British  Offices,  the  Mean  Duration  of  Policies  at 
the  epoch  in  1863  was  9.12  years;  the  average  Age  of  Entry  was  35.3  years;  and  the 
average  age  attained  by  all  the  lives  insured,  was  44.4  years.  Resuming  the  Experience 
of  the  American  Offices,  we  have  next  the  following  results. 

MEAN    PERCENTAGE    OF   MORTALITY    ACCORDING    TO    THE    YEAR    OF   INSURANCE. 

ALL    AGES.      TO    1874. 


Ykar 

OP 

Insurance. 

Male  Life. 

Female  Life. 

Year 

OF 

Insurance. 

Deaths 
Per  cent. 

Claims 
Per  cent. 

Deaths 
Per  cent. 

Claims 
Per  cent. 

0 
1 
2 
3 
4 
5 
6 
7 
8 
9 

Total, 

0.63 
0.81 
0.92 
1.00 
1.09 
1.13 
1.17 
1.22 
1.20 
1.23 

1.03 

0.63 
0.85 
1.00 
1.06 
1.19 
1.23 
1.27 
1.34 
1.27 
1.25 

1.10 

0.86 
1.08 
1.06 
1.14 
1.16 
1.28 
1.40 
1.33 
1.06 
1.73 

1.16 

0.93 
1.12 
1.09 
1.27 
1.32 
1.43 
1.54 
1.35 
1.16 
1.54 

1.23 

0 

1 
2 
3 
4 
6 
6 
7 
8 
9 

Total. 

The  preceding  abstract,  from  Tables  III  and  IV  (B),  shows  how  many  die  out  of 
100  Exposed  to  one  year's  mortality,  the  average  being  above  one  per  cent.  In  the 
"  Year  of  Insurance "  0,  as  before  explained,  the  observations  extend,  on  the  average, 
over  half  a  year  from  the  day  of  entry,  although  the  percentage  is  the  annual  rate. 
The  "Year  of  Insurance"  1  extends  from  ^  a  year  to  1^  years  from  entry;  and  so  on. 

The  principal  effect  of  the  medical  selection  is  more  correctly  exhibited  on  Pages 
31-33,  for  Equal  Ages  of  Exposure  ;  the  average  rate  being  generally  attained  within 
2^  years.  At  the  same  time,  the  counter  selections  of  the  insured  are  proceeding  by 
changes  of  amount,  so  that  the  final  claims  are  generally  about  four  per  cent,  in  excess 
of  what  would  be  the  loss  for  equal  Policies  or  amounts  insured. — Compare  p.  192. 

The  computation  of  the  following  summary  for  Male  Life  may  be  thus  illustrated. 
For  "Years  of  Insurance"  0,  for  example,  we  add  the  Deaths  and  Exposed  in  Table  I 
for  Ages  of  Exposure  30,  31,  32,  33,  34,  35  Years,  which  give  89,  90,  95,  108,  99,  94,  or 
a  total  of  575  Deaths,  and  in  like  manner  115,458.5  Exposed  to  Kisk.  These  Deaths 
divided  by  the  Exposed  give  0.498  per  cent,  as  stated  in  the  Table  on  next  page.  The 
six  middle  Ages  current, strictly  represent  the  period  29^-35^;  the  central  five  years 
of  which  are  30-35  years;  the  fraction  being  excluded  only  to  facilitate  future 
comparisons.  From  the  true  middle  age  32^,  dropping  ^  year  leaves  the  middle  initial 
age  32,  as  before  specified.  It  will  be  seen  that  the  ages  bordering  on  the  five-year 
periods,  as  25,  30,  etc.  are  added  twice.  The  ratios  of  Death  Claims  were  found  in  the 
same  manner,  subject  in  case  of  future  graduation  to  a  smaU  correction  shown  in 
Section  X,  3. 


MORTALITY  AND    LOSS   EXPERIENCE. 


31 


For  the  STimmary  of  Female  Life,  a  parallel  method  was  employed ;  the  data  being 
first  added  in  regular  five-year  periods,  such  as  30,  31,  32,  33,  34;  then  35,  36,.37,  38, 
39,  etc.,  or  29^344;  344-39-|;  etc.  To  advance  these  periods  |-  year,  that  is,  to 
30-35 ;  35-40,  etc.,  one-tenth  of  the  increase  from  one  quinquennial  to  the  next,  was 
added  to  the  former  ratio.  Thus  for  the  periods  (0)  24|-2f)|^,  29^34|^,  the  ratios  of 
Deaths  per  cent,  are  27-^3956  and  36-^4258  or  .6825  and  .8455.  One-tenth  of  their 
diflference  .0163  added  to  the  former  gives  .6988  or  .699  as  stated  in  the  abstract  on  next 
page  under  25-30  at  the  head  of  the  column.  As  a  method  of  adjustment,  there 
appears  little  or  no  ground  of  preference  between  this  and  the  former  operation  for 
Male  Life,  with  a  fair  measure  of  regularity  in  the  data. 

MALE  LIFE.     DEATHS  AND  CLAIMS   PER  CENT.     TO  1874. 


Ages  of 

Exposure. 

OF 

Insurance. 

15-20 

20- 

25 

•      25- 

30 

30-35 

1 

Deaths 

CLAms 

Deaths 

Claims 

Deaths 

Claims 

Deaths 

Claims 

PER  CENT. 

PER  CENT. 

PER  cent. 

per  cent. 

PER  CENT. 

PER  CENT. 

PER  CENT. 

PER  CENT. 

0 

.735 

.597 

.571 

.446 

.481 

.442 

.498 

•      .485 

1 

.673 

.625 

.677 

.620 

.607 

.603 

.617 

.618 

2 

.802 

.746 

.782 

.846 

.691 

.735 

.691 

.764 

3 

.634 

.544 

.685 

.626 

.777 

.737 

.744 

.758 

4 

.590 

.776 

.740 

.719 

.811 

•    .868 

.833 

.854 

5 

.400 

.421 

.899 

1.038 

.796 

.885 

.827 

.914 

6 

1.388 

.305 

1.223 

.650 

.879 

.905 

.801 

.882 

7 

2.116 

1.227 

1.003 

1.209 

.860 

.879 

.837 

.827 

8 

.306 

.548 

.812 

.897 

.799 

.856 

9 



1.022 

.337 

.561 

.459 

.801 

.841 

0     4 

.709 

.636 

.672 

.620 

.647 

.645 

.666 

.683 

5-9 

.725 

.432 

.967 

.910 

.823 

.879 

.817 

.879 

10-14 

1.890 

1.572 

1.295 

.850 

1.037 

1.194 

15-19 

.863 

.386 

1.243 

1.634 

20-24 



2.778 

1.105 

Total, 

.709 

.627 

.689 

.634 

.671 

.673 

.705 

.782 

0 

35-40 

40-45 

45- 

-50 

50- 

55 

.520 

.528 

.663 

.666 

.840 

.802 

1.186 

1.354 

1 

.709 

.831 

.845 

.839 

1.034 

1.031 

1.332 

1.309 

2 

.785 

.871 

.931 

.942 

1.126 

1.107 

1.442 

1.495 

3 

.852 

.884 

.958 

.950 

1.096 

1.118 

1.403 

1.525 

4 

.920 

1.000 

1.019 

1.108 

1.184 

1.252 

1.469 

1.512 

5 

.865 

.956 

1.045 

1.124 

1.185 

1.206 

1.392 

1.424 

6 

.914 

.963 

1.028 

1.071 

1.145 

1.241 

1.557 

1.489 

7 

.946 

1.003 

1.007 

1.038 

1.127 

1.291 

1.506 

1.611 

8 

.789 

.843 

1.013 

1.020 

1.099 

1.102 

1.525 

1.517 

9 

.889 

.918 

.900 

.961 

1.036 

1.014 

1.568 

1.398 

0-^ 

.758 

.829 

.892 

.905 

1.069 

1.074 

1.379 

1.442 

5—9 

.883 

.948 

1.013 

1.061 

1.133 

1.194 

1.497 

1.488 

10-14 

.933 

.936 

1.007 

1.015 

1.185 

1.309 

1.423 

1.467 

15-19 

.929 

1.006 

.903 

1.031 

1.134 

1.212 

1.379 

1.453 

20-24 

2.201 

2.010 

1.135 

1.566 

1.019 

1.067 

1.460 

1.567 

25-29 

3.150 

6.349 

1.393 

2.534 

1.838 

2.653 

Total, 

.802 

.866 

.938 

.963 

1.102 

1.138 

1.426 

1.469 

33 


MORTALITY  AND    LOSS   EXPERIENCE. 


MALE  LIFE.     DEATHS   AND  CLAIMS  PER  CENT.     TO  1874. 


Ages  op  ] 

Exposure. 

Years 

OF 

55- 

60 

60-65 

65-70 

70-75 

TVRTTR  A  TTPK 

Deaths 

Claims 

Deaths 

Claims 

Deaths 

Claims 

Deaths 

Claims 

FEB  CENT. 

PEB  CENT. 

PER  CENT. 

PER  CENT. 

PER   CENT. 

PER  CENT. 

PER  CENT. 

PER  CENT. 

0 

1.550 

1.739 

2.425 

2.429 

3.200 

5.010 

4.138 

3.003 

1 

1.851 

1.806 

2.721 

2.703 

3.142 

2.713 

4.902 

5.066 

2 

1.887 

2.071 

2.644 

2.423 

3.460 

3.821 

3.663 

4.484 

3 

2.021 

2.113 

2.867 

2.886 

3.610 

4.169 

3.338 

2.193 

4 

2.158 

2.018 

2.913 

3.164 

3.689 

3.899 

3.464 

3.136 

5 

2.077 

2.117 

3.008 

2.820 

3.811 

3.797 

6.452 

4.626 

6 

1.992 

2.121 

2.761 

3.402 

3.706 

4.341 

6.656 

6.849 

7 

2.079 

2.121 

2.903 

3.153 

4.631 

4.285 

4.928 

4.937 

8 

2.121 

2.179 

2.585 

2.727 

3.819 

3.339 

5.405 

6.438 

9 

2.074 

2.060 

2.724 

3.074 

3.537 

4.140 

7.355 

7.901 

0^ 

1.926 

1.968 

2.g56 

2.767 

3.482 

3.809 

3.726 

3.437 

5—9 

2.064 

2.122. 

2.820 

3.043 

3.921 

3.998 

6.109 

6.027 

10-14 

1.824 

1.920 

2.619 

2.583 

3.794 

3.819 

6.014 

5.531 

15-19 

1.875 

2.037 

2.681 

3.005 

4.211 

4.624 

5.037 

4.934 

20-24 

1.790 

2.053 

2.775 

3.214 

4.523 

5.494 

6.131 

6.396 

25-29 

1.727 

1.708 

2.871 

2.940 

3.727 

4.098 

6.061 

6.145 

TotaJ, 

1.942 

2.017 

2.756 

2.899 

3.934 

4.236 

5.631 

'  5.550 

0—4 

75-80 

80-85 

85- 

-90 

All  Ages. 

5.096 

5.150 

14.286 

9.524 

.881 

.937 

5—9 

8.430 

8.066 

3.636 

1.550 

1.179 

1.267 

10-14 

9.707 

8.808 

9.677 

9.160 

1.171 

1.433 

15-19 

7.942 

7.119 

11.834 

13.598 

4.445 

5.333 

1.679 

1.798 

20-24 

8.234 

6.943 

12.012 

9.825 

21.239 

25.478 

2.339 

2.582 

25-29 

10.836 

9.848 

11.282 

9.773 

20.779 

18.065 

2.943 

3.173 

Total, 

8.483 

7.724 

11.332 

10.342 

16.667 

17.757 

1.028 

1.096 

FEMALE  LIFE.     DEATHS  AND  CLAIMS  PER  CENT.     TO  1874. 


Ages  of 

Exposure. 

Years 

4        OP 

15- 

20 

20-25 

25- 

-30 

30-35 

Instirance. 

Deaths 

Claims 

Deaths 

Claims 

Deaths 

Claims 

Deaths 

Claims 

PEB  cent. 

PEB  CENT. 

PEB  CENT. 

PER  CENT. 

PER  CENT. 

PER  CENT. 

PEB  CENT. 

PER  CENT. 

0 

.808 

.784 

1.062 

1.042 

.699 

.621 

.840 

1.104 

1 

.585 

.463 

.952 

.944 

1.056 

1.004 

1.076 

1.148 

2 

.600 

.396 

1.049 

1.031 

1.019 

1.091 

.946 

.814 

3 

1.415 

2.307 

1.122 

1.383 

1.023 

1.113 

1.139 

1.292 

4 

.993 

.526 

1.047 

1.561 

1.018 

1.085 

5 

.380 

.455 

1.175 

1.054 

1.010 

.882 

6 

1.894 

.924 

1.065 

1.231 

1.372 

1.491 

7 

1.020 

1.193 

1.184 

.959 

1.023 

.713 

8 

1.916 

1.674 

2.083 

6.180 

1.250 

1.206 

9 

. . .  •• 

2.071 

1.388 

0—4 

.714 

.707 

1.024 

1.017 

.971 

1.015 

1.009 

1.080 

5—9 

.991 

.764 

1.180 

1.419 

1.199 

1.081 

10-14 

.949 

2.110 

1.013 

.948 

15-19 

S.310 

3.124 

Total, 

1 

.676 

.671 

1.108 

.999 

.997 

1.065 

1.052 

1.084 

MORTALITY  AND    LOSS   EXPERIENCE.  33 

FEMALE  LIFE.     DEATHS  AND  CLAIMS  PER  CENT.     TO  1874 


Years 

1 
Ages  of  Exposure. 

1 

OP 

35- 

40 

40-45 

45- 

50 

50- 

55 

Insxjbance. 

Deaths 

Claims 

Deaths 

Claims 

Deaths 

Claims 

Deaths 

Claims 

PER  CENT. 

PER  CENT. 

PER  CENT. 

PER  CENT. 

PER  CENT. 

PER  CENT. 

PER  cent. 

PER  CENT. 

0 

.795 

.946 

.838 

.955 

.975 

1.013 

1.193 

.842 

1 

1.157 

1.322 

1.101 

1.007 

.899 

.763 

1.064 

1.545 

2 

.917 

1.080 

1.009 

1.027 

.806 

.724 

1.496 

1.570 

3 

.916 

.785 

1.108 

1.159 

1.239 

1.399 

1.179 

1.470 

4 

.789 

.780 

1.145 

1.197 

1.124 

1.563 

1.550 

1.524 

5 

1.086 

1.145 

1.090 

1.390 

1.393 

1.533 

1.804 

1.943 

6 

1.264 

1.383 

1.097 

1.027 

1.287 

1.656 

1.601 

1.627 

7 

.937 

1.078 

.909 

1.118 

1.497 

1.332 

1.427 

1.470 

8 

1.509 

1.531 

.410 

.479 

.351 

.233 

.954 

.976 

9 

.913 

.868 

1.456 

1.646 

1.257 

.963 

1.941 

1.481 

0—4 

.946 

1.030 

1.051 

1.064 

.997 

1.052 

1.295 

1.441 

5-9 

1.142 

l;22l 

1.000 

1.147 

1.239 

1.312 

1.568 

1.594 

10-14 

.843 

.839 

1.294 

1.435 

1.027 

.994 

1.189 

1.153 

15-19 

2.440 

3.128 

1.031 

1.252 

.830 

.766 

1.299 

1.509 

20-24 

.940 

.678 

1.116 

.986 

.826 

.590 

25-29 

2.564 

1.786 

Total, 

1.002 

1.082 

1.049 

1.104 

1.059 

1.103 

1.341 

i.432 

0 

55- 

-60 

60-65 

65-70 

70-75 

1.388 

1.932 

28.571 

18.182 

1 

1.492 

1.964 

1.957 

1.541 

4.032 

2.899 



2 

1.862 

2.149 

3.434 

3.301 

4.496 

6.344 

6.250 

5.000 

3 

1.351 

1.962 

2.125 

2.438 

4.445 

8.375 

4 

1.898 

1.743 

3.173 

4.035 

5.489 

8.595 

3.279 

i.482 

5 

2.067 

2.521 

3.479 

5.128 

3.509 

4.301 

6 

1.936 

2.411 

1.651 

2.953 

5.368 

4.989 

10.127 

14.595 

7 

2.867 

2.842 

3.042 

3.603 

6.017 

0.049 

2.899 

5.042 

8 

1.145 

0.878 

2.406 

1.989 

3.429 

1.250 

9 

2.035 

1.242 

2.160 

2.316 

7.429 

8.154 

17.168 

10.222 

0—4 

1.601 

1.950 

2.418 

2.590 

4.211 

6.038 

4.407 

8.100 

5—9 

2.057 

2.215 

2.650 

3.585 

4.799 

4.722 

5.458 

6.171 

10-14 

1.621 

1.819 

1.847 

2.100 

4.533 

4.643 

5.262 

4.905 

15-19 

2.372 

1.877 

1.207 

2.561 

2.367 

2.124 

3.112 

6.316 

20-24 

2.251 

2.093 

3.070 

2.758 

3.292 

4.466 

5.377 

7.292 

25-29 

»    1.695 

1.064 

Total, 

1.831 

2.015 

2.385 

2.822 

4.039 

4.937 

4.783 

5.617 

0-4 

75 

-80 

80-85 

85- 

-90 

All  J 

^.ges. 

14.909 

14.107 

40.000 

28.571 

1.060 

1.135 

5—9 

8.207 

8.523 

23.000 

16.250 

50.000 

50.000 

1.329 

1.423 

10-14 

25.352 

17.391 

1.373 

1.439 

15-19 

6.203 

8.516 

9.091 

24.000 

1.545 

1.876 

20-24 

21.536 

23.482 

31.666 

35.952 

16.667 

16.667 

2.179 

2.270 

25-29 

0.717 

0.431 

Total, 

14.587 

14.428 

20.128 

22.013 

16.282 

21.363 

1.158 

1.234 

34 


MORTALITY  AND    LOSS   EXPERIENCE. 


Such  are  some  of  the  effects  in  the  aggregate.  But  a  more  exact  impression  will 
be  given  by  glancing  down  the  columns  of  these  tables,  and  noting  the  incessant 
fluctuations  of  the  rates.  For  instance,  in  the  periods  50-55,  65-70  the  claims  per  cent, 
of  the  first  year  have  exceeded  those  of  the  second  year  for  Male  Life ;  and  in  Female 
Life,  the  same  feature  prevails  as  often  as  its  opposite,  for  all  ages.  It  should  be  noted 
that  in  each  vertical  column,  the  percentages  refer  to  different  groups  of  persons 
insured.  The  percentages  for  the  same  group  proceed  forward  and  downward  in  a 
diagonal  direction,  for  five-year  periods.  Thus  for  the  same  class  of  females  entering 
at  the  Ages  25-30,  the  successive  Claims  per  cent,  in  five-year  periods  are  given  as 
1.015,  1.081,  0.839,  1.252,  0.986, 

It  may  be  proper  to  observe  that  in  the  national  census,  the  mortality  of  females, 
in  the  great  mass,  is  less  than  that  of  the  male  population.  In  life  insurance  statistics, 
the  same  feature  would  undoubtedly  prevail,  if  a  fair  representation  of  the  female  class 
in  the  community  were  insured.  But  in  practice,  the  class  that  actually  insure  have 
so  many  unhealthy  Uvea,  especially  in  the  period  of  maternity,  that  the  total  claims 
per  cent,  of  females  (1.23)  have  very  considerably  exceeded  the  rate  (1.10)  of  insured 
males.  The  principal  causes  of  this  difference  will  be  developed  hereafter  in  the 
Medical  Statistics.  Table  XIV  (B)  indicates  especially  the  risk  incident  to  the  birth 
6f  the  first  child,  which  is  well  known  to  be  far  greater  than  at  any  subsequent 
delivery,  with  compensations  in  the  future  conditions  of  life.  Compare  also  results  from 
the  Census  of  Scotland  in  the  Journal  of  the  Institute  of  Actuaries,  Vol.  22,  page  233. 

COMPARISON  OF  DEATHS  PER  CENT.  FROM  SEVERAL  TABLES  OF  MORTALITY. 


30  Amekican  Offices. 

20  British  Offices. 

American 
Life,  1858. 

Carlisle 
Table. 

Mai.es. 

Females. 

DlFF. 

Males. 

Fexales. 

DrPF. 

M.  AND  F. 

M.  AND  F. 

15^-20 

0.71 

0.68 

+  .03 

0.47  ' 

0.76 

-.29 

1.31 

0.68 

20-25 

0.69 

1.10 

-.41 

0.69 

0.85 

-.16 

1.07 

0.70 

25-30 

0.67 

1.00 

-.33 

0.69 

1.18 

-.49 

0.78 

0.82 

30-35 

0.71 

1.05 

-.34 

0.82 

1.13 

-.31 

1.04 

1.01 

35-40 

0.80 

1.00 

-.20 

0.95 

1.21 

-.26 

0.98 

1.09 

40-45 

0.94 

1.05 

-.11 

1.07 

1.28 

-.21 

0.83 

1.41 

45-50 

1.10 

1.06 

+  .04 

1.36 

1.39 

-.03 

1.13 

1.44 

50-55 

1.43 

1.34 

+  .09 

1.74 

1.57 

+  .17 

1.55 

1.52 

55-60 

1.94 

1.83 

+  .11 

2.40 

2.02 

+  .38 

1.87 

2.20 

(50-65 

2.76 

2.39 

+  .37 

3.48 

2.86 

+  .62 

4.34 

3.68 

65-70 

3.93 

4.04 

-.11 

5.02 

4.37 

+  .65 

4.15 

4.45 

70-75 

5.63 

4.78 

+  .85 

7.33 

6.84 

+  .49 

5.19 

6.97 

75-80 

8.48 

14.59 

-6.11 

11.00 

10.66 

+  .34 

8.48 

10.54 

80-85 

11.33 

20.13 

-8.80 

16.52 

12.51 

+  4.01 

.... 

13.86 

85-90 

16.67 

16.28 

+  .39 

22.35 

22.82 

-.47 

.... 

19.93 

90-95 

.... 

.... 



32.73 

22.68 

+ 10.05 

28.61 

Deaths, 

44,485 

2,058 

20,521 

3,3a5 

750 

1,840 

Entrants, 

982,734 

44,795 

130,243 

16,604 

19,725 

.... 

This  Table  represents  the  percentages  from  original  observations  simply.  Gradu- 
ation would  require  a  small  correction  described  in  Section  X,  3.  In  the  columns  of 
the  Thirty  Ofiices,  under  the  age  of  forty-five,  the  mortality  of  females  will  be  seen  to 
exceed  that  of  males  by  at  least  one-third  part,  for  a  considerable  extent ;  from  the  age 
of  forty-five  to  sixty-five,  the  order  is  reversed,  and  the  mortality  of  males  exceeds  that 


MORTALITY   AND    LOSS   EXPERIENCE.  35 

of  females  by  a  much  smaller  difference  relatively.  Above  sixty-five,  the  female 
experience  is  small  Id  numbers,  and  fluctuating  in  value.  Yet  in  the  larger  experience 
of  British  females  from  sixty-five*  to  eighty,  the  excess  of  male  mortality  is  still  contin- 
ued, though  reversed  afterward. 

The  last  column  but  one,  is  derived  from  the  published  Eeport  of  the  Experience 
of  the  Mutual  Life  Insurance  Company  of  New  York  to  Feb.  1,  1858,  pages  10,  11. 
From  its  middle  ages,  between  thirty  and  sixty,  Mr.  Sheppard  Homans,  the  Company's 
Actuary,  constructed  the  common  American  Experience  Table  of  1858,  with  some 
modifications. 

Passing  now  to  the  last  colifmn,  we  note  that  all  the  percentages  of  the  Carlisle 
Table  exceed  those  of  male  life  in  the  Thirty  Offices  Experience.  And  the  percentages 
of  the  Twenty  British  Offices,  male  as  well  as  female,  with  one  or  two  exceptions  at 
the  beginning,  show  a  similar  excess  over  that  of  American  insured  males. 


SECTION     IX. 
Continuation  of  the  Experience  of  1874  to  Final  Series. 

The  record  of  a  Life  Office  noted  upon  the  card  returns  will  now  he  regarded  as 
an  inventory  of  the  state  of  its  business  up  to  that  particular  time ;  from  which  the 
average  for  a  longer  series  of  years  remains  to  be  determined. 

The  applications  of  the  Life  Table  to  the  current  business  of  Insurance,  whether 
to  the  surrender  or  change  of  policies,  or  to  reserves,  all  presuppose  that  such  Life- 
Table  is  based  on  terminated  experience.  In  the  analogous  problem  of  the  theory  of 
probabilities,  where  the  game  is  stopped  prematurely,  it  is  proved  that  the  stakes 
should  be  divided  among  the  players,  in  proportion  to  their  probabilities  of  winning. 
Although  the  game  stops,  the  determination  of  the  several  portions  evidently  depends 
on  a  knowledge  of  the  chances,  or  law  of  the  game  when  played  through. 

In  the  present  case,  the  returns  of  1874  comprise  549,418  Existing  policies,  of 
which  the  record  closes  before  their  future  experience  is  determined.  The  column  of 
Existing  in  Tables  I  and  II  now  represents  only  first  experiences,  cut  into  dissimilar 
portions  by  the  end  of  the  1st,  the  2d,  and  other  years  after  the  medical  examination, 
according  to  the  year  chosen  for  making  out  the  cards  or  returns.  Had  the  canvass  of 
the  office  registers  been  deferred  fifteen  or  twenty  years,  the  most  of  the  policies  or 
lives  would  evidently  have  passed  to  their  termination,  and  would  have  been  returned 
as  Discontinued  or  Died.  And  this  mature  experience,  including  the  present  returns, 
would  have  furnished  the  genuine  elements  for  constructing  the  Life  Table. 

But  not  to  wait  for  such  supplementary  experience  by  natural  termination,  we 
have  found  that  it  can  be  approximately  supplied  by  carrying  forward  tlie  Existing  to 
their  proportional  terminations  in  the  cohimns  of  Discontinued  and  Died ;  and  the 
same  for  Amounts  Insured  and  Claims.  The  present  experience  down  to  1874  will 
give  the  requisite  multipliers,  and  the  products  so  found,  may  be  conveniently  termed 
Final  Series. 

Let  us  here  investigate  the  weights  or  multipliers  for  this  purpose.  On  page  25  is 
a  formula  assigning  the  probability  p"  of  surviving  one  year's  exposure  to  both  death 
and  discontinuance.  Hence  from  an.y  age  of  Entry  in  Tables  I  and  II  we  can 
determine  the  surviving  entrants,  N,  N;j,",  Njo,";?/',  ....  of  Final  Series  denoted  by 
N,  e'l,  e'a,  ....  as  they  would  be,  if  the  present  Existing,  all  proceeded  to  their  termina- 
tions in  Discontinuance  or  Death.    And  the  annual  differences,  N— e,',  e/— e^',  etc.  are 


36 


MORTALITY  AND    LOSS  EXPERIENCE. 


evidently  multipliers  of  the  corresponding  sums  of  discontinued  and  died  on  the  same 
line  of  Table  I.  Hence  their  respective  ratios  will  give  the  required  weights  or  multi- 
pliers (w)  of  Tables  III  and  IV. 

Thus  in  the  accompanying  illustration,  the  first  columns  of  Existing,  Discon- 
tinued and  Claims  are  simply  the  sums  of  the  corresponding  Amounts  from  Table  I  in 
Thousands  of  Dollars  under  Ages  of  Entry  36  and  37,  (mean  age  ^^).  The  product 
of  these  (except  Existing),  by  the  Multiplier  opposite  in  the  last  column,  gives  the 
Discontinued  Amounts  and  Claims,  (which  now  include  the  Existing  carried  forward), 
under  Final  Series. 

AMOUNTS  FROM  TABLE  I.  AGES  AT  ENTRY. 36  AND  37  TEARS. 


Years 

OF 

Insur- 

Experience 

ENDING 

1874. 

Final  Series. 

Existing 

Discon- 

Entrants 

Entrants 

DlSCON- 

Death 

Exposed  to 

Multiplier 

ance. 

(R). 

tinued. 

Claims. 

(^). 

{e). 

TINTJED. 

Claims. 

Risk. 

{w). 

0 

11,763 

7,443 

457 

196,462 

196,462 

7,443 

457 

94,509.5 

1.0000 

1 

10,058 

37,361 

1,743 

176,799 

188,563 

39,181 

1,859 

173,971.5 

1.0665 

2 

8,433 

15,564 

1,350 

137,637 

157,523 

17,813 

1,431 

148,615.5 

1.1445 

3 

7,693  • 

10,655 

959 

113,390 

138,378 

13,109 

1,180 

131,733.5 

1.3304 

4 

8,705 

7,753 

916 

93,084 

123,989 

10,337 

1,330 

118,835.5 

1.3330 

5 

9,533 

5,665 

923 

75,710 

113,442 

8,414 

1,369 

108,335 

1.4852 

6 

9,639 

3,433 

665 

59,590 

103,659 

5,914 

1,146 

99,703 

1.7228 

7 

8,991 

3,617 

470 

45,863 

95,599 

5,455 

980 

92,871.5 

2.0845 

8 

7,915 

1,508 

366 

-33,785 

89,164 

3,980 

966 

87,174 

2.6393 

9 

5.659 

707 

217 

23,996 

84,318 

3,481 

762 

82,977.5 

3.5098 

10 

3,659 

496 

179 

17,413 

80,975 

3,307 

833 

79,831.5 

4.6505 

11 

3,437 

330 

334 

13,079 

77.836 

1,964 

1,333 

76,854 

5.9515 

12 

1,107 

191 

149 

10,098 

74,539 

1,410 

1,100 

73,834 

7.3819 

13 

853 

167 

113 

8,651 

72,029 

1,391 

941 

71,333.5 

8.3364 

14 

937 

143 

134 

7,519 

69,697 

1,316 

1,149 

69,039 

9.3700 

15 

730 

78 

78 

6,316 

67,232 

830 

830 

66,817 

10.645 

16 

596 

57 

98 

5,430 

65.572 

688 

1,184 

65,328 

13.076 

17 

339 

44 

77 

4,679 

63,700 

599 

1,050 

63,400 

13.615 

18 

341 

37 

59 

4,219 

62,051 

544 

868 

61,779 

14.709 

19 

390 

40 

55 

3,782 

60,639 

641 

881 

60,318.5 

16.035 

20 

373 

45 

49 

3,397 

59,117 

807 

879 

58,713.5 

17.931 

21 

196 

16 

53 

3,930 

57,431 

313. 

1,037 

57,374.5 

19.603 

22 

198 

31 

74 

3,665 

56,081 

653 

1,557 

55,755 

31.044 

23 

364 

17 

56 

3,363 

53,873 

388 

1,378 

53,678 

33.808 

24 

347 

6 

69 

2,025 

53,306 

155 

1,783 

53,138.5 

35.781 

25 

477 

3 

48 

1,603 

50,368 

94 

1,504 

50,331 

31.363 

26 

377 

30 

30 

1,075 

48,670 

903 

1,354 

48,318.5 

45.377 

27 

345 

3 

33 

648 

46,413 

315 

3,361 

46,305.5 

71.618 

28 

160 

11 

267 

.... 

29 

35 

1 

96 





30 

56 

1 

60 



32 

1 

38 





2 

103,484 

84,439 

9,549 

The  first  column  of  Entrants  (e)  is  readily  computed  by  the  formula  of  page  25, 
preparatory  to  obtaining  the  values  of  p"  by  the  formula  there  given. 


'P 


w  = 


V 


„  _  R  +  fii 


r  =  wr. 


D'  =  wD. 


Here  e^  denotes  the  entrants  on  the  line  or  space  next  below  that  of  the  existing  R  and 
entrants  e.     Multiplying  N  or  196,462  in  this  example  by  the  first  value  of  p"  gives 


MORTALITY  AND    LOSS   EXPERIENCED 


188,562,  that  is,  the  second  value  of  e' ;  and  this  by  the  next  value  of  p"  gives  the  next 
value  of  e' ;  and  so  on.  The  entrants  e'  are  here  computed  through  27  years,  omitting 
the  rest  on  account  of  the  smallness  and  irregularity  of  the  last  data.  Now  the  first 
diflference  of  column  e'  or  7,900  divided  by  the  sum  of  the  first  Discontinued  and 
Claims  7,443  +  457  gives  1,  the  first  multiplier  in  column  {w).  The  second  difference 
of  e'  or  31,040  divided  by  27,361  +  1,743  gives  1.0665  the  second  multiplier  in  column 
{w),  and  so  on. 

Another  Solution.  Since  Entrants  (e)  always  commence  where  Existing  (E)  end, 
at  the  beginning  of  any  one  year,  we  have  first  the  proportion  ;  Entrants  :  Discon- 
tinued in  the  following  twelve  month  : :  Existing  :  proportional  Discontinued.  The 
sum  of  the  second  and  fourth  terms  gives  the  Discontinued  of  Final  Series,  on  the 
same  line  of  the  Table.  And  the  Deaths  of  Final  Series  are  found  in  like  manner. 
Adding  the  third  term  to  the  Existing  at  the  beginning  of  the  next  year,  and  then 
subtracting  the  two-fourth  terms  of  Discontinued  and  Deaths  just  found,  will  give  the 
entire  surviving  Existing  from  previous  years,  which  will  be  the  tliird  term  of  the 
proportions  for  the  next  year,  and  so  on. 

Exposed  to  Risk.  After  applying  either  solution,  the  Discontinued  and  Deaths 
so  found,  will  give  the  Exposed  to  Risk,  in  Final  Series  through  the  usual  formula  on 
page  25,  by  making  the  Existing  (E)  to  be  zero.  Or  in  a  different  way,  the  Exposed 
to  Eisk  may  be  found  by  multiplying  the  Exposed  to  Eisk  in  the  first  series  of  1874, 
by  the  same  multiplier  (w)  that  is  used  to  change  the  Discontinued  and  Died  on  the 
same  line  to  Final  Series,  from  Tables  I  or  II.  This  implies  that  the  percentages  of 
Death  and  Discontimiance,  but  not  their  absolute  numbers,  are  virtually  alike  on  the 
same  line  of  the  series  of  1S74,  and  of  Final  Series.  This  agreement  is  shown  in  the 
following  examples,  computed  with  five-place  logarithms,  from  Amounts  Insured. 

ELEMENTARY    CLAIMS    PER    CENT. 


Years 

Ages  ob 

Entry 

Ages  of 

Entry 

Years 

Ages  of  Entry 

Ages  op  Entry 

OF 

Insub- 

36  AND  37. 

56  AND  57. 

OF 

Insur- 

36 AND  37. 

56  AND  57. 

ANCE. 

(1874). 

Final 
Series. 

(1874). 

FiNAI, 

Series, 

ance. 

(1874). 

Final 
Series. 

(1874). 

Final 
Series. 

0 

0.484 

0.484 

1.352 

1.352 

13 

1.319 

1.319 

7.816 

7.817 

1 

1.069 

1.069 

1.852 

1.850 

14 

1.665 

1.664 

4.847 

4.850 

2 

0.963 

0.963 

2.206 

2.206 

15 

1.243 

1.243 

3.170 

3.175 

3 

0.896 

0.896 

2.436 

2.436 

16 

1.814 

1.815 

4.248 

4.249 

4 

1.037 

1.027 

3.125 

3.123 

17 

1.653 

1.656 

11.007 

11.012 

5 

1.265 

1.265 

2.761 

2.760 

18 

1.405 

1.405 

0.899 

0.899 

6 

1.149 

1.149 

4.243 

4.240 

19 

1.462 

1.461 

9.848 

9.852 

7 

1.055 

1.055 

3.716 

3.718 

20 

1.496 

1.497 

10.687 

10.674 

8 

1.108 

1.108 

3.200 

3.198 

21 

1.814 

1.811 

5.066 

5.072 

9 

0.918 

0.918 

3.237 

3.235 

22 

3.793 

2.793 

19.954 

19.914 

10 

1.043 

1.042 

4.200 

4.301 

23 

3.380 

2.381 

7.233 

7.339 

11 

1.735 

1.734 

5.478 

5.488 

24 

3.413 

3.420 

4.396 

4.412 

12 

1.490 

1.490 

5.071 

5.071 

25 

3.997 

2.995 

13.123 

13.115 

Weights.  The  foregoing  system  of  multipliers  (w)  will  be  seen  to  coincide  with 
the  method  of  weights,  used  in  the  process  of  average.  It  is  evident  that  the  weights 
(w)  have  the  same  relation  to  a  life  table  designed  for  questions  of  population,  without 
interest, — that  discounted  weights  {w.  v"),  where  n  denotes  the  "  Years  of  Insurance," 
have  to  a  life  table  designed  to  give  the  well  known  Commutation  Columns,  for 
different  rates  of  interest. 


38 


MORTALITY  AND    LOSS  EXPERIENCE. 


Accordingly,  discounted  weights  (w.  v"),  assuming  v  to  be  1-^1.04,  have  been 
preferred  in  Tables  III  and  IV,  for  determining  the  Claims  of  Final  Series.  In 
con§equence  of  large  irregularities  in  the  statistics  of  Female  Life,  only  the  mean 
weights,  (w)  and  {to.  v")  were  tabulated  by  their  logarithms  in  Table  IV  (0),  Deferring 
further  explanations,  and  the  construction  of  life  tables  to  Part  II,  we  subjoin  an 
example  of  the  preparatory  operation  for  a  single  Age  of  Exposure  of  Male  Life;  the 
weights  of  Table  III  being  changed  from  (w)  to  {tv.  v"). 

AGGREGATE  CLAIMS  PER  CENT.  EXAMPLE.  AGE  OF  EXPOSURE  24^  TO  25^. 


Tears  op 
Insurance. 

Age  of 
Entry. 

LOG'M 

Weight. 

(1874). 

Final  Series. 

CT.ArMS. 

Exposed. 

Ct.atms. 

Exposed. 

0 
1 
2 
3 

4 

5 
6 
7 
8 
9 

10 
11 
12 
13 

25 
24 
23 
22 
21 

20 
19 
18 
17 
16 

15 
14 
13 
12 

0.0000 
0.0142 
0.0318 
0.0510 
0.0908 

0.1348 
0.1938 
0.3009 
0.4288 
0.5670 

0.6271 
0.6781 
0.6875 
0.6559 

168.0 
305.0 
257.0 
111.0 
68.0 

52.0 

18.0 

14.0 

6.0 

1.0 

1.0 
1.0 

36,205.0 
50,185.0 
30,560.5 
17,851.0 
9,781.0 

4,374.5 

2,079.5 

951.0 

448.0 

227.5 

93.0 

67.0 

8.0 

11.5 

168.0 
315.2 
276.5 
124.8 

83.8 

70.9 
28.1 
28.0 
16.1 
3.7 

4.2 
4.8 

36,205.0 
51,856.0 
32,885.0 
20,077.0 
12,056.0 

5,966.2 
3,249.4 
1,901.5 
1,202.5 
839.7 

394.1 

319.3 

38.9 

52.1 

Sum 

1,002.0 

152,842.5 

1,124.1 

167,042.7 

Claims  p 

er  cent 0. 

656 

0.673 

1 

SECTION    X. 

Notes  on  Grraduation.  Short  Method  for  the  Expectation  of 
Life.  G-radnation  by  Formula  and  by  Divided  Differ- 
ences. Loss  relative  to  Term  and  other  species  of 
Insurances. 

In  further  preparation  for  the  construction  of  life  tables  in  Part  II,  and  other 
applications,  the  following  notes  of  investigation  are  here  placed  on  record.  To  correct 
for  minor  irregularities  in  the  data,  the  observations  may  be  grouped  in  five  or  ten-year 
periods.  And  from  these  five  or  ten-year  sums,  the  annual  values  are  again  derived  in 
a  more  regular  and  continuous  series,  by  the  process  of  graduation.  This  may  be 
done  in  several  ways. 

1.  Tlie  Graphic  Method.  On  a  base  line  representing  years,  or  one  of  the  two 
dimensions,  set  off  distances  corresponding  to  the  given  periods  of  age.  Ea<;h  of  these 
distances  is  made  the  base  of  a  rectangle,  whose  altitnde  is  the  average  obtained  by 
dividing  the  respective  group  of  observations  by  its  number  of  years.  Having  plotted 
this  series  of  rectangles,  whose  upper  contour  forms  a  broken  line,  draw  with  a  free 


MORTALITY  AND    LOSS   EXPERIENCE. 


39 


hand,  a  mean  curve  to  supersede  the  broken  line.  This  curved  line  must  be  drawn  as 
little  curved  as  the  conditions  admit  of,  and  never  change  its  direction  abruptly.  It 
will  generally  cut  off  a  triangular  space  from  one  corner  of  each  rectangle,  and  by 
compensation  take  from  without,  an  equal  space  above  the  next  corner  of  the  rectangle. 
A  preliminary  curve  is  often  drawn  in  pencil,  and  then  successively  adjusted  by 
measuring,  till  the  spaces  exterior  and  interior  to  each  rectangle  are  made  equal. 
Finally,  the  ordinates  of  the  curve  measured  year  by  year,  give  the  graduated  series 
required. 

The  living  and  the  deaths  for  the  Carlisle  Table  were  graduated  separately  by  this 
method,  as  described  in  Milne  on  Annuities  and  Insurances,  Vol.  I,  page  100,  (London, 
1815).  In  respect  to  the  vital  statistics  of  the  city  of  Carlisle  and  other  places,  he 
observes,  it  is  very  desirable  that  the  exact  numbers  be  given  monthly  for  the  first 
three  months  after  birth;  quarterly  for  the  remaining  three  quarters  of  the  first  year 
of  age  ;  and  after  that,  separately  for  the  2d,  3d,  4th  and  5th  years  of  age.  And  then 
intervals  of  five  years  to  the  extremity  of  life  may  do  very  well.  And  if  the  number 
of  inhabitants  be  very  considerable,  intervals  of  ten  years  may  be  employed  after  the 
age  of  twenty  or  thirty. 

2.  Short  Method.  When  life  tables  have  once  been  formed  by  the  graphic  or 
other  correct  method,  they  may  furnish  corrections  to  shorten  future  applications. 
From  the  three  life  tables  constructed  by  Milne,  Vol.  II,  pages  404,  405,  564,  534,  5G6, 
we  have  derived  for  future  reference,  the  followii;g  method  for  passing  directly  from 
the  original  data,  to  an  outline  of  the  Expectations  of  Life.  And  the  same  process 
might  easily  be  adapted  to  Life  Annuities.  At  the  age  of  80  years,  the  Expectation  of 
Life  is  generally  5  years,  more  or  less ;  and  the  deviations  of  the  Expectations,  and 
the  Logarithms  of  the  probabilities  of  life,  from  their  mean  values,  appear  very  nearly 
proportional  to  each  other,  in  different  Tables.  On  this  clue,  are  founded  the  equations 
below,  which  give  a  close  approximation  to  the  Relative  and  to  the  True  Expectation 
at  the  age  of  80.  From  the  Relative  Expectation  at  80,  we  derive  the  Relative  values 
at  70,  60,  50  ....  5  years,  to  which  a  small  correction  is  to  be  added  to  give  the  true 
Expectations.- 

EXAMPLE  FROM  THE  ORIGINAL  DATA  OF  THE  CARLISLE  TABLE. 


Pebiod 

n. 

Living 

L. 

Deaths 

D. 

-L-JD 

Age. 

Expectation. 

DiFPEBENCK. 

Cob. 

Calc'd. 

True. 

Cabl. 

S.  M. 

S.  F. 

0-    5 

9,868.5 

812 

1.816225 

0 

38.72 

5-  10 

8,703 

89 

1.977795 

5 

51.26 

51.25 

-.01 

-.02 

+  .02 

-.04 

10-  15 

6,853.5 

84 

1.989230 

10 

48.85 

48.82 

-.03 

+  .01 

+  .01 

-.01 

15-  20 

6,47l 

44 

1.985235 

15 

45.02 

45.00 

-.02 

CO 

+  .02 

0 

20-  30 

12,730.5 

96 

1.96725 

20 

41.49 

41.46 

-.03 

00 

+  .0;^ 

0  : 

30-  40 

8,406 

89 

1.95402 

30 

34.35 

34.34 

-.01 

-.01 

+  .01 

0 

40-  50 

8,223 

118 

1.93770 

40 

27.63 

27.61 

-.02 

00 

+  .03 

0 

50-  60 

5,638.5 

103 

1.92067 

50 

21.13 

21.11 

-.02 

-.01 

+  .02 

ikO 

60-  70 

4,194 

173 

1.82083 

60 

14.37 

14.34 

-.03 

+  .01 

+  .03 

^c 

70-  80 

1,831.3 

152 

1.63936 

70 

9.22 

9.18 

-.04 

+  .05 

00 

iVC 

80-  90 

558 

98 

1.23529 

80 

5.46 

5.51 

+  .05 

+  .01 

-.05 

c 

90-100 

94.5 

28 

2.70366 

90 

3.28 

.... 

100-105 

18 

4 

100 

.... 

2.28 

.... 

73,593 

1,840 

Xp\ 

40  MORTALITY  AND    LOSS  EXPERIENCE. 

The  third  column  shows  the  Deaths  in  the  city  of  Carlisle  during  nine  years ;  and 
the  second,  the  corresponding  Population  exposed  to  risk,  as  adjusted  from  two  cen- 
suses. The  third  column  is  derived  from  these  by  the  formula  at  the  head  of  the 
column,  where  L  and  D  correspond  to  the  period  n,  that  is,  5  or  10  years,  on  the  same 
Hne.  It  expresses  the  common  logarithm  of  an  approximate  probability  of  surviving 
the  period,  as  noted  at  the  foot  of  the  column. 

Let  s  denote  the  sum  of  the  Logarithms  of  the  three  given  probabilities  from  the 
age  of  50  to  80.     In  the  present  example  s  is  L38086  or  —0.61914. 

Also  let  e'„  e^,  denote  the  Eelative  and  the  True  Expectation  at  the  age  80,  as 
defined  by  the  following  equations  : 

e'so  =  10.844  +  10.3155,        e^  —  7.833  4-3.833s. 

The  multipliers  of  C  to  give  the  correction.  Cor.  are  shown  in  the  lower  part  of  the 
last  column  of  the  accompanying  Table.  From  e'  at  80,  the  decennial  values  of  e  are 
derived  one  from  another  successively  down  to  the  age  of  20,  by  the  relative  formula, 

e'_,o  =  5+^'V^  +  5). 

e^  =  e',  +  Cor.  C  ^  ^go — ^'so- 

Under  20  years  of  age,  the  formula  for  five-year  intervals  will  be 

eU  =  2.5+/(e'.  +  2.5). 

The  probability  y  or  p^  is  obtained  at  once  f fom  the  fourth  column  of  the  Table, 
corresponding  to  the  given  interval  of  age.  The  first  equations  applied  to  the  Carlisle 
data  give  e^  =  4.46  and  ego  =  5.46  ;  whence  their  difference  C  =  1.00.  And  the  cor- 
rections to  be  added  to  e'  are  known  from  the  last  column  of  the  Table.  From  the  age 
of  80  down  to  5,  the  Expectations  calculated  by  this  simple  process,  differ  but  slightly 
from  the  standard  results  of  the  graphic  method,  as  shown  in  the  last  column  but  three. 
And  the  next  two  columns  headed  S.  M.  and  S.  F.  derived  from  the  data  and  Tables 
of  Swedish  Males  and  Swedish  Females  found  in  Milne's  treatise,  show  even  smaller 
residuals. 

3.  Correction.  A  plausible  but  erroneous  assumption  is  occasionally  made,  that 
when  the  sum  of  the  Deaths  from  60  to  65  years  of  age,  for  example,  is  divided  by  the 
sum  of  the  Exposed  to  Risk  at  the  same  ages,  the  resulting  ratio  of  mortality  will  be 
that  of  the  middle  age,  62-63.  In  respect  to  the  values  of  /,  so  found  in  the  life  table, 
a  correction  will  be  required,  which  is  additive  up  to  about  the  age  of  72,  and  sub- 
tractive  after  that  age.  Mr.  Woolhouse  finds  the  required  correction  to  be  the  central 
second  difference  plus  one-fifth  of  the  fourth  difference  (of  the  five  values  of  I  in  the 
period),  to  be  applied  with  the  sign  just  described.  In  the  same  communication  will 
be  found  Wool  house's  Method  of  Final  Adjustment,  after  a  previous  graduation. 
{Journal,  Vol.  XXI,  p.  58,  and  Vol.  XIII,  p.  98.) 

4-  Graduation  hy  Formula.  Among  various  formulas  presented  for  choice,  let  us 
here  employ  a  modified  geometric  progression,  with  three  constants  to  be  determined 
from  the  data.  For  example,  the  observations  of  three  five-year  periods  of  age  A,  B,  C 
are  given,  to  be  resolved  into  the  series  for  single  years.  Let  u^  denote  the  number  for 
the  age  x ;  then  for  annual  and  for  five-year  periods  : 

w,  =  a  +  5(f,        Wo  =  a4-J>        Mi  =  a  +  5cS        u^:=a-\-hc^, . . ., 

K  —  ha  +  hs,        B  =  5a  +  Jsc*,        C  =  5«  +  *sc"*; 


MORTALITY  AND    LOSS   EXPERIENCE.  41 

s  =  l  +  c+c'  +  c'+c*  =  ^— ^,        c'  =  g3^, 
^.-R     ^-^  (B-A)(g-1). 

Wg  =  «  +  5c^        Mj  =  a  +  Jc',        Wg  •=  «  +  ^c^- 

Thus  from  A,  B,  C  may  be  found  u^,  w„  iig,  the  three  middle  terms  of  B.  From 
B,  0,  D  may  be  similarly  found  the  three  middle  terms  of  C,  and  so  on.  Then  u^,  Wio 
the  two  omitted  terms  between  these  triplets  can  be  supplied  by  divided  differences,  as 
presently  described.  And  the  six  other  initial  or  final  terms  of  the  whole  series,  can  be 
regularly  computed  by  the  local  process  above.  In  case  the  sum  of  any  five  computed 
terms  differ  from  the  original  given  sum,  one-fifth  of  the  excess  can  be  apportioned  to 
each  term.  Also  instead  of  five-year  periods,  the  same  solution  applied  to  ten-year 
periods  will  give  five  sums  of  two  terms  each,  which  can  afterwards  be  separated  into 
single  terms,  by  applying  series.  And  instead  of  interpolating  Deaths  D,  and  Living  L, 
separately,  it  may  be  preferable  to  take  the  combinations  L — ^D,  and  L  +  ^D,  for 
greater  regularity. 

Conversely,  it  will  sometimes  be  required  to  find  x  corresponding  to  a  value  of  u 
or  w,,  intermediate  to  Uq,  Ui,  u^,  noted  above.  In  this  case,  logarithms  can  be  applied 
to  either  of  the  results  of  elimination  below,  involving  x.  After  solution,  if  the 
suffixes  of  u,  instead  of  0, 1,  2,  are  changed  to  n,  n-\-h,  n-\-2h,  for  instance,  then  x 
should  be  changed  to  n+xh. 

>        ,  =  ^^^11^',        c'  =  l  +  '^^^^{c-l). 

Ui—Uq  U\  —  Uq 

w.-Wo~^     1.2     y^-^)+       7x7273         (<^-l)+-... 

5.  Interpolation  hy  Divided  Differences.  It  has  just  been  shown  in  3.  how  far 
the  divided  sum  or  average  of  five  terms  differs  from  the  middle  term.  But  to  sub- 
stitute the  divided  difference  of  the  extremes  at  the  middle  point,  for  the  middle 
difference,  is  much  more  accurate,  since  it  differs  from  the  truth  by  only  half  the 
central  third  difference.  Although  often  insensible,  yet  provision  will  be  made  for 
correcting  even  this  slight  residual,  whenever  it  appears.  Embarrassment  is  sometimes 
experienced  in  bringing  together  portions  of  the  life  table  interpolated  separately,  so 
that  the  differences  at  the  junctions  shall  be  free  from  break  or  abrupt  changes.  The 
new  artifice  here  suggested,  is  that  of  substituting  divided  differences  at  the  middle 
points. 

For  one  of  the  simpler  applications,  let  us  first  suppose  that  two  terms  d,  e, 
interpolated  by  different  formulas  are  to  be  reconstructed  so  as  to  present  a  regular 
continuity.     Let  the  series  be 

..\hc{d,e)fgh..  Zy  =  (/_.)_  (/=^ +5^  +  ^^]. 

d-=c^yV—^,        e=d+y+^—^,       /=e+y+_^. 

Thus,  at  first  canceling  the  terms  d,  e,  which  include  the  junction,  we  find  a  slight 
correction  y,  such  that  the  three  divided  differences  each  corrected  by  y,  shall  make  up 
the  proper  quantity  / — c.  Then  d,  e  are  computed ;  also  /,  to  prove  the  operation, 
by  coinciding  with  the  previous  value  of/,  as  above  indicated. 


42 


MORTALITY  AND    LOSS  EXPERIENCE. 


For  the  reconstruction  of  four  terms  /,  g,  h,  i  by  five  differences,  let  the  adjacent 

terms  he 

ab  c  d  e  {f  g,  h  i)  j  Tclm  n 


5y=U-e)— 


j—a     h—h     l—c    m—-d    n—e 


j—a  jy .      ,  1c — h         ,  ,        l—c    , 

f=e+y+'^,       g=f+y  +  -Q-,        h=g+y  +  -;^,eU;. 

The  same  principle  might  evidently  be  extended  to  the  omission  and  re-computation 
of  second  or  third  differences;  so  that  it  offers  facilities  of  unusual  precision  and 
importance. 

6.  Loss  Experience  on  different  Species  of  Policies.  An  inspection  of  the  ratios 
below,  may  give  the  most  correct  impression.  The  experience  of  Term  Policies  is  fluc- 
tuating, and  appears  generally  dependent  on  particular  circumstances  in  connection 
with  other  classes  of  Insurance.  Besides  ten  Companies  classified  in  regard  to  Species, 
the  statistics  of  six  Companies  in  the  general  collection,  were  classified  in  respect  to  the 
Amount  of  Policy.  A  difference  of  opinion  exists  in  respect  to  the  value  of  such  minor 
classifications,  which  might  be  indefinitely  extended  to  Paid-up  Life,  Ten  Payment 
Life,  Paid-up  Endowment  Policies,  and  others. 


LOSS  ON  DIFFERENT   SPECIES  OF  POLICIES. 


Number  op 
Companies. 

LrPK  Policies. 

Endowment  Insubancbs. 

Term  Policies. 

Pbobable  L. 

Actual  L. 

2 

Probable  L. 

Actual  L. 

6 

Probable  L. 

Actual  L. 

d 

3 
2 
2 
3 

3,661,757 
7,076,232 
3,611,112 
2,997,823 

$ 

3,799,225 

7,068,483 

3,766,759 

.  3,614,288 

100: 
104 
99 
104 
120 

645,702 

1,119,234 

302,716 

399,790 

$  ' 

533,013 

859,350 
264,537 
391,172 

100: 
83 

77 
87 
98 

169,204 

408,101 

55,419 

77,285 

$ 

165.500 

448,530 
84,067 
42,900 

lOO: 

98 

no 

152 
56 

105 

10 

17,346,924 

18,248,761 

105 

2,467,442 

2,048,072 

83 

710,009 

740,997 

LOSS  RELATIVE   TO  THE  AMOUNT  OF  POLICY. 


Spbcibs  or 

POLICIBS. 

Under  $4,000. 

$4,000  to  $10,000. 

Over  ^10,000. 

Probable  L. 

Actual  L. 

g 

Probable  L. 

Actual  L. 

© 

1 

100: 

106 

73 

90 

106 

Probable  L. 

Actual  L. 

6 

■< 
OS 

life  Policies  .  .  . 
Endowment  Ins. 
Term  Policies. . 
7  Companies . . 

$ 

1,994.890 

258,228 

88.717 

3,827,440 

$ 

1,915,905 

222,699 

101,967 

3,672,003 

100: 
96 
86 

115 
96 

$ 

2,718,160 

261,060 

82,126 

4,393,274 

$ 

2,874,100 

190,000 

74,000 

4,679,100 

$ 

33,440 

1,575 

4,750 

119,157 

$ 

35,000 

20,000 
85,000 

100: 
105 

71 

CLIMATIC   TABLES.  43 


DIVISION     SECOND. 

CLIMATIC    TABLES. 

Of  thirty  life  insurance  Companies  included  in  the  general  collection,  twenty- 
seven  have  returned  the  locality  of  the  insured,  by  States  or  Counties.  The  results  are 
given  in  Tables  V,  VI  and  VII. 

In  Table  VI,  the  Order  and  Variability  of  Ratios  is  shown  in  detail,  according  to 
twelve  Companies  whose  mean  ratios  are  less  than  94,  six  Companies  whose  mean 
ratios  were  between  94  and  100,  and  nine  Companies  whose  mean  ratios  were  greater 
than  100.  The  last  six  columns  exhibit  the  Probable  and  the  Actual  Loss  in  Thousands 
of  Dollars ;  that  is,  870  there  signifies  $870,000,  and  so  on.  For  any  State  or  group 
of  adjacent  States,  the  variability  may  be  estimated  by  comparing  the  mean  with  the 
associated  values  horizontally. 

SECTION    I. 
Computations  of  Probable  Loss. 

For  future  applications,  as  well  as  to  illustrate  the  method  of  computing  the 
columns  of  Probable  Loss,  we  here  insert  the  two  accompanying  Tables  of  multipliers 
(A),  (B),  to  three  decimals,  based  on  the  Thirty  Offices  Experience.  A  policy  of  155,000 
entered  at  the  Age  of  37,  for  example,  has  the  Duration  or  Years  of  Insurance  10\, 
and  is  in  force  or  Existing  at  the  epoch  of  Office  investigation.  The  tabular  prob- 
ability of  dying  in  this  interval  is  .101,  which  multiphed  by  5,000  gives  $505,  the  total 
Probable  Loss  since  the  day  of  Entry.  Had  the  same  policy  been  Discontinued  or 
Died,  the  other  Table  (B)  would  have  given  the  multiplier  .095,  and  the  product  of 
.095  by  5,000  or  $475  would  be  the  Probable  Loss  for  ten  years.  The  result  differs 
from  the  former  for  Existing,  by  half  a  year's  exposure,  according  to  the  general  system 
of  reduction  described  in  Division  I,  page  24.  Accordingly,  the  values  (A)  are  simply 
the  means  of  the  adjacent  values  (B).     Thus  the  first  Table  gives  Multipliers  for  tlie 

sum  of  Probable  Losses  for  |,  1|,  2^,  Z\, years  Existing,  and  the  second  Table  for 

0,  1,  2,  3,  ... .  years  till  Death  or  Discontinuance. 

A  modification  to  give  the  annual  values  separately,  has  been  practiced  by  several 
Life  Offices,  that  compute  the  Probable  Loss  at  the  end  of  every  business  year.  For 
this  object,  Table  XXVI  will  give  the  annual  multiplier  q  for  every  age  attained, 
denoted  by  x-\-n.  A  policy  of  $6,000  exposed  for  the  half  or  third  of  a  year,  is 
accounted  as  $3,000  or  $2,000  respectively  exposed  for  the  whole  year;  and  so  for  other 
fractional  parts.  A  joint-life  policy  terminates  at  the  first  death.  To  shorten  the 
labor,  sometimes,  the  tabular  multipliers  represent  only  the  two  nearest  decimals  ;  and 
a  compensation  of  positive  and  negative  errors  is  assumed  in  the  final  sum. 


44 


CLIMATIC   TABLES, 


(A). 


THIRTY    OFFICES    EXPERIENCE. 

Multiplier  for  Existing  to  give  the  whole  Probable  Loss, 


Dura- 

Age of  Entry 

z. 

DUBA- 

tion 

TIOK 

10-14 

15-19 

30-34 

25-29 

30-34 

35-39 

40^4 

45^9 

50-54 

55-59 

60-64 

65- 

89   "■''^• 

0^ 

.003 

.003 

.003 

.003 

.004 

.004 

.005 

.006 

.008 

.011 

.016 

.023        OJ 

IJ 

.010 

.010 

.011 

.011 

.012 

.013 

.015 

.019 

.024 

.033 

.047 

.069        1^ 

2| 

.017 

.017 

.017 

.018 

.020 

.033 

.036 

.032 

.041 

.*056 

.079 

.116        2i 

3^ 

.033 

.034 

.025 

.026 

.037 

.031 

.037 

.045 

.059 

.080 

.114 

.16 

5    3i 

^ 

.029 

.030 

.033 

.033 

.035 

.040 

.047 

.059 

.077 

.105 

.149 

.21 

6    4i 

5* 

.036 

.037 

.038 

.040 

.044 

.050 

.059 

.074 

.096 

.132 

.186 

.2C 

7  -   5i 

6i 

.043 

.044 

.045 

.048 

.052 

.059 

.070 

.089 

.117 

.160 

.325 

.31 

9       6i 

7i 

.049 

.050 

.053 

.055 

.061 

.069 

.083 

.104 

.138 

.189 

.264 

.3'; 

2        7i 

8i 

.055 

.057 

.059 

.063 

.069 

.079 

.096 

.121 

.159 

.219 

.305 

.4S 

-5       8i 

91 

.063 

.064 

.066 

.071' 

.079 

.090 

.109 

.138 

.183 

.350 

.347 

.4'3 

7       9^ 

10^ 

.068 

.070 

.074 

.079 

.088 

.101 

.122 

.156 

.207 

.283 

.389 

.52 

9      10^ 

IH 

.074 

.077 

.081 

.087 

.097 

.113 

.137 

.175 

.232 

.317 

.433 

.56 

so     11 J 

12i 

.081 

.084 

.088 

.095 

.106 

.124 

.152 

.194 

.259 

.352 

.477 

.6? 

0     12^ 

13i 

.087 

.091 

.096 

.103 

.116 

.136 

.167 

.215 

.286 

.388 

.521 

.e-; 

7     13i 

i4 

.094 

.098 

.103 

.112 

.126 

.149 

.184 

.237 

.315 

.425 

.565 

.72 

2  m 

15^ 

.100 

.104  • 

.110 

.121 

.137 

.162 

.201 

.259 

.345 

.462 

.608 

.76 

.5     15^ 

16J 

.107 

.111 

.118 

.130 

.148 

.175 

.218 

.283 

.376 

.500 

.650 

.8C 

>4     16i 

'  17^ 

.113 

.118 

.136 

.139 

.159 

.189 

.337 

.308 

.408 

.539 

.692 

.88 

(8     17i 

1  is! 

.119 

.136 

.134 

.148 

.170 

.205 

.356 

.333 

.440 

.578 

.731 

.8-; 

'0     18i 

m 

.137 

.133 

.143 

.158 

.183 

.220 

.277 

.360 

.474 

.616 

.769 

.8J 

>8     19^ 

20^ 

.133 

.140 

.151 

.168 

.195 

.236 

.298 

.388 

.509 

.654 

.804 

.92 

Jl     20i 

21i 

.139 

.148 

.159 

.178 

.208 

.253 

.321 

.417 

.544 

.692 

.837 

.9^ 

tl     2U 

22  i 

.147 

.155 

.169 

.189 

.221 

.271 

.344 

.446 

.579 

.728 

.866 

M 

»7     22^ 

23  i 

.154 

.163 

.178 

.200 

.336 

.289 

.369 

.477 

.614 

.763 

.892 

.9'- 

ro     23* 

m 

.161 

.171 

.187 

.212 

.351 

.309 

.394 

.509 

.650 

.796 

.915 

M 

^1     24i 

25i 

.168 

.1-79 

.196 

.224 

.366 

.330 

.420 

.541 

.685 

.827 

.934 

.96 

58     25i 

26| 

.175 

.187 

.307 

.237 

.383 

.351 

.447 

.574 

.719 

.856 

.951 

.9{ 

)3     26i 

27i 

.183 

.196 

.317 

.350 

.300 

.374 

.476 

.607 

.753 

.882 

.964 

.9{ 

)6     27i 

28^ 

.190 

.205 

.328 

.264 

.318 

.397 

.505 

.640 

.784 

.905 

.975 

.9t 

)8     28i 

29i 

.198 

.214 

.339 

.278 

.337 

.431 

.535 

.673 

.814 

.925 

.984 

.9J 

)9     291 

30^ 

.305 

.223 

.351 

.293 

.356 

.446 

.565 

.705 

.843 

.942 

.989 

.9$ 

)9     30i 

31i 

.313 

.233 

.363 

.309 

.377 

.473 

.596 

.737 

.868 

.957 

.994 

M 

)9     31i 

32i 

.333 

.343. 

.376 

.336 

.398 

.499 

.627 

.768 

.893 

.969 

.997 

32i 

331 

.331 

.254 

.389 

.343 

.431 

.537 

.659 

.798 

.913 

.978 

.999 

.     33i 

34J 

.240 

.265 

.303 

.361 

.444 

.555 

.690 

.826 

.932 

.986 

.999 

.     34i 

35^ 

.349 

.276 

.318 

.379 

.468 

.585 

.721 

.853 

.947 

.991 

.999 

.     35J 

36^ 

.358 

.287 

.333 

.399 

.493 

.614 

.751 

.877 

.960 

.995 

.999 

.     36i 

37i 

.367 

.300 

.349 

.420 

.519 

.644 

.781 

.898 

.971 

.997 

21* 

38i 

.378 

.313 

.366 

.441 

.546 

.674 

.809 

.919 

.980 

.999 

.     38i 

39^ 

.288 

.326 

.383 

.463 

.573 

.704 

.835 

.936 

.987 

.999 

.     39J 

40^ 

.298 

.340 

.401 

.487 

.601 

.733 

.860 

.951 

.992 

.999 

.     40i 

41i 

.310 

.355 

.430 

.513 

.630 

.763 

.883 

.963 

.995 

.999 

•     -*!* 

42^ 

.322 

.370 

.440 

.537 

.658 

.790 

.904 

.973 

.997 

!2* 

43i 

.335 

.386 

.461 

.562 

.687 

.817 

.923 

.982 

.999 

.     43i 

44^ 

.349 

.403 

.483 

.588 

.716 

.842 

.940 

.988 



.     44J 



10-14 

15-19 

30-24 

25-29 

30-34 

35-39 

40^4 

45^9 

50-54 

55-59 

60-64 

65- 

69 

Fo 

RMULA 

Multi 

jlier  = 

-H 

^_±\ 

CLIMATIC   TABLES. 


45 


THIRTY   OFFICES'   EXPERIENCE. 
(B).        Multiplier  for  Discontinued  and  Died  to  give  the  whole  Probable  Loss. 


DCBA- 

Age  of  Entry 

X. 

DUBA- 

TION 

n. 

_      TION 

10-14 

15-19 

30-34 

35-39 

30-34 

35-39 

40^4 

45-49 

50-54 

55-59 

60-64 

65-6 

9      "• 

0 

.000 

.000 

.000 

.000 

.000 

.000 

.000 

.000 

.000 

.000 

.000 

.OOC 

>       0 

1 

.006 

.007 

.007 

.007 

.008 

.008 

.010 

.013 

.016 

.022 

.031 

Mt 

•      1 

2 

.013 

.013 

.014 

.014 

.016 

.017 

.030 

.035 

.033 

.044 

.063 

.09S 

i        2 

3 

.030 

.020 

.031 

.033 

.023 

.036 

.031 

.038 

.050 

.068 

.096 

.14( 

)       3 

4 

.036 

.037 

.038 

.039 

.031 

.035 

.043 

.053 

.068 

.092 

.131 

.19( 

)       4 

5 

.033 

.033 

.035 

.036 

,039 

.045 

.053 

.066 

.086 

.118 

.167 

.34] 

^       5 

6 

.039 

.040 

.041 

.044 

.048 

.054 

.064 

.081 

.106 

.146 

.305 

.39( 

i       6 

7 

.045 

.047 

.049 

.051 

.056 

.064 

.076 

.096 

.137 

.174 

.344 

.34{ 

)        7 

8 

.053 

.053 

.056 

.059 

.065 

.074 

.089 

.113 

.148 

.203 

.384 

.39^ 

^        8 

9 

.058 

.060 

.063 

.067 

.074 

.084 

.103 

.139 

.171 

.234 

.336 

.45] 

L        9 

10 

.065 

.067 

.070 

.074 

.083 

.095 

.115 

.147 

.194 

.266 

.368 

.mi 

5      10 

11 

.071 

.073 

.077 

.083 

.093 

.106 

.139 

.165 

.219 

.299 

.411 

.55^ 

»      11 

12 

.077 

.080 

.084 

.091 

.101 

.118 

.144 

.184 

.245 

.334 

.455 

.60f 

5      12 

13 

.084 

.087 

.093 

.099 

.111 

.130 

.159 

.304 

.272 

.369 

.499 

.654 

I      13 

14 

.090 

.094 

.099 

.107 

.131 

.143 

.175 

.335 

.300 

.406 

.543 

.70( 

)      14 

15 

.097 

.101 

.106 

.116 

.131 

.155 

.193 

.248 

.329 

.443 

.586 

.744 

t      15 

16 

.103 

.107 

.114 

.135- 

.143 

.168 

.309 

.271 

.360 

.481 

.639 

.78f 

i      16 

17 

.110 

.114 

.133 

.134 

.153 

.183 

.337 

.395 

.391 

.519 

.671 

.825 

5      17 

18 

.116 

.133 

.130 

.143 

.164 

.197 

.346 

.330 

.434 

.558 

.713 

.85{ 

>      18 

19 

.133 

.139 

.138 

.153 

.176 

.313 

.366 

.346 

.457 

.597 

.751 

.88f 

5      19 

2b 

.130 

.136 

.147 

.163 

.188 

.328 

.387 

.374 

.491 

.685 

.787 

.91( 

)      20 

21 

.136 

.144 

.155 

'.173 

.301 

.344 

.309 

.403 

.526 

.673 

.831 

.93S 

J      21 

22 

.143 

.151 

.164 

.183 

.314 

.363 

.333 

.431 

.561 

.710 

.853 

.941 

)      22 

23 

.150 

.159 

.173 

.194 

.338 

.380 

.356 

.461 

.596 

.746 

.879 

.964 

t     23 

24 

.157 

.167 

.183 

.306 

.343 

.399 

.381 

.493 

.632 

.780 

.904 

.97f 

i      24 

25 

.164 

.175 

.191 

.318 

.358 

.319 

.407 

.524 

.667 

.813 

.935 

.98^ 

}     25 

26 

.171 

.183 

.301 

.330 

.374 

.340 

.433 

.557 

.702 

.843 

.943 

.99] 

L      26 

27 

.179 

.191 

.313 

.343 

.391 

.363 

.461 

.590 

.735 

.869 

.958 

.99{ 

>      27 

28 

.186 

.300 

.333 

.356 

.308 

.385 

.490 

.623 

.768 

.894 

.970 

.99'- 

^     28 

29 

,194 

.309 

.333 

.371 

.337 

.408 

.519 

.656 

.799 

.915 

.980 

.99J 

)     29 

30 

.301 

.318 

.345 

.385 

.346 

.433 

.550 

.689 

.828 

.934 

.987 

.99J 

)     30 

31 

.309 

.338 

.357 

.301 

.366 

.459 

.580 

.721 

.856 

.950 

.993 

.991 

)     31 

32 

.317 

.338 

.369 

.317 

.387 

.485 

.611 

.753 

.880 

.963 

.995 

.991 

)      32 

33 

.336 

.348 

.383 

.334 

.409 

.513 

.643 

.783 

.903 

.974 

.998 

33 

34 

.335 

.359 

.396 

.351 

.433 

.541 

.674 

.812 

.923 

.982 

.999 

34 

35 

.344 

.370 

.310 

.370 

.456 

.570 

.705 

.840 

.940 

.989 

.999 

35 

36 

.353 

.381 

.335 

.389 

.480 

.599 

.736 

.865 

.954 

.993 

.999 

36 

37 

.363 

.393 

.340 

.409 

.506 

.639 

.766 

.888 

.966 

.996 

.999 

37 

38 

.373 

.306 

.357 

.430 

.533 

.659 

.795 

.909 

.976 

.998 

38 

39 

.383 

.319 

.374 

.453 

.559 

.689 

.833 

.928 

.984 

.999 



39 

40 

.393 

.333 

.393 

.475 

.587 

.718 

.848 

.944 

.990 

.999 

40 

41 

.304 

.347 

.410 

.499 

.615 

.748 

.873 

.957 

.994 

.999 

41 

42 

.316 

.363 

.430 

.524 

.644 

.776 

.894 

.968 

.996 

.999 

42 

43 

.338 

.378 

.450 

.549 

.673 

.804 

.914 

.978 

.998 

43 

44 

.341 

.395 

.471 

.575 

.701 

.830 

.932 

.985 

.999 

.... 

44 

10-14 

15-19 

30-24 

35-39 

30-34 

35-39 

40-44 

45-49 

50-54 

55-59 

60-64 

65-6 

9 

% 

F 

OmSXTLi 

V,  Mult 

iplier  = 

-'i 

Ht 

46 


CLIMATIC   TABLES. 


The  climatic  Tables  being  already  in  use,  are  retained  in  the  original  form,  based 
on  multipliers  from  the  common  American  Table  of  1858.  Parallel  computations  of 
the  total,  lead  to  the  following  precepts :  To  change  the  Probable  Loss  Am.  1858,  in 
Tables  V,  VI,  or  VII,  to  the  standard  of— 


The  Thirty  American  OflBces  Table  ; 
«    Twenty  British  "  «     H**- 

"    Seventeen  British      "  " 


Deduct  ^th  part. 
Add  5^  per  cent. 
Add  8f  per  cent. 


The  corresponding  factors  are  0.9667,  1.0519,  1.0837,  and  their  logarithms  1.98530, 
0.02198,  0.03492.  The  columns  of  Actual  Loss  of  course  remain  unchanged.  By 
these  precepts,  a  present  Probable  Loss  of  $1,204,521  to  be  represented  on  the  basis 
of  the  Thirty  Offices  Table,  is  changed  to  $1,164;370.  And  the  tabular  ratio  of  100  :  134 
becomes  96f  ;  134,  or  100  :  139  nearly. 


SECTION     II.  • 

Classification  of  Counties.    Misoellaneons  Statistics. 

Preparatory  to  the  classification  of  Counties  in  respect  to  Mortality,  the  simple 
division  shown  on  the  common  Geological  maps  of  the  United  States  may  be  noted. 
First,  the  lowland  or  Alluvial  Counties  commencing  with  the  eastern  shores  of  Maryland 
and  Virginia,  and  following  the  line  of  tide-water  on  the  Atlantic  and  Gulf  coasts  to 
the  borders  of  Mexico,  and  up  the  valley  of  the  Mississippi  to  the  mouth  of  the  Ohio 
river.  These  alluvial  Counties  are  denoted  in  Table  VII  by  one  dot  annexed.  Between 
these  and  the  line  of  400  feet  elevation,  are  the  Middle  Counties,  of  which  the  tertiary 
portion  are  here  denoted  by  three  dots,  and  the  few  cretaceous  by  two  dots.  The 
remaining  or  Upland  Counties  above  the, line  of  400  feet  elevation,  according  to 
Prof.  Guyot,  are  here  indicated  by  the  absence  of  dots.  The  Counties  of  Indiana  admit 
of  separate  consideration.  Also  the  present  object  may  be  found  to  require  a  modifica- 
tion of  these  divisions. 

CLASSIFICATION    OP    COUNTIES 


AiiLuviAii  Count's. 

Middle  Counties. 

Upland  Counties. 

Total  Counties. 

States 

Pbob.  Loss. 

Act.  Loss. 

Prob.  Loss. 

Act.  Loss. 

Pkob.  Loss. 

Act.  Loss. 

Pbob.  Loss. 

Act.  Loss. 

Alabama  . . 

396,236 

544,453 

175,977 

194,580 

523,007 

729,014 

1,204,521 

1,618,048 

Arkansas . . 

98,449 

221,995 

125,202 

196,084 

46,238 

80,040 

295,413 

508,119 

Florida 

133,347 

224,596 

28,758 

32,550 

.  .  •  • 

.... 

181,635 

303,852 

Georgia 

2,117 

7,500 

524,221 

603,540 

355,738 

257,860 

950,653 

911,536 

Louisiana. . 

1,252,180 

2,194,255 

23,901 

30,660 

.... 

.  .  •  . 

1,363,520 

2,400,915 

Mississippi 

301,087 

552,260 

416,636 

585,344 

13,491 

15,660 

795,476 

1,308,632 

N.  Carolina 

225,053 

353,555 

390,924 

443,633 

178,804 

201,721 

843,815 

1,069,409 

S.  Carolina. 

374,487 

446,433 

192,307 

183,198 

179,009 

227,004 

753,060 

864,635 

Tennesee. . 

708,436 

1,488.636 

181,460 

209,380 

467,280 

544,055 

1,383,648 

2,262,121 

Texas 

214,043 

511,467 

332,901 

572,267 

184,655 

264,238 

778,713 

1,358,972 

Virginia. . . 

3,567 

13,009 

385,727 

349,100 

141,204 

202,750 

646,188 

673,350 

Total 

3,709,002 

6,558,155 

2,778,004 

3,398,331 

2,089,436 

2,522,342 

9,196,642 

13,279,589 

Ratio  (Am.  1858),            100:177 

100  :  122 

100  :  121 

100  :  144 

By  30  Offices  Table,         100  : 1 83 

100  :  127 

100:125 

100  :  149 

By  20  Offices  Table,  HM.,  100 :  168 

100  :  116 

100  :  115 

100  :  137 

By  1 7  Offices  Table,         100 : 1 63 

100  :  113 

100  :  111 

100  :  133 

CLIMATIC    TABLES. 


47 


A  singular  feature  is  presented  in  the  close  agreement  of  the  climatic  Katios  for 
Middle  and  Upland  Counties,  indicating  that  these  may  be  united ;  or  that  hereafter, 
two  (AoE&e^  Alluvial  and  Upland,\i\\\  generally  be  sufficient.  A  wide  contrast  is  shown 
between  their  characteristic  Ratios,  100  :  183  and  100  :  126,  by  the  Thirty  Offices  Table. 
It  will  also  be  noted  that  the  Upland  Counties  of  Georgia  at  the  southern  termination 
of  the  Alleghany  mountains  are  exceptionally  healthy  in  the  ratio  of  100  :  72. 

In  the  State  of  Indiana,  the  experience  of  eleven  smaller  Companies  gave  a 
Probable  Loss  of  $563,770  and  an  Actual  Loss  of  $743,866;  Ratio  100  :  132.  By  the 
accession  of  other  Companies,  the  total  ratio  was  materially  altered,  as  shown  at  the 
end  of  Table  VIL  The  less  healthy  Counties  are  reported  to  lie  in  the  north-eastern 
part  of  the  State,  and  along  the  Wabash  and  Ohio  rivers. 

The  following  additional  data  pertaining  to  the  Southern  States,  are  arranged  from 
the  statements  of  particular  Companies,  more  especially  to  show  in  the. last  column  the 
Age  corresponding  to  the  mean  Rate  of  Probable  Loss  divided  by  the  number  Exposed 
to  Risk.  The  results  of  the  27  Companies  in  Table  V,  and  the  3  other  Companies,  for 
the  whole  United  States,  are  subjoined. 

AGE  OP  MEAN  RATE  OP  PROBABLE  LOSS. 


COXFANIBS. 

Deaths 

OB 

Loss. 

Exposed 

TO 

Risk. 

Pbobable 
Deaths 
OK  Loss. 

Rate 
OP  Prob- 
able. 

Age 

OI" 

Rate. 

Table 
employed. 

Pbob.  :  Act. 
As  100: 

.^tna  Life  (III) 

1,366.3 
677 
243.3 
459.8 
139 

74,270 
37,940 
17,594 
20,937 
5,966 

966.90 
442.96 
203.95 
249.31 
79.94 

1.3019 

1.1675 
1.1592 
1.1910 
1.3400 

46.27 
46.26 
46.07 
4456 
46.60 

*17  Offices 

Am.  1858 
<<      It 

20  Offices 

141 
153 
119 

184 
174 

St.  Louis  Mutual 

Covenant       "       

Continental,  N.  Y 

Scottish  Amicable 

27  Companies,  U.  S 

3         «             "     

192,049.0 
35,961 

9,327,400 
2,909,037 

104,531.5 

37,580.7 

1.1209 
1.2919 

45.11 
48.69 

Am.  1858 

.98 

85 

It  may  here  be  noted  that  the  Experience  of  the  ^Etna,  Covenant  and  Continental, 
also  of  the  27  Companies  and  3  Companies,  is  stated  in  thousands  of  dollars.  Three- 
fourths  of  the  business  of  the  Covenant  of  St.  Louis  was  located  in  the  State  of 
Missouri.  The  Experience  of  the  Scottish  Amicable  here  represents  only  the  portion 
located  in  the  British  colonies  of  the  West  Indies ;  where  the  climatic  ratio  by  the 
20  Offices  Table,  100  :  174  so  far  exceeds  the  like  ratio  100  :  168  before  found  for 
Alluvial  counties  in  the  Southern  States.  With  the  omission  of  the  Continental,  N.  Y., 
whose  business  appears  somewhat  exceptional,  the  Age  of  the  mean  Rate  of  Probable 
Loss  relative  to  exposure,  differs  little  from  46.3  years,  in  the  Southern  or  tropical 
experience  of  the  other  four  Companies. 

With  regard  to  the  comparative  Mortality  of  insured  Females,  the  Southern 
experience  of  the  St.  Louis  Mutual,  comprising  628  deaths  of  Males,  and  48  of 
Females,  gave  the  ratio  of  Probable  to  Actual  Loss  (Am.  1858)  for  Males  1.51,  and 
for  Females  1.70;  thus  indicating  greater  mortality  on  the  part  of  Females. 

In  relation  to  the  Mortality  iy  Policy  years,  the  total  experience  of  the  St.  Louis 


48 


CLIMATIC   TABLES. 


Mutual,  comprising    1486  deaths,  North  and  South,  gave  the  following  ratios  of 
Probable  Loss,  denoted  by  1,  to  Actual  Loss  (Am.  1858) : 


ST.   LOUIS   MUTUAL. 


Policy  Years. 

Deaths 

Ratios 


1st. 

3d. 

3d. 

4th. 

5th. 

6th. 

7th. 

8th. 

9th. 

10th. 

Total. 

360 

330 

232 

180 

146 

87 

73 

40 

20 

7.. 

1486 

1.13 

1.85 

1.55 

1.26 

1.68 

1.21 

1.52 

1.81 

1.34 

1.36.. 

1.33 

SCOTTISH  AMICABLE  IN  THE  WEST  INDIES. 


Deaths 

9 
1.59 

10 
0.97 

13 
1.47 

12 
1.59 

14 
2.12 

6 
1.03 

After  6th  year,   75 
(Am.  1858),         1.91 

139 
1.65 

Ratios 

The  mean  rate  1.33  of  the  former  Company  is  reached  in  the  second  year;  that  of 
the  latter,  nearly  in  the  first  year,  but  the  ratios  are  irregular  from  paucity  of  data. 
For  information  upon  other  portions  of  the  globe,  reference  may  be  made  especially  to 
the  following  articles  in  the  Journal  of  the  Institute  of  Actuaries : 


On  the  rates  of  extra  premium  for  foreign  travelling  and  residence. 
H.  Bailt,  Esq.      Actuary  of  the  London  Assurance  Corporation. 
77-94,  1869. 


By  Arthur 
Vol  15,  pp. 


By 


On  the  Additional  Premium  required  for  Residence  in  Foreign  Climates, 
the  Honorary  President,  James  Meikle,  Felloiv,  etc.    Vol.  19,  p.  268,  1876. 

On  the  Death  Rate  among  Assured  Lives  in  the  West  Indies,  heing  the  Experience 
of  the  Scottish  Amicable  Life  Assurance  Society  during  Tliirty  Years,  184.6-76.  By 
John  Stott,  late  Manager  of  the  Society,  Fellow,  etc.    Vol.  21,  p.  153,  1878. 

In  proceeding  from  the  temperate  to  the  torrid  zone,  it  is  generally  admitted  that, 
"  other  things  being  equal, — height,  soil,  and  river  drainage, — the  mortality  will  increase 
as  we  go  South ;  and  that  heat  stimulates  the  vital  functions,  so  that  maturity  is 
reached  earlier,  and  decay  commences  earlier." 

Climate  Bxtra.  The  net  extra  to  meet  the  additional  risk,  is  roughly  found 
by  dividing  the  excess  of  the  Actual  above  the  Probable  Loss,  by  the  Exposure.  Thus 
among  the  examples  given  by  the  distinguished  actuary  and  manager  T,  B.  Sprague,  in 
the  Journal  of  the  Institute,  Vol.  19,  page  297,  the  years  of  Life  exposed  in  India  Avere 
229,  Actual  Deaths  11,  Probable  Deaths,  H«  3.499.  And  (11— 3. 499)^229=. 03276 ; 
or  the  Climate  Extra  is  3.276  per  cent,  of  the  sum  insured.  By  a  more  extensive 
method,  Mr.  A.  H.  Baily  now  President  of  the  Institute, -in  his  memoir  above  quoted, 
first  constructed  a  life  table  from  the  foreign  experience,  and  thence  a  scale  of  annual 
premiums ;  the  difference  between  this  and  the  home  scale,  gave  the  climate  extras  for 
the  several  ages  of  exposure.  Besides  the  ordinary  extra,  which  averaged  one  per  cent, 
in  the  West  Indies,  the  difference  between  unacclimated  and  acclimated  lives  led  the 
Scottish  Amicable  to  charge  an  additional  extra  of  one  per  cent,  of  the  sum  insured, 
during  the  first  three  years  of  foreign  residence.  On  returning  to  reside  in  Great 
Britain,  with  ordinary  health,  all  extras  are  omitted. 


CLIMATIC   TAB  LBS. 


49 


.      SECTION     III. 
The  Life  Table  graded  for  different  Climates. 

Let  us  now  consider  the  application  of  Table  VI  to  permanent  life  insurances  for 
different  grades  of  mortality.  In  a  State,  for  example,  where  the  ratio  of  Probable  to 
Actual  Loss  by  Table  VI  corrected  to  the  Thirty  Offices  Table,  has  been  100  :  139  in 
the  mean  Experience  of  27  Companies ;  and  the  ratios  were  100  :  112,  100  :  153,  and 
100  :  161  in  the  three  component  groups  of  Companies,  the  most  experienced  actuaries 
and  managers  could  best  determine  the  single  resultant  or  probable  climatic  ratio  for 
Office  premiums.  Such  examination  would  be  influenced  by  the  probable  extent  of 
new  business,  the  medical  and  counter  selections,  prevailing  causes  of  death, — and 
south  of  the  latitude  of  36°  30',  also  extending  north  of  it,  the  alluvial  Counties 
distinguished  in  Table  VII.  For  convenience,  the  net  ratio  thus  conventionally  adopted 
may  be  denoted  by  100  :  lOOp,  that  is  1  :  p. 

The  Thirty  Offices  collection  defines  the  experience  of  insured  mortality  along  a 
wide  belt  of  the  temperate  zone,  the  middle  line  centering  nearly  on  the  latitude  of 
the  city  of  New  York.  The  resulting  standard.  Table  XXVI  has  the  advantage  of 
unusually  large  data,  critical  accuracy  and  improved  construction.  To  construct  other 
life  Tables,  from  the  small  numbers  of  more  distant  climates.  North  or  South,  would 
involve  great  labor  and  complexity.  The  difficulties  are  marvellously  reduced  by  the 
discovery  of  a  double  gradation.  That  is.  Table  XXVI  being  graduated  in  the  direction 
of  the  scale  of  ages,  is  virtually  graded  in  another  direction  also,  by  its  commutation 
columns,  which  represent  life  tables  for  so  many  different  climates,  or  climatic  ratios. 
And  the  values  for  intermediate  ratios,  can  be  found  by  simple  interpolation. 

This  improvement  was  first  suggested  by  the  entire  agreement  of  Table  XXVI 
with  the  well-known  law  of  Gompertz,  modified  by  Makeham,  observing  that  in  previous 
comparisons  of  the  annual  rate  or  (log  p),  change  of  the  first  term  (log  s)  of  Make- 
ham's  formula,  corresponded  with  changes  of  mortality  due  to  local  or  climatic  causes; 
the  other  term  or  power  of  {q)  being  nearly  constant  for  a  long  series  of  years  or  ages. 

Again,  from  a  different  source,  but  on  the  same  principle,  the  experience  of  the 
Scottish  Amicable  in  the  West  Indies,  was  stated  by  the  late  manager  and  actuary  to 
be  represented  by  the  Northampton  table  better  than  any  other  of  the  current  life 
tables.  Yet  our  examination  indicates,  that  by  a  simple  change  of  the  rate  of  interest, 
the  Carlisle  Table  might  be  substituted,  as  shown  by  the  following  comparison  of  life 
annuities ;  and  the  same  might  be  extended  to  life  premiums,  with  a  simple  modification 
presently  described. 

LIFE    ANNUITIES. 


Age,  Years 

Northampton  4  per  cent. 
Carlisle  5  per  cent. .... 

Northampton  5  per  cent, 
Carlisle  6  per  cent 


25 

35 

45' 

55 

65 

15.44 

14.04 

12.28 

10.20 

7.76 

15.30 

14.13 

12.65 

10.35 

7.77 

75 
4.fi6 
4.99 


13.57 
13.46 


12.50 
12.57 


11.11 
11.43 


9.38 
9.52 


7.28 
7.28 


4.74 
4.76 


50  .  CLIMATIC    TABLES. 

In  the  first  publication  of  the  climatic  Tables,  it  was  provisionally  assumed  that, 
above  the  age  of  twenty  or  some  lower  limit,  the  different  grades  of  mortality  [q)  are 
proportional  to  those  of  the  standard  Table.  The  preceding  comparison  of  annuities 
as  well  as  other  reasons,  afterwards  suggested  to  the  writer  the  more  convenient  and 
exact  hypothesis,  to  which  Mr.  McClintock  appears  to  have  arrived  in  a  different  way, 
that  the  prohahilities  of  survival  {p)  for  differetit  grades  of  mortality,  are  proportional 
to  those  of  the  standard  Life  Table.  In  another  expression,  the  rates  of  survival  and 
of  interest  may  be  commuted.  That  is,  so  far  as  relates  to  life  annuities,  an  increase 
of  the  rate  of  mortality,  may  be  represented  by  an  increase  in  the  rate  of  interest; 
and  conversely. 

For  illustration,  let  us  distinguish  the  Northampton  values  by  an  accent,  and  write 
the  well-known  formulas  below  ;  then  since  annuities  are  assumed  to  be  equal: 

Northampton  Jf.  p>er  cent.  Carlisle  5  per  cent.  Relation, 

a'x  =  v'p'xO-  +  «'«+i)-  «x  =  vpx{l  +  ax+i).  v'p'x  =  vpx. 

-~,  ,1  JJ  x+n        I^aj+n 

Consequently         --------         — - —  =  — - — . 

1  +  ax-^^-j^^-l+ax.  D'.-D,-d/d,- 

-X  =  lOOo]  ^^  -  (!-.')  [,  nx  =  lOOo]  ^^  -  (l-v)  [. 

Ordinary  Life,     Tr'ar  =  7ra;  +  1000(v'— v). 
Reserve  =  l  _1±^  =  1  _1 +^£±!L. 

1  +  ax  l  +  «ar 

m  *•!.'««         Na;+l  —  -N^ai+a+l 

Temporary  Annuity,     a^  =  a^  = ^r . 

^  *  \Jx 

Premium  of  Term  Insurance,     P'  =  «;'-  ^%i^=^!^±^ii,        P'  =  P  +  1000(t;'-2;).  - 

JN  X — ^  x+n 

Hence  it  appears  that  with  very  simple  modifications,  the  Northampton  values  at 
4  per  cent,  can  all  be  derived  virtually  from  the  5  per  cent.  Carlisle  values. 

In  like  manner,  the  values  corresponding  to  different  grades  of  climatic  mortality, 
can  be  conveniently  derived  from  the  columns  of  the  Thirty  Offices  Table.  The  age  of 
the  mean  ratio  of  mortality  has  been  determined  on  page  47  to  be  about  46  years.  For 
tlie  present  purpose,  this  determination  will  supply  the  place  of  another  element,  the 
mean  ratio  of  probable  loss  to  the  number  exposed  to  risk,  in  the  climatic  district. 

In  a  given  locality,  let  the  probable  loss  as  computed  by  the  Thirty  Offices  Table,  be 
to  the  actual  loss  as  1  :  p.  That  is,  let  p  denote  the  climatic  ratio  ;  and  let  an  accent 
distinguish  the  values  of  v,  q,  p  for  the  locality.  Then  by  the  Relation  preceding, 
and  by  page  47, 

v'p'46  =  vpu,        or  v'{l—q't6)  =  vp^^.  ? «  =  PQw 

Elimmatmg  g  «,        p  =  --7- — • 

Let  the  value  of  v'  depend  constantly  on  4  per  cent,  interest ;  that  of  pt^,  q^^  on 
the  Thirty  Offices  Table.  Then  if  v  depends  on  4,  4^  or  5  per  cent,  interest,  the 
values  of  p  thus  found  will  be  1,  L405,  1.805  respectively;  which  may  be  termed 
Special  Climatic  Ratios. 


CLIMATIC   TABLES.  61 

For  the  First  Special  Ratio  1.405,  we  have  p'x  =  y~c^P^'     -^^'^^  ^^^®»  ^^  might 

construct  a  special  life  table,  and  4  per  cent,  commutation  columns,  which  would  give 
the  net  life  premium  on  1000,  at  the  age  of  30  years  for  example,  19.50.  But  the 
same  can  be  found  much  more  easily  by  the  preceding  formula,  -n'x  =  {"^Xf  4^  per  cent.) 

+  1000(v'— v);  where -^-——^  =  0.00460066,  to  be  multiplied  by  1000.     And  so 

for  other  similar  formulas. 

1.04 

For  the  Second  Special  Ratio  1.805,  we  have  p'x  =  -:r-^px. 

Also  tt'x  =  (ttx,  5  per  cent.)  +  1000(v'— v) ;  where  Y7iA~T7\'K  =  0.00915751  to  be  mul- 
tiplied  by  1000. 

Therefore  for  the  D,  N,  S  columns  according  to  4  per  cent,  interest  and  the 
Climatic  Ratio  1,405,  we  have  in  Table  VIII  substituted  the  4^  per  cent,  columns  of 
the  Thirty  OflBces  standard.  And  for  the  D,  N,  S  columns  corresponding  to  4  per  cent, 
and  the  Climatic  Eatio  1.805,  Table  VIII  gives  the  equivalent  5  per  cent,  columns  of 
the  standard.  But  it  is  needful  to  observe,  that  this  substitution  could  not  be  extended 
to  the  C,  M,  R  columns,  without  modification.  Nor  is  it  necessary,  since  all  the  formulas 
can  be  expressed  in  terms  of  D,  N,  S,  v'  and  v. 

In  conclusion,  the  Climatic  Ratios  given  in  Tables  V,  VI  and  VII,  being  first 
changed  to  the  basis  of  the  Thirty  Offices  Table,  the  corresponding  4  per  cent, 
premiums  and  annuities  may  be  found  from  those  of  the  Special  Ratios  in  Table  VIII 
by  proportion  or  interpolation.  And  the  preceding  formulas  may  be  extended  to  other 
species  of  Premiums  and  Reserves.  The  relation  v'p'  =  vp  also  occurs  in  the  treatise 
on  Policy  Life  Lines,  by  James  Meikle,  Edinburgh,  1871. 


52  MEDICAL   STATISTICS, 


DIYISION     THIED. 

MEDICAL     STATISTICS. 

Statistics  of  Diseases  or  Causes  of  Death  have  been  returned  by  twenty-seven  of 
the  thirty  Companies  included  in  the  general  collection.  These  twenty-seven  are  the 
same  which  gave  the  Climatic  Statistics,  with  one  exception.  The  total  number  of 
Deaths  from  All  Causes  was  37,624 ;  of  which  35,442  were  Deaths  of  Males,  and  2,182 
of  Females;  also  there  were  8,919  Deaths  additional  in  the  three  Companies  not 
specifying  diseases.  Under  experienced  medical  advice  and  direction,  the  results  are 
given  in  the  most  approved  forms  for  reference  in  Tables  IX-XVII.  The  classification 
of  diseases  accords  nearly  with  the  last  plan  of  Dr.  Farr,  as  recently  applied  in  the 
Medical  Report  of  the  Mutual  Life  of  New  York. 

An  examination  of  medical  treatises,  including  special  works  on  Medical  Examina- 
tion for  Life  Insurance,  like  Brinton  or  Allen,  will  suggest  many  inquiries,  to  which 
the  present  Tables  will  often  give  an  instructive  answer.  "What  diseases  increase,  and 
what  diminish  as  age  advances?  What  diseases  or  causes  of  death  are  beyond  the 
cognizance,  and  what  are  most  easily  recognized  by  medical  examination,  and  at  what 
ages  ?  What  is  the  distribution  of  diseases  in  different  parts  of  the  United  States  ? 
On  these  and  kindred  topics,  the  statistics  give  valuable  information,  and  will  suggest, 
in  lieu  of  extended  commentary,  a  ready  reference  to  the  Tables  themselves. 

In  examining  these  records,  we  are  reminded  of  the  more  numerous  unrecorded 
cases,  in  which,  the  innate  vital  force  has  reverted  from  morbid  or  diseased  conditions 
into  the  old  channels  of  health.  The  struggle  to  rise  from  a  diseased  condition,  may 
be  short  and  decisive,  terminating  in  death  or  in  convalescence,  or  it  may  be  longer 
prolonged  with  varying  fortunes.  The  contending  forces  often  appear  so  equally 
balanced,  that  a  very  little  will  turn  the  scale.  The  struggle  between  the  tendency  to 
health  and  the  tendency  to  disease,  acute  or  chronic,  may  last  from  a  day  to  months, 
and  even  years.  Thus  medical  statistics  illustrate  the  nature  of  the  mysterious  vital 
force,  by  its  final  developments  under  varied  conditions  of  age,  duration,  sex  and  climate. 

SECTION    I. 

Description  of  the  Tables. 

The  first  of  the  series.  Table  IX,  is  a  general  Table  giving  firstly  the  Number  of 
Deaths  of  insured  males,  and  similarly  of  females,  by  160  Diseases,  in  seven  classes, 
commencing  with  zymotic.  The  next  three  columns  give  the  results  for  two,  for  five, 
and  for  twenty  Companies  arranged  to  include  about  one-third  of  the  whole,  or  nearly 
12,541  in  each  group.  By  glancing  across  the  three  columns  horizontally,  the 
Variability  by  each  disease  is  ordinarily  indicated.  For  example,  the  deaths  by 
Typhoid  Fever,  at  the  head  pf  the  list,  appear  to  have  been  quite  uniformly  distributed. 


MEDICAL    STATISTICS.  63 

In  the  last  column,  the  37,624  deaths  are  represented  on  the  percentage  scale  of 
100.00  distributed  proportionally  to  the  number  of  deaths  by  each  disease.  The  prin- 
cipal or  leading  diseases  in  order,  are  Typhoid  Fever  5.99  per  cent,  other  Fevers  4.35, 
Consumption  18.31,  Apoplexy  4.70,  Paralysis  and  Disease  of  Brain  4.34,  Heart  Disease 
3.61,  Pneumonia  or  Inflammation  of  the  Lungs  7.68,  Accidents  and  Injuries  7.21  per 
cent,  of  all.  These  and  other  results  may  be  deemed  as  correct  as  can  possibly  be 
obtained  under  existing  circumstances.  Some  allowance  is  to  be  made  for  the  inexact- 
ness of  medical  science,  with  gradual  changes  and  transposition  of  medical  terms. 
Also  when  one  disease  is  accounted  as  the  producing  cause  of  another,  the  last  or  fatal 
disease  is  the  one  noted  in  these  statistics,  from  Office  registers. 

Table  X,  XI,  XII  contain  only  the  absolute  numbers  of  Deaths,  which  constitute 
one  of  the  two  terms  of  ratio  or  comparison  in  the  Tables  following,  with  separate 
columns  for  males  (A),  and  Females  (B). 

Tables  XIII  and  XV  are  a  further  development  of  Table  X  with  respect  to 
Duration  of  Insurance.  After  the  seven  general  classes,  the  statistics  are  subjoined  for 
thirty-nine  leading  Diseases.  The  corresponding  Exposure  of  the  living  is  given  at 
the  foot  of  the  columns  in  Table  XIII.  For  example,  in  the  first  column,  2,445 
Deaths  divided  by  356,210  years  Exposed  gives  0.00686,  that  is,  0.686  Deaths  per  cent. 
or  68.6  in  10,000  Exposed  to  Eisk,  as  shown  at  the  head  of  the  column.  It  will  be 
noticed  that  during  the  first  two  or  three  years  of  Male  Life,  the  deaths  from  Zymotic 
diseases,  and  from  Accidents  and  Injuries,  have  generally  exceeded  the  average,  thus 
showing  this  part  of  the  mortality  to  be  uncontrolled  by  the  Medical  examination. 
And  the  same  may  be  remarked  in  Female  Life,  including  Childbirth  and  Puerperal 
Diseases.  On  the  other  hand  the  efficient  diagnoses  of  Constitutional  and  Heart 
diseases,  and,  in  general,  of  "  All  Causes,"  is  very  evident  from  the  inspection. 

Tables  XIV  and  XVI  give,  according  to  the  Ages  of  Life  or  Exposure,  in  extension 
from  Table  XI,  the  ratio  of  deaths  to  the  Living,  and  the  ratio  to  total  Deaths.  The 
Exposed  to  Risk  by  Ages  are  inserted  at  the  foot  of  Table  XIV ;  and  the  number  of 
diseases  is  further  reduced  in  Tables  XV  (B)  and  XVI  (B)  for  female  life.  All  these 
results  by  Ages  of  Life,  will  be  found  not  less  valuable  than  those  from  the  difierent 
point  of  view  of  the  Durations  of  insurance. 

Finally,  Tables  XII,  and  XVII  (A),  (B),  (C),  indicate  the  Climatic  Distribution 
of  Diseases  in  the  United  States.  These  figures  relate  to  Actual  Deaths,  while  the 
Climatic  Tables  V,  VI,  and  VII  are  based  on  Amounts  Insured;  the  one  class  may 
supplement  the  other.  In  comparing  the  deaths  of  703  Foreign  Males,  Table  XVII  (A), 
with  ail  equal  number  of  the  native-born  insured,  the  greater  exemption  of  foreigners 
from  Zymotic  and  Constitutional  Diseases  is  counterbalanced  by  an  excess  of  deaths 
from  Apoplexy  (chiefly  of  Germans  in  one  Company),  from  Abscess,  Hemorrhage  etc. 
of  Lungs,  and  Accidents  and  Injuries.  About  two-thirds  of  this  experience,  however, 
occurred  in  British  America,  and  the  remaining  numbers  are  too  small  for  final 
conclusions. 

Again,  comparing  insured  Male  Deaths  with  those  of  the  TJ.  S.  Census  of  1870, 
shown  in  Table  XVII,  for  equal  totals,  the  proportions  dying  from  three  of  the  seven 
classes,  that  is,  from  Circulatory,  Respiratory  and  Miscellaneous  Diseases,  are  nearly 
equal.  And  the  decreased  mortality  of  insured  lives  from  Constitutional  Diseases  is 
counterbalanced  by  a  marked  excess  of  deaths  from  Nervous  and  Digestive  Diseases, 
and  a  small  excess  from  Zymotic  Diseases.  In  respect  to  Female  life  the  difierences  of 
distribution  evidently  follow  a  different  order. 

Representing  the  total  deaths  by  100,  in  each  of  the  seven  groups  of  States,  ve 
have  in  Table  XVII  (B)  the  relative  proportions  of  insured  males  dying  from  thirtj- 


54 


MEDICAL    STATISTICS. 


seven  principal  diseases.     It  is  the  comparison  of  a  part  with  the  whole,  that  is,  deaths 
with  total  deaths,  since  the  living  or  Exposed  to  Risk  are  liere  omitted. 

But  the  last  Table,  XVII  (C)  gives  a  sanitary  survey  of  the  United  States,  according 
to  the  deaths  and  diseases  among  10,000  living  insured  in  each  group  of  States.  To 
arrive  at  the  living,  the  following  process  was  employed.  First,  as  verified  in  the  mean 
of  two  of  the  largest  Life  Companies,  the  ratio  of  Probable  to  Actual  Claims  in  Table  V 
was  assumed  to  be  the  same  as  the  like  ratio  for  Deaths ;  and  the  Age  of  mean  Probable 
Deaths,  to  be  46  years,  as  already  indicated,  page  47.     That  is,  in  any  group  of  States, 


Probable  Deaths      Probable  Claims     Probable  Deaths 


Actual  Deaths 

Actual  Deaths 
Exposed 


Actual  Claims  '  Exjyosed 

Actual  Claims        Tabular  Deaths 


946 ',  or 


=  q4iX 


Probable  Claims        10,000  Living  ' 


Here  the  second  equation  is  divided  by  the  first,  to  give  the  third.  By  changing 
the  middle  member  to  a  decimal,  then  multiplying  both  numerator  and  1  the  denom- 
inator by  10,000  we  obtain  the  last  member,  as  shown  at  the  head  of  Table  (C).  The 
value  of  q  or  0.011562  corresponds  to  the  Actual  and  Probable  Claims  found  in 
Table  V.  The  rest  of  the  values  in  Table  C  were  then  readily  found  by  multiplying 
the  head  of  the  column  into  the  proportional  parts  of  Table  XVII  (B).  By  this 
technical  process,  an  additional  and  very  important  Table  is  obtained. 


SECTION    II. 

Statistics  of  Consiimption  Compared.     Sanitary  Survey  of 

the  United  States. 

To  illustrate  the  relation  of  the  statistics  to  any  specified  disease,  let  us  take  for  a 
first  example.  Consumption,  the  most  fatal  of  all.  Firstly  in  Table  IX,  the  deaths 
2,283,  2,231,  and  2,372  in  three  groups,  prove  the  deaths  from  Consumption  to  have 
occurred  at  a  nearly  uniform  rate  of  frequency  in  all  the  Life  Insurance  Companies. 
Again,  the  18.31  per  cent,  of  total  deaths  shown  in  the  last  column,  when  increased,  as 
it  probably  should  be,  by  one-thirteenth  of  the  deaths  by  Pneumonia  (chronic  cases),  and 
by  deaths  registered  from  Abscess  of  Lungs,  Hemorrhage  of  Lungs  and  Disease  of 
Lungs,  becomes  20.67  per  cent.,  or  more  than  one-fifth  of  the  whole  mortality. 

Table  XIII  confirmed  by  XV,  shows  the  effect  of  medical  selection  exhausted  and 
the  average  mortality  of  consumptive  cases  reached  in  the  third  year  of  Duration  of 
the  Insurance.  Table  XIV  confirmed  by  XVI,  shows  the  largest  mortahty  by  con- 
sumption to  occur  between  the  Ages  of  20  and  30  years.  But  after  this  period,  the 
proportion  of  consumptive  deaths  of  Males,  bears  a  two-fold  aspect.  That  is,  when 
compared  with  the  number  of  living  exposed  (Table  XIV),  it  slowly  decreases  to  a 
minimum  rate  between  50  and  60  years,  and  then  gradually  rises  again,  with  a  heavy 
mortality  all  the  while,  in  every  period  of  age. 

FKOM    TABLE    XIV  (A). 
Ratio  of  Consumptive  Deaths,  to  10,000  Living  at  each  Age. 


Afire 

Under  20 
12.0 

2a-30 

22.7 

30-40 
19.6 

40-60 
17.4 

50-60 

15.8 

60-70 
17.6 

70-80 
19.i 

All  Ages. 
18.6 

Ratio 

MEDICAL    STATISTICS. 


65 


But  when  compared  with  the  total  contemporary  deaths  (Table  XVI),  the  propor- 
tion from  consumption  continually  decreases,  as  the  complementary  proportion  from 
other  causes,  increases  above  the  age  of  thirty  years.  For  Female  Life,  with  more 
extensive  data,  the  general  statement  would  doubtless,  be  similar  to  that  before  given 
for  males. 

FEOM    TABLE    XVI  (A). 

Ratio  of  Consumptive  Deaths,  to  100  total  Deaths  at  each  Age. 


Affe 

20-30 
80.8 

80-40 
25.8 

40-50 

17.8 

50-60 
10.8 

60-70 
6.5 

70-80 
3.5 

All  Ages. 

18.3 

1 

Ratio 

Passing  now  to  the  Climatic  Distribution  in  Table  XVII  (A)  we  observe  that 
North  of  latitude  36°  30',  the  deaths  from  consumption  are  18.7  per  cent,  of  the  total 
Deaths  for  male  life,  and  19.3  for  females.  \  While  soutli  of  36°  30',  the  percentages  are 
12.3  and  9.0  respectively.  The  apparent  deficiency  from  consumption  in  the  latter, 
proceeds  only  from  comparison  with  a  larger  total,  including  an  excess  from  malarial 
or  other  diseases. 

Compared  with  the  United  States  Census  of  1870,  the  percentage  of  consumptive 
deaths  18.3  in  a  total  of  100  deaths  of  insured,  is  less  than  the  result  erf  the  Census, 
which  is  represented  by  26.2  for  males,  and  by  29.7  for  females.  Thus  the  rejection  of 
lives  uninsurable  from  incipient  consumption  is  manifest. 

Table  XVII  (B)  exhibits  in  more  full  detail,  the  percentage  of  insured  males 
dying  from  consumption  regarded  as  a  part  of  a  total  of  100  deaths  in  each  group  of 
States.  In  the  composition  of  100  deaths,  the  consumptive  element  will  be  seen  to 
decrease  in  the  following  order  of  groups,  iii,  i,  iv,  ii,  v,  vii,  vi :  as  the  numbers  21,  20, 
18,  17,  16,  15,  12.  Thus  in  proceeding  towards  the  tropical  regions,  the  ratio  of  deaths 
by  consumption  to  those  from  other  diseases,  gradually  diminishes.  But  further  statis- 
tics in  the  next  Table  (C)  will  prove  such  change  of  ratio  to  proceed,  not  from  absolute 
decrease  of  consumptive  deaths,  but  entirely  from  increased  mortality  by  other  causes. 

The  practical  question,  what  part  of  the  United  States  is  most  favorable  to  con- 
sumptive invalids,  can  now  be  satisfactorily  answered,  so  far  as  average  yearly  results 
are  concerned,  from  Table  XVII  (C). 

Ratio  of  Consumptive  Deaths.,  to  10,000  Living. 


Group  of  States 

Ill 
22.3 

V 
21.5 

VI 
21.0 

I 
20.8 

IV 

18.5 

li 

16.9 

VII 

16.9 

Ratio 

Group  III  comprises  New  Jersey  and  Pennsylvania ;  V,  Delaware,  Maryland,  Dist. 
of  Columbia,  Virginia,  Kentucky  and  Missouri ;   VI,  States  south  of  lat.  36°  30' ; 

I,  New  England  and  New  York;    IV,  Ohio,  Indiana,  lUinois,  Iowa  and   Kansas; 

II,  Michigan,  Wisconsin,  Minnesota  and  Nebraska ;   VII,  Washington,  Oregon,  Cali- 
fornia, Utah,  Dacotah  and  New  Mexico. 

By  an  obvious  generalization,  the  first  four  groups,  comprising  the  A  tlantic  and 
Gulf  States,  from  Maine  to  Florida  and  from  Florida  to  the  borders  of  Mexico,  have 
very  nearly  the  same  rate  of  consumptive  deaths,  or  21  annual  deaths  to  10,000  living. 
The  Western  States  show  a  decrease  of  the  consumptive  rate  to  \%\  in  group  IV; 
while  the  groups  II,  and  VII,  or  the  Northwestern  and  Pacific  States  agree  in  the 


56 


MEDICAL    STATISTICS. 


A  SANITARY  SURVEY  OP  THE   UNITED   STATES. 

The  bold  figures  refer  to  the  seven  groups  of  States  in  the  margin.  The  respective  annexed  figures  are  arranged  In 
ascending  order,  to  show  the  Proportional  Deaths  by  each  disease,  among  10,000  Insured  Males,  living  in  each  group  of 
States.  From  Table  XVII  (C). 


Diseased. 


AH  Causes. 


Zymotic  Diseases 

Constitutional  Diseases. 

Nervous  Diseases 

Circulatory  Diseases 

Respiratory  Di  seases .... 

Digestive  Diseases 

Miscellanous  Diseases. . . 

Typhoid  and   Typhus  I 

Fever J 

Malarial  Fever 

Erysipelas 

Dysentery 

Diarrhoea 

Cholera 

Alcoholism 

Other  Zymotic  Diseases. 

Dropsy 

Cancer 

Consumption 

Other     Constitutional } 
Diseases f 

Apoplexy 

Congestion  of  Brain 

Paralysis,     Softening,  J 

etc.  of  Brain      J 

Epilepsy  and  Convul- 1 

sions ( 

Other  Nervous  Diseases. 

Diseases  of  Heart 

Other  Circulatory  Dis- ) 
eases J 

Pneumonia 

Congestion  of  Lungs 

Bronchitis  and  Pleurisy. 
Abscess,  Hemorrhage,  ) 

etc.  of  Lungs J 

Other  Respiratory  Dis- 1 

eases ( 

Diseases  of  Stomach 

Diseases  df  Bowels 

Peritonitis 

Diseases  of  Liver 

Other   Digestive   Dis-  I 
eases... ~. f 

Diabetes...; 

Diseases  of  Kidneys 

Other  Urinary  Diseases. 
Abscess,  Hemorrhage,  I 

Old  Age ( 

Debility,    Exhaustion,  (^ 

Prostration ) 

Accidents  and  Injuries.. 

Suicides 

Unknown  Causes 


Least  Mortality. 


2    97.7    4  104.5    1  105.3    3  107.1 


15.9 
21.4 
11.5 

4.4 
12.1 

8.6 
16.0 


1.6 

1.1 

16.9 

1.0 


16.6 
22.1 
14.4 

4.6 
13.3 

9.1 
16.6 


1.8 
1.5 
16.9 
1.0 


17.6 
23.0 
15.4 
6.6 
14.6 
10.0 
17.3 


1.9 
1.6 
18.5 
1.4 


18.5 
26.3 
15.4 
6.7 
14.6 
11.2 
17.4 


1.9 

1.9 

20.8 

1.4 


Greatest  Mortality. 


7   112.2    5   130.5    6  170.5 


18.7 
26.4 
18.4 
6.8 
16.6 
11.2 
18.9 


6.9 
3.3 
1.3 
1.7 
1.0 
2.0 
.4 
3.7 


2.2 

2.1 

21.0 

1.4 


27.5 
27.3 
20.1 
7.3 
18.1 
11.9 
22.9 


2.2 

2.1 

21.5 

1.7 


10.8 
2.2 
2.2 
3.4 
.9 


.6 
3.1 
1.1 
1.2 
1.3 
12.8 
2.1 
1.8 


48.4 
27.9 
22.3 
9.2 
21.5 
22.0 
23.2 


8.5 
11.8 
2.2 
5.8 
3.6 
3.5 
.6 
18.2 


2.6 

2.2 

22.2 

2.0 


12.6 
2.2 
3.4 
2.4 
1.4 


3.5 
1.2 
1.3 
24 
13.3 
3.3 
2.5 


Mean 


118.3 


2.3.3 
24.9 
16.8 
6.5 
15.8 
12.0 
18.9 


6.6 
3.8 
1.4 
2.3 
1.3 
1.7 
.4 
5.9 


2.0 
1.8 
19.7 
1.4 


5.8 
2.4 
6.8 
.6 
1.1 


6.0 
.6 


9.2 
1.7 
2.1 
2.1 

.8 


2.3 
2.7 
.7 
.3.6 
2.6 

.5 
2.4 

.9 
1.0 
1.2 
9.6 
1.8 
i.5 


Groups. 

1. 

New  England. 
New  York. 

2. 

Northwest. 

Michigan. 
Wisconsin. 
Minnesota. 
Nebraska. 


New  Jersey. 
Pennsylvania. 

4. 

Ohio. 

Indiana. 
Illinois. 
Iowa. 
Kansas. 

5. 

Delaware. 

Maryland. 

Dist  Columbia. 

Virginia. 

Kentucky. 

Missouri 

6. 

South  of  36°  30'. 

North  Carolina. 

South  Carolina. 

Tennessee. 

Gteorgia. 

Florida. 

Alabama. 

Mississippi. 

Arkansas. 

Louisiana. 

Texas. 


Pacific,  etc. 

Washington. 

Oregon. 

California. 

Utah. 

Dakotah. 

New  Mexico. 


MEDICAL    STATISTICS.  57 

more  favorable  rate  of  17  consumptive  deaths  to  10,000  living.  In  establishing  these 
important  conclusions,  the  statistics  entirely  concur  without  discordance.  Invalids 
experiencing  this  or  any  other  disease  will  be  interested  to  note  the  effect  of  climatic 
conditions  shown  in  the  accompanying  Sanitary  Survey  of  the  United  States. 

Relation  of  Height  and  "Weight. 

For  convenient  reference,  the  following  Standard  Table  is  introduced,  showing  the 
average  or  most  healthful  Weight  relative  to  a  given  Height  or  stature.  The  medium 
circumference  around  the  chest  is  added,  although  of  less  importance.  "As  a  rule, 
twenty  per  cent,  or  one-fifth  is  almost  the  maximum  variation  from  this  within  the 
limits  of  health."  The  Table  is  especially  applicable  to  the  medical  examination  of 
males  between  30  and  60  years  of  age,  relative  to  consumption. 

Height.  Weight. 


5  feet 

1 

inch 

5'    « 

2 

(( 

5     '' 

3 

« 

5     " 

4 

(( 

5     " 

5 

a 

5    « 

6 

(( 

5    " 

7 

(I 

5     " 

8 

li 

5     " 

9 

u 

5     « 

10 

li 

5     " 

11 

« 

6    « 

0 

a 

Should 

weigh 

120  lbs. 

a 

(I 

125   « 

a 

a 

130   " 

(( 

i( 

135   « 

a 

li 

140   « 

<( 

11 

143   « 

a 

11 

145   « 

(( 

li 

148   « 

(( 

11 

155   " 

ti 

11 

160  « 

ti 

11 

165   " 

u 

ii 

170   " 

Medium 

Chest. 

34.06 

inches. 

35.13 

11 

35.70 

11 

36.26 

(I 

36.83 

11 

37.50 

« 

38.16 

(( 

38.53 

11 

39.10 

11 

39.66 

11 

40.23 

u 

40.80 

li 

SECTION     III. 

Tlie  G-erm  Theory  of  Malarial  Diseases.     Table  of  Sickness 
and  Recovery  in  Adult  Life. 

The  statistics  of  Fever  in  Table  IX  comprise  nine  or  ten  kindred  varieties,  all  of 
which  are  included  in  the  general  class  of  Zymotic  diseases,  of  which  the  family  of 
fevers  constitutes  about  three-fifths.  Malarial  Fever  is  used  to  designate  yellow  fever, 
remittent  fever,  and  intermittent  fever  or  fever  and  ague ;  to  which  some  would  add 
one  or  two  other  varieties,  with  a  part  of  the  cases  of  fever  unspecified.  Table 
XVII  (C)  will  show  that  Zymotic  diseases  including  fevers,  have  been  the  most 
prevalent  in  the  groups  of  States,  V  and  VI.  And  the  more  extended  Table  VII  will 
suggest  the  separation  of  Alluvial  counties,  as  a  class,  in  which  the  greatest  mortality 
has  occurred.  It  may  also  be  observed,  that  a  large  portion  of  the  insurances  in 
group  V  are  located  in  the  chief  cities,  including  Baltimore,  Washington  and  St.  Louis. 

The  space  already  given  to  medical  Statistics,  will  here  forbid  a  more  extended 
discussion  of  fevers  and  other  diseases.  Yet  the  growing  importance  of  the  germ 
theory  of  miasm,  and  its  favorable  acceptance  among  physicians,  may  claim  a  passing 
notice. 

Our  knowledge  of  the  phenomena  of  fevers,  is  announced  to  be  especially  pro- 
moted by  discoveries  with  the  microscope.  In  examining  the  organs  and  secretions 
of  persons  who  have  died  of  fever,  the  membrane  lining  the  stomach  was  almost 


55 


MEDICAL    STATISTICS. 


invariably  covered  with  a  multitude  of  microscopic  plants.  These  often  covered  the 
whole  intestinal  tract ;  some  were  found  on  the  surface  of  the  lungs,  and  some  were 
detected  in  the  blood.  On  living  patients,  these  parasites  have  been  found  in  the 
substance,  which  is  formed  at  an  advanced  stage  of  the  fever,  at  the  corners  of  the 
mouth  and  eyes.     In  the  secretions  of  persons  in  full  health  they  cannot  be  detected. 

Water  taken  up  and  placed  in  the  rays  of  the  sun  till  stagnant,  became  coated  with 
a  green  superficial  film,  on  which  the  microscope  showed  plants  closely  resembling 
those  found  in  the  human  body.  Some  of  these  parasites  showed  cell-articulations; 
others  were  hollow  and  others  showed  nuclei  and  spores. 

A  writer  on  the  causes  of  Ague  remarks  that  of  these  "ague  plants"  is  formed 
the  greyish  film  wherever  black  damp  earth  is  turned  up  and  exposed  to  the  sun. 
Thence  issue  innumerable  atomic  seeds  or  spores  which  rise  into  the  air,  carrying 
pestilence  with  them.  The  danger  from  their  growth  is  greatest  in  a  hot  dry  season 
following  a  wet  one. 

By  day,  the  atmosphere  is  shown  by  the  microscope  to  be  free  from  those  organ- 
isms. After  sunset,  the  spores  of  the  "ague  plants"  rise  with  the  evening  dews, 
recalling  "  the  pestilence  that  walketh  in  darkness." 

In  different  parts  of  the  world,  these  cryptogamic  spores  rise  in  the  night  mists, 
to  definite  heights.  In  the  United  States,  they  seldom  rise  more  than  thirty-five  to 
sixty-five  feet  above  the  low  levels ;  in  England,  not  more  than  from  fifteen  to  thirty  feet. 
But  the  spores  of  the  "ague  plants"  having  risen  and  become  entangled  in  the  mists, 
may  all  be  carried  by  the  wind,  far  perhaps  from  the  place  of  germination. 

"Around  the  entire  continent  of  Africa,  except  where  the  headlands  jut  out  into 
the  sea,  there  extends  a  belt  of  low  malarious  country  from  twenty  to  sixty  miles  wide. 
Within  this  belt  it  is  unsafe  for  an  unacclimated  person  to  spend  a  night,  although,  as 
the  malaria  does  not  extend  higher  than  about  twelve  feet  from  the  ground,  it  is 
believed  that  it  greatly  conduces  to  health  to  sleep  in  the  second  or  third  story. 
Travelers  visiting  Africa  should  at  once  go  to  the  higher  lands,  not  allowing  themselves 
to  sleep  a  single  night  on  the  coast." 

According  to  this  theory,  the  therapeutical  effect  of  cinchona  bark  and  its  alka- 
loids, in  malarial  fevers,  is  due  to  a  process  of  withering  or  destroying  the  fast  growth 
of  the  poisonous  fungoids  in  the  human  system.  Recently,  Pasteur  has  extended  inocula- 
tion with  "cultivated  "  germs  of  disease,  to  protect  life  against  the  more  malignant  tvpes. 


TABLE  OF  SICKNESS,  RECOVERY  AND  MORTALITY.* 


At  the  BEGmNiNG  of  the 

Yb.  or  AoB. 

In  the  ensuing  Twelve  Months. 

Pbecise 
AeE. 

4 

Weeks  of  Sickness. 

AVEBAGE. 

Numbeb 

NUMBEB 

NuitBEB 

Casks  of 

Cases  of 

Died. 

^ 

Living. 

Healthy. 

Sick. 

Sickness. 

Kecovebt. 

25 

1000 

981.3 

18.7 

222.4 

214.2 

7.0 

.969 

(1872.) 

0.78 

30 

1000 

980.5 

19.5 

206.6 

197.1 

8.5 

.998 

0.86 

35 

1000 

980.7 

19.2 

206.6 

197.5 

8.5 

1.024 

1.01 

40 

1000 

977.7 

22.3 

209.4 

198.0 

11.4 

1.160 

1.17 

45 

1000 

975.3 

24.7 

212.4 

199.8 

12.0 

1.304 

1.48 

50 

1000 

968.8 

31.2 

227.1 

211.6 

14.8 

1.644 

1.98 

65 

1000 

962.2 

37.8 

244.4 

224.6 

19.8 

1.973 

2.72 

60 

1000 

950.4 

49.6 

2651 

233.8 

27.6 

2.684 

4.03 

65 

1000 

927.6 

72.4 

282.6 

242.9 

34.4 

3.913 

630 

70 

1000 

885.4 

114.6 

303.7 

236.1 

55.1 

6.306 

10.08 

75 

1000 

811.8 

188.2 

307.8 

231.8 

78.2 

9.760 

15.07 

80 

1000 

723.6 

276.4 

298.6 

183.6 

135.4 

13.664 

20  71 

*  Abstract  of  800,000  observations  in  Friendly  Societies,  from  Assurance  Magazine,  Vol.  16,  p.  413.  To  show  Healthy 
Life,  cases  of  chronic  sickness  and  the  returns  from  sailors,  miners  and  colliers  were  left  out  by  Mr.  Finlaison.  Only  the 
last  column,  from  Mr.  Batcliffe's  collection  in  (1873),  iuclodes  AU  Classes. 


TIME  AND   MONETARY   TABLES.  59 


DIVISION     FOURTH, 

TIME     AND     MONETARY     TABLES. 
Fob  Interest  and  Annuiiies  Certain. 

SECTION    I. 
The  System  of  Interest  and  Annuities. 

By  general  custom,  interest  is  understood  to  increase  uniformly,  by  equal  incre- 
ments of  interest  in  equal  times,  during  twelve  months  or  the  period  of  conversion,  and 
is  then  added  to  the  principal,  to  form  a  new  principal.  When  the  interest  is  added  at 
the  end  of  each  successive  year,  it  is  said  to  be  compounded  annually ;  when  the  interest 
is  added  to  the  principal  at  the  end  of  every  six  months,  it  is  said  to  be  compounded 
semi-annually,  and  so  on. 

When  the  rate  of  interest  is  6  per  cent,  for  example,  the  increase  on  $1  principal  is 
$0,005  monthly,  which  at  the  end  of  twelve  months  or  a  year,  amounts  to  $1.06.  Or 
omitting  the  character  $  or  £  the  yearly  interest  on  1  unit  of  money  is  in  this  case 
0.06.  Let  i  denote  .04,  .05,  .06  or  any  other  rate  of  interest  on  1  for  one  year;  then 
will  1  +  1  denote  the  amount  at  the  end  of  a  year.  By  proportion,  1  :  l  +  ^ :  :  new 
principal  \-\-i\  (l  +  i)*,  the  amount  at  the  end  of  two  years.  In  like  manner  (1  +  i)^ 
will  be  the  amount  of  1  at  the  end  of  three  years.  And  in  general,  (1  +  iY  expresses 
the  amount  of  1  at  the  end  of  n  years,  with  compound  interest. 

The  'present  value  of  1  payable  at  the  end  of  a  year,  is  such  a  sum  v  as  with 
its  interest,  will  exactly  amount  to  1.      By  proportion  1  :  1  +  t  : :  v  :  1 ;    whence 

V  =  - — :  =  (l  +  i)-i.     Thus  defined,. V  is  the  present  value  of  1  receivable  at  the  end 

of  a  year;  and  v"  is  the  present  value  of  1  payable  at  the  end  of  n  years. 

Annuities.  On  this  principle,  the  whole  amount  of  1  per  annum,  payable  at  the 
end  of  each  year,  with  compound  interest,  will  at  the  end  of  any  number  n  of  years, 
evidently  be  the  sum  of  the  geometric  series, 

(l+^•)«-l4.(l  +  ^);^2+  ....  +(i4.f)  +  i  =  (l+t)»-l  ^  ^ 

In  like  manner,  the  whole  present  value  of  1  per  annum,  payable  and  discounted 
at  the  end  of  each  year,  will  be,  for  n  years, 

\  —  V  I 

It  may  be  proper  to  observe,  that  the  sum  of  the  preceding  series  has  long  since 
been  demonstrated  without  geometrical  progression.     Thus  at  the  rate  of  interest  i, 


60-61  TIME   AND    MONETARY   TABLES. 

the  annual  income  from  the  so-called  perpetuity  -  will  evidently  be  1,  to  continue  for- 

ever.     Deducting  from  this,  the  present  value  of  tlje  perpetuity  deferred  n  years,  that  is 

^      .  — ,  we  have  the  expression  equal  to  V  above,  or  the  present  value  of  n  annual 

payments  of  1.    And  multiplying  this  whole  present  value  by  (1  +  t)",  we  reproduce  the 
above  amount  A  for  the  end  of  n  years. 

In  practice,  these  formulas  are  seldom  computed ;  since  time  and  labor  are  saved 
by  recourse  to  the  standard  Monetary  Tables  of  present  values  and  amounts,  calculated 
for  various  rates  of  interest.  And  ge^ierally,  $1  and  its  tabular  result,  or  the  latter 
alone  when  multiplied  hy  the  proposed  principal  or  number  of  dollars,  gives  the  value 
required,  in  practical  business. — For  the  Value  of  an  Increasing  Annuity,  see  page  376. 

Tabic  XVIII  is  a  Time  Table  gi^■ing  in  triple  columns  the  day  of  the  month  and 
the  day  of  the  year,  also  the  corresponding  decimal  of  a  year  of  365  days.  The  star  (*) 
designates  Monday,  or  one  day  in  the  week  (as  shown  in  the  last  column),  from  which 
any  adjacent  day  of  the  week  is  readily  noted.  Also  from  any  given  date,  the  interval 
to  the  end  of  the  year  is  found  by  subtracting  the  day  of  the  year  from  365,  in  com- 
mon years,  or  the  corresponding  decimal  of  a  year  from  1;  to  be  increased  for  any 
extension  into  the  following  year. 


SECTION     II. 
Interest  Tables  for  Days. 

Required  the  interest  on  $4500  from  May  27  to  Sept.  8  at  6  per  cent.  The 
difference  of  the  days  of  the  year  in  the  Time  Table,  147  and  251,  gives  the  interval  104 
days  ;  which  guides  in  the  same  Table,  to  the  fraction  of  a  year  0.28493.  The  interest 
for  a  whole  year  is  4500  x.06;  that  is  270;  and  the  product  of  270  by  the  preceding 
fraction  gives  $76.93,  the  interest  required.  But  the  next  Table  is  designed  to  give 
the  interest  by  a  more  convenient  process. 

Copy  Multiplication  Table.  In  this  Table,  from  which  the  Interest  Table  origi- 
nated, the  carrying  figure  is  added  to  the  next  product  figure,  as  usual,  and  the  sum 
given  by  inspection.  It  presents  within  a  convenient  compass,  a  generalization  of  the 
common  process,  and  was  suggested  to  the  writer,  by  the  early  design  of  "Napier's 
rods  or  bones,"  by  the  first  Table  of  Crelle,  the  Tables  of  Laundy,  and  others.  For 
large  numbers,  or  "contracted  multiplication,"  it  appears  specially  adapted,  as  well  as 
for  "  proof,"  or  correction  of  the  common  method,  and  various  otlier  objects. 

The  bold  types  or  figures  of  the  Table,  taken  singly,  represent  every  possible 
multiplicand,  however  extended.  These  are  repeated  immediately  over  their  product 
figures,  which  may  be  copied  rapidly  in  any  order,  as  from  left  to  right.  In  a  few 
places,  the  construction  of  the  Table  required  10  to  be  tabulated  as  a  single  figure, 
denoted  by  X  or  z,  and  so  written.  But  after  the  usual  addition,  this  character  will 
disappear  in  the  final  product.  Also  by  practice,  an  easy  habit  may  be  acquired  of 
reading  off  two  figures  at  a  time.  Thus  on  reading  94  (nine,  four)  of  the  multiplicand, 
look  first  under  9  only,  to  read  off  its  product  figure  7,  passing  immediately  under  4  to 
find  the  other  figure  1,  and  copy  71.  The  same  routine  must  be  strictly  followed  in 
every  example,  as  follows : 

1.  Prefix  a  small  cipher  to  the  multiplier  to  distinguish  it,  and  to  be  used  as  its 
first  figure.  On  account  of  "carrying  figures"  in  the  construction  of  the  Table,  all 
single  ciphers,  when  effective,  are  to  be  treated  like  significant  figures. 


TIME   AND    MONETARY   TABLES. 


MULTIPLICATION. 


0 

100 

200 

300 

400 

( 

00 

01  23  45  67  89 

00  00  00  00  00 

01  23  45  67  89 

01  23  45  67  89 

0123  45  67  89 

03  46  80  24  68 

01  23  45  67  89 

03  69  35  81  47 

01  23  45  67  89 

04  83  60  48  36 

00 

12 
13 
15 
17 

01  23  45  67  89 

00  00  00  00  01 

01  23  45  67  89 
00  00  00  00  11 
0123  45  67  89 

00  00  00  01  11 

01  23  45  67  89 

00  00  00  11  n 

01  23  45  67  89 

01  23  45  67  8x 
01  23  45  67  89 
01  33  45  67  9x 
0123  45  67  89 
01  23  45  68  9x 
0123  45  67  89 
01  33  45  78  9x 

01  23  45  67  89 

02  46  80  24  69 

01  23  45  67  89 

02  46  80  24  79 
01  23  45  67  89 

03  46  80  25  79 
01  23  45  67  89 
03  46  80  35  79 

01  23  45  67  89 

03  69  25  81  48 
01  23  45  67  89 
03  69  35  81  58 
01  23  45  67  89 
03  69  25  82  58 
01  23  45  67  89 
03  69  25  92  58 

01  23  45  67  89 

04  83  60  48  27 
01  23  45  67  89 
04  82  60  48  37 
0123  45  67  89 
04  82  60  49  37 
01  23  45  67  89 
04  82  60  59  37 

12 
13 

15 
17 

20 
23 
25 
29 

012345  67  89 

00  00  01  11  11 

01  23  45  67  89 

00  00  01  11  12 

01  23  45  67  89 
00  00  11  11  22 
0123  45  67  89 

00  00  11   13  22 

0123  45  67  89 

01  23  46  78  90 
01  23  45  67  89 
01  33  46  78  91 
01  23  45  67  89 
01  33  56  78  xl 
01  23  45  67  89 
01  23  56  79  xl 

01  23  45  67  89 

03  46  81  35  79 
01  23  45  67  89 
03  46  81  35  7x 

01  23  45  67  89 

02  46  91  35  8x 

01  23  45  67  89 

02  46  91  36  8x 

0123  45  67  89 

03  69  26  93  58 
01  23  45  67  89 
03  69  26  92  59 
0123  45  67  89 
03  69  36  92  69 
0123  45  67  89 
03  69  36  93  69 

01  23  45  67  89 

04  83  61  59  37 
01  23  45  67  89 
04  82  61  59  38 
0123  45  67  89 
04  82  71  59  48 
01  23  45  67  89 
04  82  71  5x  48 

20 
23 
25 
29 

30 
34 
38 

01  23  45  67  89 

00  00  11  12  22 

01  23  45  67  89 

00  01  11  32  33 

01  23  45  67  89 

00  01  11  33  33 

01  23  45  67  89 

01  23  56  79  01 
01  23  45  67  89 
01  34  56  89  03 
01  23  45  67  89 

01  24  56  89  12 

01  23  45  67  89 

02  46  91  36  80 

01  23  45  67  89 

02  47  91  46  81 

01  23  45  67  89 

02  47  91  46  91 

01  23  45  67  89 

03  69  36  93  69 
01  23  45  67  89 
03  6x  36  x3  6x 
0123  45  67  89 

03  6x  36  x3  7x 

01  23  45  67  89 

04  82  71  50  48 
01  23  45  67  89 
04  83  71  60  49 
01  23  45  67  89 

04  83  71  60  59 

30 
34 
38 

40 
43 
45 

01  23  45  67  89 

00  01  13  33  33 

01  23  45  67  89 

00  01  13  33  33 

01  23  45  67  89 

00  01  13  33  34 

01  23  45  67  89 

01  24  57  89  12 
01  23  45  67  89 
01  24  57  8x  12 
0123  45  67  89 

01  24  57  8x  13 

0123  45  6789 

02  47  92  46  91 

01  23  45  67  89 

02  47  92  47  91 
01  23  45  67  89 

03  47  93  47  92 

0123  45  6789 

03  60  37  03  70 
01  23  45  67  89 
03  60  37  04  70 
01  23  45  67  89 
03  60  37  04  71 

01  23  45  67  89 

04  83  72  60  59 
01  23  45  67  89 
04  83  73  61  59 
01  23  45  67  89 

04  83  73  61  5x 

40 
43 
"45 

50 
56 
58 

01  23  45  67  89 

00  11  33  33  44 

01  23  45  67  89 

00  11  33  33  45 

01  23  45  67  89 
00  11  33  34  45 

01  23  45  67  89 

01  34  67  90  23 
01  23  45  67  89 
01  34  67  90  34 
01  23  45  67  89 

01  34  67  91  34 

0123  45  67  89 

02  57  02  57  02 
01  23  45  67  89 

03  57  03  57  03 
01  23  45  67  89 

03  57  03  58  03 

01  23  45  67  89 

03  70  47  14  81 
0123  45  67  89 
03  70  47  14  82 
01  23  45  67  89 

03  70  47  15  82 

01  23  45  67  89 

04  93  83  71  60 
01  23  45  67  89 
04  93  83  71  61 
01  23  45  67  89 

04  93  83  73  61 

50 

56 
58 

60 
63 
67 

0123  45  6789 

00  11  33  34  45 

01  23  45  67  89 

00  11  33  34  55 

01  23  45  67  89 

00  12  23  44  56 

01  23  45  67  89 

01  34  68  91  34 
01  23  45  67  89 
01  34  68  91  34 
01  23  45  67  89 
01  85  68  xl  35 

01  23  45  67  89 

03  57  03  58  03 
01  23  45  67  89 
03  57  03  58  13 
01  23  45  67  89 

03  58  03  68  14 

01  23  45  67  89 

03  70  48  15  82 
0123  45  67  89 
03  70  48  15  92 
01  23  45  67  89 

03  71  48  25  93 

01  23  45  67  89 

04  93  83  73  61 
01  23  45  67  89 
04  93  83  72  71 
01  23  45  67  89 

04  94  83  82  72 

60 
63 
67 

70 
72 
75 
78 

01  23  45  67  89 

00  12  23  44  56 

01  23  45  67  89 

00  13  33  45  56 

01  23  45  67  89 

00  13  33  45  66 

01  23  45  67  89 
00  13  33  45  67 

01  23  45  67  89 

01  35  68  01  35 
01  23  45  67  89 
01  35  68  03  35 
01  23  45  67  89 
01  35  78  02  45 
01  23  45  67  89 
01  35  78  02  46 

01  23  45  67  89 

03  58  03  68  14 

01  23  45  67  89 

02  58  03  69  14 

01  23  45  67  89 

02  58  13  69  24 
0123  45  67  89 

03  58  13  69  35 

01  23  45  67  89 

03  71  48  25  93 
01  23  45  67  89 
03  71  48  26  93 
0123  45  67  89 
03  71  58  26  x3 
0123  45  67  89 
03  71  58  26  x4 

01  23  45  67  89 

04  94  83  82  72 
01  23  45  67  89 
04  94  83  83  72 
01  23  45  67  89 
04  94  93  83  82 
01  23  45  67  89 
04  94  93  83  83 

70 
72 
75 
78 

80 
84 
86 
88 
89 

01  23  45  67  89 

00  13  34  45  67 

01  23  45  67  89 

00  12  34  55  67 

01  23  45  67  89 

00  12  34  56  67 

01  23  45  67  89 

00  12  34  56  77 

01  23  45  67  89 
00  12  34  56  78 

0123  45  6789 

01  35  79  02  46 
01  23  45  67  89 
01  35  79  12  46 
01  23  45  67  89 

01  35  79  13  46 

0123  45  67  89 

01  35  79  13  56 

0123  45  67  89 

01  35  79  13  57 

01  23  45  67  89 

03  58  14  69  35 

01  23  45  67  89 
03  58  14  79  25 
0123  45  67  89 

02  58  14  7x  35 
01  23  45  67  89 

03  58  14  7x  35 
0123  45  67  89 
03  58  14  7x  36 

01  23  45  67  89 

03  71  59  36  04 
0123  45  67  89 
03  71  59  36  04 
0123  45  6789 
03  71  59  37  04 
01  23  45  67  89 
03  71  59  37  14 
01  23  45  67  89 
03  71  59  37  15 

01  23  45  67  89 

04  94  94  83  83 
01  23  45  67  89 
04  94  94  93  83 
01  23  45  67  89 
04  94  94  94  83 
01  23  45  67  89 
04  94  94  94  93 
01  23  45  67  89 
04  94  94  94  94 

80 

84 
86 
88 
89 

90 

01  23  45  67  89 

00  13  34  56  78 

01  23  45  67  89 

01  35  79  13  57 

01  23  45  67  89 

02  58  14  70  36 

01  23  45  67  89 

03  71  59  37  15 

01  23  45  67  89 

04  94  94  94  94 

90 

0 

100 

200 

300 

400 

For  intermediate  nombers  in  the  side  colamn,  use  the  upper  or  less.    Thus,  for  85,  86,  87,  or  88,  use  the  line  of  85. 


TIME   AND    MONETARY   TABLES. 


63 


MULTIPLICATION. 


500 

600 

700 

800 

900 

00 

01  23  45  67  89 

05  05  05  05  05 

01  23  45  67  89 

06  28  40  62  84 

01  23  45  67  89 

07  41  85  39  63 

01  23  45  67  89 

08  64  30  86  43 

01  23  45  67  89 

09  87  65  43  21 

00 

12 
13 
15 
17 

01  23  45  67  89 

05  05  05  05  06 
01  23  45  67  89 
05  05  05  05  16 
01  23  45  67  89 
05  05  05  06  16 
0123  45  67  89 
05  05  05  16  16 

01  23  45  67  89 

06  38  40  62  85 
01  23  45  67  89 
06  28  40  62  95 
01  23  45  67  89 
06  28  40  63  95 
01  23  45  67  89 
06  28  40  73  95 

01  23  45  67  89 

07  41  85  39  64 
01  23  45  67  89 
07  41  85  39  74 
01  23  45  67  89 
07  41  85  2x  74 
01  23  45  67  89 
07  41  85  3x  74 

01  23  45  67  89 

08  64  20  86  43 
01  23  45  67  89 
08  64  30  86  53 
01  23  45  67  89 
08  64  20  87  53 
0123  45  67  89 
08  64  20  97  53 

0123  45  67  89 

09  87  65  43  22 
01  23  45  67  89 
09  87  65  43  32 
01  23  45  67  89 
09  87  65  44  32 
01  23  45  67  89 
09  87  65  54  33 

12 
13 

15 
17 

20 
23 
25 
29 

012345  67  89 

05  05  06  16  16 
01  23  45  67  89 
05  05  06  16  17 
01  23  45  67  89 
05  05  16  16  27 
01  23  45  67  89 
05  05  16  17  27 

01  23  45  67  89 

06  28  41  73  95 
01  23  45  67  89 
06  38  41  73  96 
01  23  45  67  89 
06  38  51  73  x6 
01  23  45  67  89 
06  28  51  74  x6 

01  23  45  67  89 

07  41  86  30  74 
01  23  45  67  89 
07  41  86  30  75 
01  23  45  67  89 
07  41  96  30  85 
01  23  45  67  89 
07  41  96  31  85 

01  23  45  67  89 

08  64  21  97  53 
01  23  45  67  89 
08  64  21  97  54 
01  23  45  67  89 
08  64  31  97  64 
01  23  45  67  89 
08  64  31  98  64 

01  23  45  67  89 

09  87  66  54  33 
01  23  45  67  89 
09  87  66  54  33 
01  23  45  67  89 
09  87  76  54  43 
01  23  45  67  89 
09  87  76  55  43 

20 
23 
25 
29 

30 
34 
38 

01  23  45  67  89 

05  05  16  17  27 
01  23  45  67  89 
05  06  16  27  28 
01  23  45  67  89 

05  06  16  27  38 

01  23  45  67  89 

06  38  51  74  06 
01  23  45  67  89 
06  39  51  84  07 
01  23  45  67  89 

06  39  51  84  17 

01  23  45  67  89 

07  41  96  31  85 
01  23  45  67  89 
07  42  96  41  86 
01  23  45  67  89 
07  42  96  41  96 

01  23  45  67  89 

08  64  31  98  64 
01  23  45  67  89 
08  65  31  x8  65 
01  23  45  67  89 

08  65  31  x8  75 

01  23  45  67  89 

09  87  76  55  43 
01  23  45  67  89 
09  88  76  65  44 
01  23  45  67  89 

09  88  76  65  54 

30 
34 
38 

40 
43 
45 

01  23  45  67  89 

05  06  17  27  38 
01  23  45  67  89 
05  06  17  38  38 
01  23  45  67  89 

05  06  17  28  39 

01  23  45  67  89 

06  39  52  84  17 
01  23  45  67  89 
06  29  52  85  17 
01  23  45  67  89 

06  29  52  85  18 

01  23  45  67  89 

07  42  97  41  96 
01  23  45  67  89 
07  42  97  42  96 
01  23  45  67  89 

07  42  97  42  97 

01  23  45  67  89 

08  65  32  08  75 
01  23  45  67  89 
08  65  32  09  75 
01  23  45  67  89 
08  65  82  09  76 

01  23  45  67  89 

09  88  77  65  54 
01  23  45  67  89 
09  88  77  66  54 
01  23  45  67  89 

09  88  77  66  55 

40 
43 
45 

50 
56 
58 

60 
63 
67 

01  23  45  67  89 

05  16  27  38  49 
01  23  45  67  89 
05  16  37  38  4x 
01  23  45  67  89 
05  16  27  39  4x 

01  23  45  67  89 

06  39  62  95  28 
01  23  45  67  89 
06  39  62  95  29 
01  23  45  67  89 
06  39  62  96  29 

01  23  45  67  89 

07  52  07  52  07 
01  23  45  67  89 
07  52  07  52  08 
01 23  45  67  89 
07  52  07  53  08 

0123  45  67  89 

08  75  42  19  86 
0123  45  67  89 
08  75  42  19  87 
01  23  45  67  89 
08 .75  43  Ix  87 

01  23  45  67  89 

09  98  87  76  65 
01  23  45  67  89 
09  98  87  76  66 
01  23  45  67  89 

09  98  87  77  66 

50  i 

56 

58 

01  23  45  67  89 

05  16  28  39  40 
01  23  45  67  89 
05  16  28  39  50 
01  23  45  67  89 

05  17  28  49  51 

012345  67  89 

06  39  63  96  29 
01  23  45  67  89 
06  39  63  96  39 
01  23  45  67  89 
06  3x  63  x6  3x 

01  23  45  67  89 

07  53  08  53  08 
01  23  45  67  89 
07  53  08  53  18 
01  23  45  67  89 
07  53  08  63  19 

01  23  45  67  89 

08  75  43  10  87 
0123  45  67  89 
08  75  43  10  97 
01  23  45  67  89 
08  76  43  30  98 

01  23  45  67  89 

09  98  88  77  66 
0123  45  67  89 
09  98  88  77  76 
01  23  45  67  89 

09  99  88  87  77 

60 
63 
67 

70 
72 
75 
78 

01  23  45  67  89 

05  17  28  49  51 
01  23  45  67  89 
05  17  28  4x  51 
01  23  45  67  89 
05  17  38  4x  61 
01  23  45  67  89 
05  17  38  4x  62 

01  23  45  67  89 

06  30  63  06  30 
01  23  45  67  89 
06  30  63  07  30 
01  23  45  67  89 
06  30  73  07  40 
01 23  45  67  89 
06  30  73  07  41 

01  23  45  67  89 

07  53  08  63  19 
01  23  45  67  89 
07  53  08  64  19 
01  23  45  67  89 
07  53  18  64  39 
0123  45  67  89 
07  53  18  64  3x 

01  23  45  67  89 

08  76  43  30  98 
01  23  45  67  89 
08  76  43  31  98 
0123  45  67  89 
08  76  53  31  x8 
0123  45  67  89 
08  76  53  31  x9 

01  23  45  67  89 

09  99  88  87  77 
01  23  45  67  89 
09  99  88  88  77 
01  23  45  67  89 
09  99  98  88  87 
01  23  45  67  89 
09  99  98  88  88 

70 
72 
75 
78 

80 
84 
88 
88 
89 

01  23  45  67  89 

05  17  39  40  62 
01  23  45  67  89 
05  17  39  50  63 
01  23  45  67  89 
05  17  39  51  62 
0123  45  67  80 
05  17  39  51  72 
01  23  45  67  89 
05  17  39  51  73 

01  23  45  67  89 

06  30  74  07  41 
01  23  45  67  89 
06  30  74  17  41 
0123  45  67  89 
06  30  74  18  41 
0123  45  67  89 
06  30  74  18  51 
0123  45  67  89 
06  30  74  18  53 

01  23  45  67  89 

07  53  19  64  30 

01  23  45  67  89 

07  53  19  74  20 
01  23  46  67  89 
07  53  19  75  30 
01  23  45  67  89 
07  53  19  75  30 
01  23  45  67  89 
07  53  19  75  31 

0123  45  67  89 

08  76  54  31  09 
01  23  45  67  89 
08  76  54  31  09 
0123  45  67  89 
08  76  54  32  09 
01  23  45  67  89 
08  76  54  32  19 
01  23  45  67  89 
08  76  54  32  Ix 

01  23  45  67  89 

09  99  99  88  88 
01  23  45  67  89 
09  99  99  98  88 
01  23  45  67  89 
09  99  99  99  88 
01  23  45  67  89 
09  99  99  99  98 
01  23  45  67  89 
09  99  99  99  99 

80 
84 
86 
88 
89 

90 

01  23  45  67  89 

05  17  39  51  73 

01  23  45  67  89 

06  30  74  18  53 

01  23  45  67  89 

07  53  19  75  31 

01  23  45  67  89 

08  76  54  32  10 

01  23  45  67  89 

09  99  99  99  99 

90 

500 

600 

700 

800 

900 

• 

64  TIME   AND   MONETARY   TABLES. 

2.  The  rule  of  arithmetic  requires  "  the  multiplicand  to  be  successively  multiplied 
by  each  figure  of  the  multiplier."  So  here  the  left-hand  pointer  is  to  be  located  in  the 
Table  once  for  each  single  figure  of  the  multiplier,  by  finding  such  single  figure  at  the 
head  of  the  column,  and  passing  down  to  its  two  right-hand  companion  figures,  found 
at  the  side ;  such  three  figures  may  be  termed  a  triplet.  At  each  location  of  a  triplet, 
the  single  figures  of  the  multiplicand  are  all  to  be  read,  and  the  product  figures  under 
them  copied ;  each  line  beginning  one  place  to  the  right. 

3.  When  the  right-hand  figure  of  the  triplet,  noted  above,  locates  between  two  given 
figures  of  the  side  column  in  the  Table,  always  use  the  upper,  or  less  of  the  two.  And 
when  such  two  nght-hand  figures  of  a  triplet  are  one  or  both  lacking  on  the  right 
hand  of  the  multiplier,  let  ciphers  be  assumed  in  their  place. 

Example.  Multiply  34986  by  753.  To  the  multiplier  752  prefix  a  cipher  making 
"752,  which  shows  there  will  be  four  locations  of  triplets.  First  "locate "  the  left-hand 
pointer  in  column  0,  under  the  line  75.  Here  finding  each  figure  of  the  multiplicand, 
as  34,  etc.  read  off  and  copy  the  figures  underneath,  as  23  etc.  from  left  to  right,  with 
the  right  hand. 

Common  Process.        34986  By  the  Table.        34986  Locations 

752  0  752  in  Table. 

69972  23664    -    -    -     075 

174930  20705     -    -    -     752 

244902      ,  50611     -    -    -    52» 

,      68862     -    -    -    2o« 


Product,       26309472 


Product,       26309472 


Again,  locate  the  left-hand  finger  or  pointer  for  the  triplet  752,  in  the  column 
7,  under  line  52,  or  rather  line  50  which  is  the  next  "  upper,"  and  beginning  to  copy 
20  etc.  one  place  to  the  right,  proceed  as  before.  Again,  locate  in  column  5,  under 
line  20,  etc.  Again  and  lastly,  locate  in  column  2,  under  line  00,  and  copy  as  before. 
In  adding  up  to  obtain  the  total  product,  the  sum  of  each  vertical  column  is  the  same 
as  when  found  by  the  common  method.  The  separately  written  triplets  "75,  752,  etc. 
noted  on  the  right  of  the  example,  for  illustration,  are  to  be  omitted  in  practice. 


SECTION     III. 

CompoTind  Interest  and  Discount  Tables.    For  Twelve  Kates 
of  Interest  and  for  100  Years. 

Table  XX.     The  Amount  of  $1  at  the  end  of  any  number  of  years;  or  (1  -ft)'*. 

Table  XXI.     The  Present  Value  of  $1  due  at  the  end  of  any  number  of  years ; 
that  is  v^  or  (1  -f  i)—^. 

Table  XXII.     The  Amount  of  $1  per  annum,  at  the  end  of  any  number  of  years ; 


or 


or 


The  annuity  of  II  is  payable  at  the  end  of  each  year. 

Table  XXIII.    The  Present  Value  of  II  per  annum,  for  any  number  of  years ; 


or 


TIME   AND    MONETARY    TABLES.  «5 

Table  XXIV.    The  Annuity  which  $1  will  purchase  for  any  number  of  years ; 

i 


1—(1 +  *■)-« 

It  is  the  Annual  Payment  or  Annual  Sinking  Fund  to  pay  a  present  debt  of  $1 
with  its  interest,  in  any  number  of  years. 

Table  XXV.  Common  LogaritJim  of  the  Present  Value  of  $1  due  at  the  end  of 
any  number  of  years;  a(14-i)-»,  or  Xv^. 

As  in  Milne's  treatise,  a  denotes  the  common  logarithm  of  the  quantity,  before 
which  it  is  placed. 

The  above  named  Monetary  Tables  are  derived  from  the  original  series  published 
by  John  Smart,  London,  1726.  A  portion  of  Smart's  Tables,  for  half  years  depend  on 
y/l  +  i  as  the  interest  factor  for  six  months.  But  mercantile  usage  has  decided  in 
favor  of  (1  +  0  as  the  yearly  factor,  and  (1+^i)  as  the  factor  for  the  odd  six  months  ; 
hence  the  half-yearly  columns  in  his  Tables  are  not  now  in  use.  A  part  of  Smart's 
Tables,  those  tinder  7  per  cent.,  we  have  here  collated  with  new  values  computed  with 
four  extra  decimals,  or  with  the  accurate  Tables  of  Chisholm. 

Connection  of  the  Tables.  It  will  be  observed  that  for  a  given  value  of  n  and  *, 
Tables  XX  and  XXI  are  each  the  reciprocal  of  the  other.  Tables  XXIII  and  XXIV, 
are  another  couple  haviug  the  same  reciprocal  property. 

Again,  the  amounts  in  Table  XX,  are  the  annual  differences  of  Table  XXII ;  and 
the  present  values  in  Table  XXI,  are  the  differences  of  Table  XXIII,  as  will  be  seen  by 
inspection. 

Amount  of  Premiums  paid.  For  illustration,  the  annual  premium  of  $50  has 
just  been  paid  at  the  beginning  of  the  seventh  year.  Eequired  the  amount  at  that 
date,  of  the  seven  premiums,  at  4  per  cent.  By  Table  XXII  the  amount  of  $1  annual 
premium  is  given  at  $7.89829;  the  product  of  this  by  50  is  $394.91,  the  amount 
required.  Had  it  been  a  single  premium  of  $50  paid  six  years  ago,  the  different  Table 
XX  would  give  50  x  1.2653  =  $63.27,  the  amount  at  compound  interest  4  per  cent. 

Deferred  Annuity.  If  the  annuity  of  $1  for  n  years  is  to  be  deferred  t  years  and 
then  commence,  the  present  value  is  evidently  shown  in  the  expression, 

,.      .,   ,     1— (l  +  «)-"      ,^ 
(l-f«)-<x ^  7  '      =Y,  or 

V 

\-(\  +  i)-t-n      l_(l.^,-)-<  ^  ^ 
i  i 

That  is,  from  the  present  value  of  an  annuity  for  t  +  n  years,  withdraw  that  of  t 
years.  A  deferred  annuity  is  sometimes  called  a  reversion  or  a  reversionary  annuity. 
Another  phrase  for  the  present  value  of  an  annuity  of  1,  is  "  the  number  of  years' 
purchase,"  or  "  years'  purchase,"  which  occurs  on  page  66,  Example  3. 

SECTION     IV. 
To  find  the  Rate  of  Interest  of  an  Annuity. 

In  these  Monetary  Tables  at  3,  3^,  4, ,  per  cent,  the  differences  of  |-  or  1  per 

cent.,  prove  to  be  so  large,  that  the  corresponding  columns  cannot  be  correctly  inter- 
polated by  first  differences,  horizontally,  except  when  the  correction  is  small.    Among 


66  TIME   AND    MONETARY    TABLES. 

various  methods,  an  approximate  solution  of  the  analytic  formula  was  given  by  Francis 
Baily  in  the  appendix  of  his  Doctrine  of  Interest  and  Annuities  in  1808.  But  the 
writer's  examination  of  this  noted  problem  was  suddenly  brought  to  a  close,  by  observing 
that  the  tabular  quantities  to  be  interpolated  are  nearly  in  geometrical  progression. 
Consequently,  interpolation  must  be  applicable  to  their  logarithms,  adjusted  by  induc- 
tion, as  follows : 

Let  n  =  the  given  number  of  years, 

X  =   "       "      amount,  or  the  present  value  of  $1  annuity ;  and 
i  =  its  rate  of  interest 

Entering  the  proper  Table  XXII  or  XXIII,  let  n,  X  guide  to  the  tabular  values 
A,  B,  nearest  to  X  which  falls  Ijetween  them,  and  let  a,  h  denote  their  respective  rates 
of  interest.   As  before  mentioned,  let  common  log.  A  be  denoted  by  AA,  and  so  generally. 

For  Amounts  in  Table  XXII,  /i  =  B„+i-B„.  For  Values  in  Table  XXIII, 
1i  =  ^Ai 

Example  1.  From  David  Jones  on  Annuities,  page  36.  "  At  what  rate  per  cent, 
will  £20  per  annum,  amount  in  10  years  to  £232.07?  " 

Here  n  =  10,  and  232.07^20  =  11.6035  =  X  amount  of  1  per  annum.  Table 
XXII,  13.14199—11.73139  =  h;    or    h  =  1.41.  k{X—h)  =  1.00832333. 

a  =  0.03,  A  =  11.463879,  A(A— A)  =  1.00233365. 

b  =  0.035,  B  =  11.731393,  A  (B— //)  =  1.01373832. 

*  =  .03  +  .005x^|^  =  0.0326260. 
.0114047 

The  true  value  is  0.0326261,  showing  a  difference  of  1  only  in  the  last  decimal 
place.  A  less  correct  result  0.03239  was  found  from  first  differences  of  the  numbers 
X,  A,  B. 

Example  2.  An  annual  payment  of  II  at  the  end  of  each  year,  has  amounted  to 
1763.387795  at  the  end  of  81  years.  Required  the  rate  of  compound  interest,  to  be 
interpolated  from  the  columns,  at  4  and  5  per  cent,  in  Table  XXII. 

Here  M  =  81,         7^  =  Bs^—Bs,  =  52.039513,        a  =  .04,        5  =.05. 

A(X— A)  =  2.8520823,        A(A— A)  =  2.7178828,        A(B—7i)  =  2.9862120. 

1341995 
i  =  0.04  +  .01x^-^r^  =  .045001;   true  value  .045000. 

Example  3.  "  The  Long  Annuities,  which  have  30  years  to  run,  are  now  sold  at 
19  years'  purchase  ;  what  rate  of  interest  does  the  purchaser  obtain  for  his  money  ? " 
From  David  Jones'  treatise,  page  42. 

By  Table  XXIII,    since  w  =  30,      ^  =  ^Ajs  =  5.968968,      a  =  .03,      h—  .035. 

X  =  19;   A(X-70  =  1.1149788,      A(A-70  =  1.1345428,     a(B-70  =  1.0942292. 

•         01 9*1840 
f  =  0.03  +  . 005  x;^j3-^  =  0.033426. 

The  true  value  found  by  Woolhouse,  is  0.032425.  The  preceding  method  can  also 
be  applied  to  interpolate  Life  Annuities,  according  to  the  relations  of  Makeham's  law. 


TIME  AND   MONETARY   TABLES.  67 

Note. — Since  the  ratio  1+i  differs  not  greatly  from  unity,  the  known  average  of  the  sum  of 
the  terms  must  be  nearly  equal  to  the  unknown  middle  term  of  the  geometric  series.  With  some 
adjustment,  we  have  thxis  found  a  ready  approximation  from  the  amount  of  $1  annuity : 


'(^  +  *'^=(^-4)"'l=I'-"^"^y- 


This  formula  when  applied  to  the  first  two  of  the  preceding  examples,  gives  approximately 
.03250  and  .04537,  which  may  be  further  corrected  by  the  method  of  trial  and  error  with  the  following 
formula  for  X  or  A. 

The  other  elements,  amount,  present  value  and  the  time  n  are  precisely  determined 
by  the  formulas : 

For  Amount,    A  =  '^        : ,  n  =   ,\,      ./. 

For  Present  Value,    V  =  ^-(1  +  ^')""  n  =  -  ^^f^. 


SECTION     V. 

To  find  the  Rate  of  Interest  on  the  Price  of  Funded  Stocks 

or  Bonds. 

In  the  first  case,  let  us  suppose  that  the  stocks  are  arranged  to  pay  a  fixed  interest 
forever,  or  perpetuities,  so  called,  as  in  most  of  the  government  debts  of  Europe. 
For  illustration,  if  £100  in  the  3  per  cent.  British  consols  are  sold  for  £93 ;  the  simple 
proportion  93  :  3  : :  100  :  a;,  gives  3.226  the  rate  of  interest,  to  be  realized  on  the 
purchase.  Although  the  £3  is  paid  half-yearly,  the  difference  from  an  annual  payment 
is  not  here  regarded,  on  account  of  the  frequent  change  of  rate,  or  delays  in  the 
re-investment  of  small  sums. 

In  the  second  case,  as  in  the  public  funds  of  the  United  States,  let  the  interest 
cease,  and  the  principal  be  repaid,  at  the  end  of  a  stated  number  of  years. 

Example  1.  A  Bond  bearing  6  per  cent,  interest,  and  having  20  years  to  run,  the 
principal  being  then  payable,  is  bought  at  the  price  of  $1. 05  on  the  dollar  of  par  value. 
What  rate  of  interest  will  the  purchaser  have  received  at  maturity  ? 

Let  i'  =  the  required  rate  of  interest  on  the  transaction. 
i  =  the  given  rate  of  interest  on  the  Bond. 
p  =  the  purchase  price  per  dollar  of  the  principal  of  the  Bond. 
n  =  the  number  of  years  the  Bond  is  to  run. 

Strictly,  the  annual  interest  i  is  to  be  regarded  as  an  annuity  for  n  years ;   the 

present  value  of  which  at  the  rate  i',  is  evidently ---X   ^ —  x  i  or  (1— v'")v,. 

V  'h 

The  purchase  price  p  must  be  equated  to  this,  plus  the  present  value  v'n  of  each  $1 
of  the  principal,  stipulated  to  be  paid  at  the  end  of  n  years.     That  is, 

'1 


— 1 
p  =  (1— v'«)  x-,  +  v'";  whence  i'=  — | — ^ 


p^p{l  +  i')^—l' 

^,^i{l-v''')^-    i{l-p) 
»—!;'»    ■  p—v'^' 


88 


TIME   AND    MONETARY   TABLES. 


For  _p  =  1,  i'  =  i.    For  n  =  \,  *'  =  -  + 1 — 1  j .    For  Perpetuities,  n  =  co,  i=-. 

As  the  period  n  approaches  40  years  and  upward,  this  last  formula  gives  a  close 
approximation. 

For  a  more  general  approximation,  we  assume  the  amount  p{l-\-i')'^  =:  (1  +  t)". 
Substituting  this  in  the  right-hand  member  preceding,  we  have  a  very  convenient 
second  approximation,  which  being  further  corrected  by  an  interpolated  time  n',  for 

ordinary  rates,  leads  to     ?i'  =  w  +  0. 6 1  —  1  j  n, 


<P 


i'  =zi+ 1 — 1  .V„';   where  Yn>  —  z -„  given  in  Tahle  XXIV. 


1— v" 


TABLE  OF   THE  AUXILIARY  FACTOR 


(i-0- 


Pbicb  on 
100. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

5 

1.0000 

0.9608 

0.9231 

0.8868 

0.8519 

0.8182 

0.7857 

0.7544 

0.7241 

0.6949 

6 

0.6667 

.6393 

.6129 

.5873 

.5625 

.5385 

.5152 

.4925 

.4706 

.4493 

7 

0.4386 

.4085 

.3889 

.8699 

.3514 

.3333 

.3156 

.2987 

.2821 

.2658 

8 

0.2500 

.2346 

.2195 

.2048 

.1905 

.1765 

.1628 

.1494 

.1364 

.1236 

9 

0.1111 

.0989 

.0870 

.0753 

.0638 

.0526 

.0417 

.0309 

.0204 

.0101 

10 

-.0000 

-.0099 

-.0196 

-.0291 

-.0385 

-.0476 

-.0566 

-.0654 

-.0741 

-.0826 

11 

-.0909 

-.0991 

-.1071 

-.1150 

-.1228 

-.1304 

-.1379 

-.1453 

-.1525 

-.1597 

12 

-.1667 

-.1736 

-.1803 

-.1870 

-.1935 

-.2000 

-.2063 

-.2126 

-.2187 

-.2248 

13 

-.2308 

-.2366 

-.2424 

-.2481 

-.2537 

-.2593 

-.2647 

-.2701 

-.2754 

-.2806 

14 

-.2857 

-.2908 

-.2958 

-.3007 

-.8056 

-.3103 

-.3151 

-.3197 

-.3243 

-.3289 

The  new  expression  for  i'  will  be  sufficient  for  most  purposes.  By  successive  sub- 
stitution, however,  in  the  right-hand  member  of  the  original  formula  preceding,  the 
approximation  <;an  be  carried  to  any  extent  of  accuracy. 

In  the  Example  stated  above,  the  price  on  100  is  105,  or  j»  =  1.05.  Also  n'  =  20 — 
0.6  X  .0476  X  20  =  19.4  years ;  whence  the  required  rate  of  interest 

i'  =  .06— .048  X  .088  =  .06— .0042  =  .0558. 

Here  the  factor  —.048  or  rather  .0476  is  found  in  the  above  Table,  corresponding 
with  the  price  105;  and  the  other  factor  V  or  .088  corresponds  to  n'  or  19.4  years  and 
6  per  cent,  in  Table  XXIV.  Provided  the  Bond  is  continued  to  maturity,  the  approxi- 
mate interest  realized  on  the  purchase  will  be  5.58  per  cent. 

Example  2.  Required  the  rate  of  interest  to  be  realized  when  the  price  is  75 
on  the  100,  or  p=:0. 75,  the  rate  of  interest  i  being  7  per  cent.,  and  the  Bond  to  be 
redeemed  in  40  years.  Here  ^i' =  40  +  0.6  x.  333  x  40  =  48  years;  then  i'=.07  + 
.333  x  .0728  =  .0942  ;  that  is,  9.42  per  cent,  on  the  purchase  price. 

Example  3.    When  n  =  30  years,  i  =  .06,p  =  0.5.     Then  w'  =  30  + . 6  x  1  x  30  = 
48  years,  i'  =  .06  +  1  x. 0639  =  .1239.     The  result  12.39  per  cent,  is  correct  to  four- 
places,  as  verified. 

It  is  worthy  of  remark  that  in  these  three  arbitrary  examples,  having  periods  of  20, 
40  and  30  years,  the  approximate  formula,  i'  =  i-^p,  should  give  results  so  near  the 
truth  as  5.71,  9.33  and  12.00;  the  true  rates  being  5.58,  9.42,  and  12.39  per  cent 
respectively. 


TIME   AND    MONETARY    TABLES.  69 

SECTION    VI. 
Interest  Compounded  Oftener  than  Once  a  Year.. 

When  interest  is  compounded  at  m  equal  intervals  in  a  year,  the  amount  at  the 
end  of  the  first  of  them  is  [  1 H —  j ;  and  this  raised  to  the  with  power,  gives  the  amount 
at  the  end  of  m  terms,  or  one  year ;  thus : 


H) 


When  interest  is  compounded  momently  or  at  the  end  of  every  instant,  the  number 
of  intervals  w  in  a  year  becomes  very  great  or  infinite,  which  evidently  causes  m  to 
vanish  in  the  right-hand  member,  leaving  at  the  year's  end, 

i  \m  1  1 


Here  e  is  the  number  whose  Napierian  logarithm  is  1;  that  is  e  =  2.7182818285. 
Thus  on  the  supposition  of  compounding  momently,  the  amount  of  $1  principal  at  the 
end  of  n  years,  will  be  £'«. 

In  the  common  formulas  of  compound  interest,  the  interest  for  one  interval  may 
take  the  place  of  annual  interest,  when  periods  of  conversion  are  substituted  for  the 
number  of  years.  And  if  there  are  m  equal  periods  in  one  year,  there  will  evidently 
be  nin  equal  periods  in  n  years.  Writing  m  equal  to  1,  2,  4,  or  infinity,  let  Y,  H,  Q, 
M  denote  the  Amount  of  $1  with  its  compound  interest,  at  the  end  of  n  years,  accord- 
ing as  the  interest  is  convertible  into  principal,  Yearly,  Half-yearly,  Quarterly,  or 
Momently. 


4n 


Then        Y  =  (l  +  *)~  Q=\^+4 

H^^l+I)"",  M=ein. 

The  Present  Value  of  1  due  n  years  hence,  with  interest  compounded  m  times  in 

the  year,  is 

y  \  — »i« 

1+- 
m) 

In  the  case  of  Annuities  payable  half-yearly,  quarterly,  or  generally  m  times  in 
the  year,  let  us ^rs/?^  assume  the  interest  to  be  compounded  in  the  same  way,  or  m  times 
in  the  year,  and  that  the  annuity  or  yearly  payment  of  1  is  divided  into  m  payments  of 

each,  at  equal  intervals.    Then  by  substitution  as  shown  by  Dr.  Price: 


m 


Amount  of  Annuity  for  n  years  =  — .  — 
Present  Value  of  Annuity  for  n  years  =  - 


1  +  :^)     -ij- 


ml 
1  + 


^n 


When  payable  yearly,  m  —  l;  half-yearly,  wi  =  2 ;  quarterly,  w  =  4. 


70  TIME  AND   MONETARY   TABLES. 

Secondly  and  more  generally,  let  interest  be  convertible  m  times  in  a  year,  and  the 
annuity  be  payable  m!  times,  each  payment  being  — ,.    In  this  case,  the  discount  factor 


m 

—m 


to  give  the  present  value  for  one  year,  is  I IH — j      ;  or  for  ^  years,  or  a  fraction,  the 

/  J  \—mt 

factor  is    IH — 1       .      Now  dividing  one  year  by  the  number  of  its  payments  of 

annuity,  we  have  —,  =  t,  the  time  or  interval  from  one  payment  to  another.    Hence 

the  present  value  of  the  pi'n  payments  in  n  years,  will  be  the  sum  of  the  geometric 
progression  ;  since  77i't  =  1 : 

w  1_\       mj  \       m)  \      m)  J 

I  \  —mt       j  i  \  — nm — mt  j  j  \  — mn 


.         .1+-  -    1+-  1        1-    1+- 

1      \       m  \       m  1  \       m 


m'  ,      L  .  i\-^^  m'       L  .  *\'^ 


1-  1+-  1  +  -      -1 

\       mj  \       mj 

When  m  and  m'  are  equal,  tbis  manifestly  coincides  with  the  last  formula  on 
page  69. 

In  the  denominator,  developing  by  the  binomial  theorem,  since  —;,  =  t, 


mj  m 


m 

m'     }nJ2     \7n'     m)\m'     in)l.2.d 


i+{~^]l+{^.-^M^.--.]~+---~\ 


Substituting  the  series  in  the  above  denominator,  and  dividing. 


iii-^ 


Present  Value  =  R+l(i_l\-(i,_i,).l-,-^+  .  ..1  x  fl-fl  ^^Y'^']. 
\_i     2\m     m  j      \m^     my        12  J      L       V       ^/       J 

In  the  case  of  annual  interest,  or  w  =  1,  we  have, 

Present  Value  =  (-+^  ~   ].[1— (l-ht)-^],  nearly, 
1— (l  +  t)-«     m'—l  ,  ^r    ,  m'—l 


When  the  annuity  is  half-yearly,  or  m'  =  2,  the  last  term  becomes  0.25;  which 
agrees  with  the  usual  approximate  correction  for  Life  Annuities.  More  accurately, 
when  i  =  .04,  the  third  term  of  the  series  above,  when  united  to  the  second,  gives 
0.24755.  This  correction  from  Annuities  Certain,  strikingly  agrees  with  those  com- 
puted by  Mr.  Sprague  from  Life  Annuities  at  ages  where  the  initial  rate  of  mortality 
plus  that  of  interest  equals  4  per  cent.  Compare  Journal  of  the  Institute,  Vol.  13, 
pp.  212,  308. 

Finally  for  illustration,  the  annexed  Table  from  David  Jones  on  Annuities  will 
indicate  the  effect  of  compounding  oftener  than  once  a  year  to  increase  the  yearly  rate 
of  interest.    In  long  periods  of  years,  the  difference  becomes  more  material: 


TIME   AND    MONETARY    TABLES. 


n 


AMOUNT    OF    $1    IN    ONE    YEAR,    AND    ITS    LOGARITHM. 


AlfNUAL 
BATE  OP 

Ikterest. 

Pat- 
able. 

Amount  in 
ONE  Yeae. 

LOGABITHH. 

Annual 

BATE  OP 

Intebest. 

Pay- 
able. 

Amount  in 
ONE  Ybab. 

Logarithm. 

2 

Y 

1.020000 

.00860  01718 

5 

Y 

1.050000 

.0^118  92991 

per  cent. 

H 

1.020100 

.00864  27476 

per  cent. 

H 

1.050625 

.02144  77808 

Q 

1.020150 

.00866  42470 

Q 

1.050946 

.02158  0:275 

M 

1.020201 

.00868  58896 

M 

1.051271 

.0217147241 

2| 

Y 

1.025000 

.01072  38654 

6 

Y 

1.060000 

.02530  58653 

per  cent. 

H 

1.025156 

.01079  00638 

per  cent. 

H 

1.060900 

.02567  44494 

Q 

1.025235 

.01082  35735 

Q 

1.061364 

.02586  41690 

M 

1.025315 

.01085  73620 

M 

1.061837 

.02605  76689 

3 

Y 

1.030000 

.01283  72247 

7 

Y 

1.070000 

.0293837777 

per  cent. 

H 

1.030225 

.01293  20845 

per  cent. 

H 

1.071225 

.02988  06996 

Q 

1.030339 

.01298  02193 

Q 

1.071859 

.03013  76716 

M 

1.030454 

.01302  88345 

M 

1.072508 

.03040  06137 

3i 

Y 

1.035000 

.0149403498 

8 

Y 

1.080000 

.03342  37555 

per  cent. 

H 

1.035306 

.01506  88358 

per  cent. 

H 

1.081600 

.03406  66786 

Q 

1.035462 

.01513  41909 

Q 

1.082432 

.03440  06870 

M 

1.035630 

.01520  03069 

M 

1.083287 

.0347435586 

4 

Y 

1.040000 

.0170333393 

9 

Y 

1.090000 

.03742  64979 

per  cent. 

H 

1.040400 

.01720  03435 

per  cent. 

H 

1.092025 

.03823  25809 

Q 

1.040604 

.01728  54951 

Q 

1.093083 

.03865  32667 

M 

1.040811 

.0173717793 

M 

1.094175 

.03908  65034 

Note. — The  period  required  for  a  given  principal  to  double  itself  at  compound  interest,  ia 
defined  by  the  well-known  equation  for  n  years, 

(1-Ht>  =  2,      n=, — Ti—K  =  — ^+0.35  nearly.  Also  (l-f-)     =2. 

Thus,  dividing  70  by  the  rate  of  interest  as  an  integer,  will  give  a  close  approximation,  easily 
remembered.  In  the  last  formula  making  m  =  l,  2,  4,  and  infinite  as  before,  we  find  the  following 
more  exact  series. 


Doubling  Period  in  Years  and  Decimals. 

Interest  compounded  yearly: 

Rate  per  cent.  2  3  4 

Doubling  Period. 


35.004       23.450       17.673 


Interest  compounded  semi-annually: 

Rate  per  cent.  2  3  4 

Doubling  Period.      34.830       23.278  17.502 

Interest  compounded  quarterly: 

Rate  per  cent.  2  3  4 

Doubling  Period.       34.743       23.191  17.415 

Interest  compounded  momently: 

Ratp,  per  cent.  2  3  4 

DouDllng  Period.      34.657       23.105  17.329 


5 

14.207 


5 
14.036 


5 
13.946 


5 

13.863 


6 
11.896 


6 
11.725 


6 
11.639 


6 
11.552 


7 
10.245 


7 
10.075 


7 
9.989 


7 
9.902 


8 
9.006 


8.837 


8 
8.751 


8 
8.665 


TABLES    IN    PART    FIRST, 


MORTALITY  AND  LOSS  EXPERIENCE,  Tables  I-IV.  Pages    74-166 

CLIMATIC  TABLES,      -    - "      V-VIH.         **      167-181 

MEDICAL  STATISTICS, "      IX-XVI.        "      182-198 

TIME  AND  MONETARY  TABLES,  -    -    -        «      XYII-XXV.  ''      199-231 


74 


TABLE    I. 


MALE  LIFE.     SUMMAKY  (A).     OBSERVATIONS  CLASSIFIED  ACCORDING  TO  THE  AGE 

OF  EXIT  OR  EXPOSURE. 


Age 

of 

Whole  Number  < 

jp  Ektbants,  982,734. 

2,568,856  Thousand  Dollabs 

Insubed. 

Age  at 

Exit  or 

Exposure. 

lib 

Exit. 

Existing. 

Discon- 
tinued. 

Died. 

Exposed  to 
Risk. 

Amounts 

Existing. 

Amounts 
Discontln'd. 

Death 
Claims. 

Exposed  to  Risk. 

0 

1 

3.5 

1 

6.5 

0-   i 

^  1 

9 

1 

34 

18 

2 

G6 

i-  H 

2 

8 

7 

69 

19 

9 

144.5 

H-n 

3 

6 

8 

86 

13 

26 

186 

2i-3i 

•4 

5 

8 

99 

11 

15 

211.5 

H-  4^ 

5 

10 

12 

107 

19 

25 

230 

4i-  H 

6 

8 

9 

105.5 

16 

19 

230.5 

H-6i 

7 

10 

10 

2 

110 

20 

21 

6 

241 

6i-  n- 

8 

14 

15 

108.5 

31 

'     24 

237 

7i-  8i- 

9 

7 

11 

1 

107.5 

23 

25 

1 

228.5 

8^-  9i 

10 

20 

14 

139 

49 

20 

289.5 

9i-10i 

11 

20 

28 

174 

42 

43 

361.5 

10^11% 

12 

32 

35 

239 

58 

59 

490.5 

lli-12^ 

13 

34 

46 

2 

361.5 

76 

77 

3 

741.5 

12i-13^ 

U 

•     74 

97 

3 

732.5 

129 

199 

3 

1,499 

13i-Ui 

15 

96 

212 

3 

1,405 

226 

388 

4 

2,863 

14i-15i 

16 

224 

394 

11 

2,375.5 

411 

764 

17 

4,632.5 

15^-16^ 

17 

353 

615 

24 

3,693 

667 

1,132 

36 

7,134 

16i-17^ 

18 

639 

972 

32 

5,736.5 

1,188 

1,817 

55 

11,035.5 

17l-18^ 

19 

940 

1,782 

68 

8,857.5 

1,666 

3,261 

118 

16,774.5 

18i-19^ 

20 

1,536 

2,845 

116 

13,773.5 

2,783 

5,308 

200 

26,120 

19^-20^ 

21 

2,383 

4,323 

158 

21,040.5 

4,376 

8,210 

266 

41,378.5 

20^21i 

22 

3,246 

6,335 

200 

30,596 

6,297 

12,672 

333 

62,732 

21^-22^ 

23 

4,452 

8,488 

312 

42,003 

8,711 

17,543 

609 

89,221.5 

22^-23^ 

2U 

6,044 

10,333 

326 

54,367:5 

12,056 

22,187 

707 

119,483 

23^24i 

25 

7,309 

11,753 

468 

67,546.5 

14,780 

26,663 

1,002 

152,867.5 

24^-25} 

26 

8,879 

13,346 

530 

80,629 

18,739 

30,876 

1,229 

186,725 

25^-261 

27 

10,221 

13,891 

639 

92,781 

21,831 

33,441 

1,452 

218,231.5 

26^27i 

28 

11,799 

14,782 

758 

106,513 

25,843 

35,733 

1,734 

250,743.5 

27i-28\ 

29 

12,876 

15,751 

784 

118,901 

28,841 

38,245 

1,925 

281,450 

28^-29^ 

30 

17,480 

16,082 

819 

129,868 

32,578 

40,227 

2,093 

312,842.5 

29i-30^ 

31 

15,092 

16,571 

961 

136,354 

34,273 

42,664 

2,410 

339,736 

SOiSli 

32 

15,991 

16,130 

979 

143,956.5 

37,781 

42,288 

2,444 

361,484 

31I-32I 

33 

16,618 

16,148 

1,057 

151,141 

38,901 

42,554 

2,788 

381,961 

32^-33^ 

34. 

17,784' 

'16,351 

1,193 

157,277.5 

42,133 

43,599 

3,213 

400,764.5 

33^-34^ 

35 

17,712 

16,286 

1,196 

161,673.5 

43,697 

43,855 

3,234 

414,914.5 

34i-35^ 

36 

18,444 

16,477 

1,218 

165,280.5 

46,172 

44,175 

3,380 

427,076 

35^-361 

37 

18,806 

15,497 

1,299 

166,330 

47,066 

43,243 

4,028 

432,046 

36i-37^ 

38 

18,850 

14,888 

1,403 

166,100 

45,893 

41,408 

3,865 

432,402 

37^-38^ 

39 

19,317 

14,325 

1,398 

164,729.5 

47,916 

40,246 

3,931 

432,874 

38l-39i 

40 

19,351 

13,675 

1,401 

162,619 

48,845 

38,935 

3,823 

430,914.5 

39^-40^ 

41 

19,683 

13,234 

1,430 

158,904.5 

49,273 

37,094 

4,091 

425,161.5 

401^4H 

^ 

18,465 

12,134 

1,401 

152,323 

46,579 

35,982 

4,023 

413,268 

4H-42i 

4-5 

17,165 

11,438 

1,456 

146,097 

44,676 

33,604 

3,941 

401,060 

42i-43i 

U 

17,305 

10,671 

1,446 

139,838 

44,846 

31,433 

4,055 

387,327 

43i-m 

45 

16,605 

9,847 

1,244 

133,033.5 

43„646 

29,657 

3,453 

372,103 

44h-45^ 

46 

16,518 

9,235 

1,339 

126,308.5 

43,846 

27,922 

4,012 

356,838.5 

45^4H 

47 

15,230 

8,397 

1,325 

117,740 

41,080 

25,782 

3,827 

336,969 

46i-47i 

48 

13,811 

7,536 

1,280 

109,560.5 

37,684 

24,249 

3,905 

317,001 

47i-48i 

49 

13,191 

6,891 

1,157 

102,105 

36,291 

21,180 

3,565 

298,249.5  \48i-49i 

TABLE    1. 


'3'0 


MALE  LIFE.    SUMMARY  (A).    OBSERVATIONS  CLASSIFIED  ACCORDING  TO  THE    AGE 

OF  EXIT  OR  EXPOSURE. 


Age 

Wholb  Number  < 

)p  Entbants 

,  982,734. 

2,568,856  Thocsand  Dollabs  Imscbed. 

"I 
Age  at 

n.t 

Exit  or 

at 

Exit. 
50 

Existing. 

Difecon- 

tinued. 

Died.        ^ 

Exposed  to 
Risk. 

Amounts 
Existing. 

Amounts 
Discontin'd.     C 

Death 
laimB. 

Exposed  to  Risk. 

Exposure. 

12,511 

6,243 

1,192       1 

34,951.5 

34,761 

19,532     3 

,554 

280,485 

49^-50^ 

51 

11,365 

5,780 

1,187     i 

^7,291 

32,004 

18,619     3 

,606 

260,386 

50^1^ 

52 

10,643 

4,935 

1,108     ' 

^9,336.5 

30,397 

16,366     3 

,487 

238,306.5 

5'H-52i 

53 

9,686 

4,413 

1,032      ' 

a,  744 

27,339 

14,529     3 

,227 

216,122 

524,-53'^ 

54 

9,480 

3,849 

988     ( 

34,574.5 

27,483 

13,619     2 

,975 

195,270 

53^54h 

55 

8,335 

3,294 

982     I 

)7,089.5 

25,161 

11,550     3 

,183 

172,957.5 

54^-55^ 

56 

7,582 

2,824 

876     { 

)0,184 

22,555 

9,552     2 

,744 

151,660 

55%-56\ 

57 

6,519 

2,360 

813     ^ 

t3,729 

19,400 

8,194     2 

,718 

132,555 

56^^-57^ 

58 

5,612 

1,922 

756     { 

58,164.5 

16,246 

6,837     2 

,313 

115,575 

57i>-58\ 

59 

4,985 

1,640 

721      c 

53,284.5 

14,851 

5,756     2 

,300 

101,140.5 

58^-59i 

6'0 

4,178 

1,348 

733     ^ 

J8,892 

12,630 

4,891      2 

,102 

87,621 

59^-60^ 

61 

3,637 

1,060 

649     ^ 

J4,959.5 

11,274 

3,784     2 

,130 

75,419.5 

60^-61^- 

62 

3,313 

798 

531      ^ 

Jl,189 

9,528 

2,915      1 

,624 

63,379.5 

61^-62^^ 

63 

2,849 

605 

509     ] 

L7,725 

8,712 

2,275      1 

,686 

53,175 

62^-63^ 

64 

2,333 

499 

457     ] 

L4,678.5 

6,748 

1,907     1 

,336 

43,325  - 

63^-641 

65 

2,056 

407 

416     ] 

.2,116.5 

6,023 

1,258     1 

,517 

35,712 

64i-6H 

66 

1,634 

311 

368 

9,732 

4,797 

1,204     1 

,080 

28,233 

65^-661 

67 

1,395 

246 

271 

7,716.5 

3,867 

798 

815 

22,082.5 

66i-67i 

68 

1,071 

150 

259 

6,042.5 

3,176 

601 

792 

17,188.5 

674j-68i 

69 

837 

130 

224 

4,694 

2,610 

431 

600 

13,025.5 

68^-69^ 

70 

586 

95 

189 

3,595.5 

1,602 

334 

528 

9,625 

69^-70^ 

71 

469 

68 

134 

2,783.5 

1,289 

211 

353 

7,322 

70^-71^ 

72 

365 

52 

136 

2,148 

1,043 

134 

348 

5,576.5 

71^-72^ 

73 

300 

31 

93 

1,627 

749 

77 

236 

4,131.5 

72^-73^ 

n 

216 

24 

80 

1,221.5 

612 

73 

176 

3,104.5 

73^-74i 

75 

146 

20 

60 

914.5 

426 

37 

143 

2,382 

74i-75i 

76 

94 

7 

53 

701.5 

305 

11 

129 

1,800 

75i-76i- 

77 

77 

10 

54 

547.5 

244 

20 

96 

1,353 

76^-77^ 

78 

51 

8 

47 

410 

135 

16 

102 

998.5 

77i-78^- 

79 

39 

7 

29 

306.5 

86 

14 

86 

749 

78i-79i 

80 

39 

6 

21 

232 

109 

13 

50 

563.5 

79^-80^ 

81 

28 

3 

18 

168.5 

77 

7 

36 

395.5 

80^-81^ 

82 

16 

7 

21 

119 

46 

15 

38 

273 

81^-82^j 

83 

12 

7 

79 

43 

20 

182 

82^-831 

84 

3 

1 

7 

59.0 

11 

1 

13 

118.5 

83^-84^ 

85 

12 

2 

6 

48 

29 

4 

11 

92 

84^-85^ 

86 

3 

5 

29 

10 

11 

50 

85^-86^ 

87 

1 

4 

21 

3 

5 

29 

86^-87^ 

88 

4 

2 

16.5 

5 

2 

21.5 

87^-88^ 

89 

1 

3 

11 

1 

7 

15 

88^-89^ 

90 

1 

2 

6.5 

1 

2 

6.5 

89^-90^ 

91 

4 

4 

90^—91^ 

92 

1 

1 

4 

1 

1 

4 

9^-92^ 

93 

1 

2 

1 

2 

92^-93^ 

94 

1 

1 

93^-94i 

95 

1 

1 

1 

1 

94^-95^ 

527,157 

411,092 

44,485  4,3 

27,086.0 

1,328,404 

1,114,487  12^ 

),965 

11,493,967.5 

% 


TABLE    I. 


MALE  LIFE.     SUMMAKT  (B).     OBSERVATIONS  CLASSIFIED  ACCORDING  TO  YEARS  OF 

INSURANCE. 


09  o3 

Whole  Numbeb 

OF  Entbants,  982,734. 

2,568,856  Thousand  Dollars  Insubbd. 

Duration 

of 
Insmance. 

Existing. 

Discon- 
tinued. 

Died. 

EzDosed  to 
Risk. 

Amounts 
Existing. 

Amomits 
Discontin'd. 

Death 
Claims. 

Exposed  to  Kisk. 

0 

60,190 

46,913 

2,943 

467,910.5 

153,950 

99,417 

7,787 

1,234,719.5 

0-    i 

1 

51,189 

158,722 

6,428 

793,327 

132,847 

378,590 

18,131 

2,118,407 

i-  H 

2 

49,307 

67,850 

5,733 

622,424 

113,202 

208,799 

16,668 

1,673,734.5 

n-  H 

3 

45,000 

44,573 

5,114 

511,172.5 

105,929 

140,830 

14,531 

1,369,050 

2i-3i 

4 

48,697 

30,418 

4,623 

423,563 

117,147 

98,064 

13,409 

1,129,143 

3f-4i 

5 

48,237 

21,452 

3,911 

344,308 

126,106 

69,899 

11,213 

914,605.5 

4i-  5i 

6 

48,663 

14,043 

3,205 

274,412.5 

127,146 

44,140 

9,166 

720,267 

5i-  6i 

7 

45,160 

11,563 

2,569 

209,741.5 

117,454 

30,606 

7,311 

546,582 

6i-  n 

8 

38,200 

5,352 

1,837 

153,555 

100,312 

15,703 

5,045 

398,662.5 

7i-  8i 

9 

28,037 

3,231 

1,344 

109,226.5 

69,922 

8,937 

3,525 

280,985.5 

8^9i 

10 

18,210 

2,146 

982 

77,157 

43,800 

6,006 

2,619 

200,067 

^h-m 

11 

10,977 

1,359 

751 

56,212.5 

26,698 

3,688 

2,153 

148,801 

lOi-lH 

12 

5,120 

830 

647 

43,390 

13,301 

2,349 

1,805 

116,931.5 

lli-12^ 

13 

3,779 

586 

519 

36,915 

10,656 

1,730 

1,472 

99,786 

12i-13i 

14 

4,123 

574 

469 

32,037 

11,331 

1,624 

1,290 

85,981 

13i-14| 

15 

3,110 

304 

399 

27,006 

8,506 

843 

1,080 

72,126.5 

14^15^ 

16 

2,254 

261 

401 

23,214.5 

6,229 

734 

1,201 

61,752 

15i-16i 

17 

1,916 

180 

349 

20,339 

4,706 

528 

987 

53,691 

16i-17i 

18 

1,707 

157 

298 

17,905.5 

4,452 

390 

951 

47,539 

17i-18i 

19 

1,377 

124, 

303 

15,760 

3,914 

325 

758 

41,778.5 

18i-19i 

20 

1,148 

110 

270 

13,963 

3,114 

337 

758 

36,775.5 

19i-20i 

21 

950 

95 

269 

12,442.5 

2,499 

261 

771 

32,604.5 

20i-21i 

22 

1,019 

77 

274 

11,137.5 

2,529 

230 

837 

29,089 

211-22^ 

23 

1,541 

61 

261 

9,775.5 

3,790 

184 

768 

25,516 

22^23| 

24 

2,140 

35 

218 

7,925.5 

4,977 

82 

605 

20,825 

23i-24| 

25 

1,946 

24 

155 

5,538 

4,679 

53 

490 

15,175.5 

244-251 

26 

1,420 

28 

105 

3,411 

4,094 

85 

329 

9,937.5    25|-26| 

27 

930 

10 

54 

1,867 

2,838 

23 

161 

5,460.5    26|-27i 

28 

467 

6 

31 

875 

1,391 

9 

83 

2,445.5    27^28^ 

29 

189 

6 

10 

371.5 

453 

17 

15 

958.5 

28i-29i 

30 

154 

1 

8 

169.5 

432 

3 

31 

480.5 

29^30i 

31 

7 

16 

30f-3H 

32 

1 

7 

1 

16 

31h32i 

33 

1 

6 

5 

15 

32^33^ 

34 

2 

1 

4 

1 

2 

9.5 

33^34^ 

35 

2 

7 

34^-354 

36 

2 

7 

36i-36i 

37 

2 

7 

36|-37i 

38 

1 

2 

-      2 

7 

37i-38i 

39 

1 

1 

5 

5 

38^39^ 

527,157 

411,092 

44,485 

4,327,086.0 

1,328,404 

1,114,487 

125,965 

11,493,967.5 

TABLE    I. 

OBSERVATIONS  ON  MALE  LIFE. 


77 


Excepting  the  first  Aggregates,  the  Amounts  Insured  are  stated  in  THOUSAND  DOLLABS  in  the 
columns  $,  where  1  denotes  $1000,  etc. 


Age  at  Entry,  0  Years. 


Age  at  Entry,  2  Years. 


ii 


0 

1 

2 
3 

4 

5 
6 

7 
8 
9 

10 
11 
12 


0 
1 
2 
3 
4 

5 
6 

7 
8 
9 

10 
11 
12 
13 

14 

15 
16 
17 
18 
19 

20 
21 


No.  OF  Entbants,  7. 


&« 


3.5 

6 

5.5 

4.5 

4 

4 
2 
2 

2 
2 

2 
1 

1 


39.5 


$13,000  Insubed. 


Si    Q      QU 


^3 


$ 

6.5 
12 
11-5 

9.5 


91.5 


Age  at  Entry,   1  Year. 


bo 

< 


5 
6 
7 
8 
9 

10 
11 
12 


No. 

OF  Entrants,  57. 

$110,000  Insubed. 

9 

1 

28 

18 

2 

54 

4 

6 

44 

9 

8 

86 

5 

37 

11 

73 

3 

3 

30.5 

8 

5 

59.5 

1 

4 

24 

2 

7 

45.5 

4 

21 

8 

40 

2 

17 

3 

32 

4 

2 

14 

10 

3 

27.5 

1 

8.5 

2 

15 

2 

8 

3 

14 

2 

6 

4 

11 

1 

4 

1 

7 

2 

3 
1 

5 

6 

1 

1 

.5 

1 

.5 

39 

18 

253.5 

;82 

1 

28 

479.0 

1 

2 
3 

-4 
5 

6 
7 
8 
9 
10 

11 
12 
13 

u 

15 

16 
17 
18 
19 

20 

21 

22 


3g 


0 

1 

2 
3 

4 

5 
6 
7 
8 
9 

10 
11 
12 
13 


No.  OP  Entrants,  39, 


5"" 


15 


19.5 

32 

27.5 

24.5 

19 

16 
9.5 
6 
5 
1 

1 
1 
1 
1 


164.0 


$94,000  Insured. 

611 

"C  >J 

'55 
» 

T 

o  a 

Is 

$ 

$ 

10 

47 

22 

73 

1 

6 

59 

9 

2 

54 

2 

4 

42 

10 

3 

1 

36.5 

8 

3 

22.5 

2 

13 

8 

11 
3 

3 
3 
3 

3 

3 

53 

40 

1 

373.0 

Age  at  Entry,  3  Years. 


Age  at  Entry,  4  Years. 


4 
5 
6 

7 

8 

9 

10 

11 

12 
13 

U 

15 


No. 

OF  Entrants,  26. 

162,000  Insured. 

0 

1 

1 

12.5 

2 

1 

30.5 

1 

2 

23 

4 

57 

2 

1 

5 

19.5 

1 

13 

48.5 

3 

3 

14.5 

8 

37 

4 

1 

12.5 

3 

31.5 

6 

2 

2 

11 

5 

3 

28.5 

6 

1 

1 

7.5 

3 

5 

19.5 

7 

1 

6 

2 

14 

8 

3 

5 

7 

12 

9 

1 

2 

3 

5 

0 

1 

1 

2 

2 

11 

15 

114.5 

25 

37 

285.5 

3 

5 
6 
7 

8 

9 

10 

11 

12 

13 


No.  OF  E 

ntrants,  28. 

$56,00G 

Insured. 

1 

14 

2 

28 

2 

26 

3 

52.5 

1 

2 

24 

2 

4 

49 

2 

3 

20.5 

4 

5 

42.5 

1 

16.5 

2 

35 

78 


TABLE    I. 

OBSERVATIONS  ON  MALE  LIFE. 


Age  at  Entry,  4  Years. 

Age  at  Entry,  7  Years. 

«! 

No.  OP  Entrants,  28. 

$56,000  Insured. 

4J 

No.  OF  Entrants,  24. 

$53,000  Insured. 

•a 

M 

1 

.2 
"P. 

1.1 

■q  1   hS 

1 
II 

5'" 

Si 

^2 

? 
be 

< 

•5  '  5  §  i    • 

. 
II 

T 

% 

$ 

% 

$ 

$ 

$ 

■  1 

5 

1 

16 

2 

34 

9 

0 

1 

1 

11.5 

1  2 

1 

26 

7 

6 

1 

3 

13.5 

3 

5 

29.5 

10 

1 

1 

4 

20 

2 

7 

46.5 

<§ 

7 

1 

1 

10.5 

2 

1 

23.5 

11 

2 

1 

1 

1 

16.5 

12 

2 

1 

40 

9 

8 

2 

9 

5 

21 

12 

3 

1 

3 

12.5 

1 

5 

23.5 

10 

9 

3 

7 

7 

16 

13 

4 

3 

8.5 

4 

18 

11 

10 

3 

4 

4 

9 

u 

5 

2 

7 

5 

16 

12 

11 

1 

2 

3 

5 

15 

6 

1 

5 

3 

11 

13 

12 

1 

2 

16 

7 

1 

4 

2 

8 

U 

13 

1 

1 

2 
36 

20 

— 

2 
349.0 

17 

8 
9 

1 

1 

1 

3 
1.5 

1 
3 

31 

2 

6 
4 

15 
16 

16 

12 

165.0 

10 

13 

1 

89.5 

21 

1 

199.0 

Age  at  Entry,  5  Years.. 

1 

Age  at  Entry,  8  Years. 

No.  OF  Entrants,  18. 

$43,000  Insured. 

0 

1 

_ 

2 

9 

5 

21.5 

5 

1 

1 

1 

1 

15.5 

2 

2 

37 

6 

0 

2 

1 

10.5 

2 

1 

17.5 

8 

2 

1 

2 

1 

13 

1 

7 

5 

30.5 

7 

1 

2 

3 

1  17.5 

2 

7 

29.5 

9 

3 

1 

9.5 

2 

20 

8 

2 

3 

12.5 

3 

22.5 

10 

4 

1 

1 

8.5 

2 

3 

17.5 

9 

3 

4 

1 

2 
1 

10 

7.5 

1 

4 

2 

19 
15 

11 

12 

5 

2 

7 

4 

14 

10 

6 

1 

5 

2 

10 

11 

5 

7 

14 

13 

7 

1 

3.5 

1 

7.5 

12 

6 

1 

6.5 

1 

13.5 

U 

8 

1 

3 

3 

7 

13 

7 

6 

13 

15 

9 

1 

2 

2 

4 

U 

8 
9 

1 

2 

6 
5 

2 

4 

13 
11 

16 
17 

10 

1 

2 

lb 

11 

1 

2 

16 

10 

3 

7 

18 

12 

1 

1 

2 

2 

17 

11 

3 

7 

19 

11 

6 

1 

79.0 

23 

15 

5 

175.0 

12 
13 
14 

3 
3 
3 

7 
7 
7 

20 
21 

22 

Age  at  Entry,  6  Years. 

15 
16 

1 

2.5 
2 

1 

6.5 
6 

23 

No.  OF  Entrants,  20. 

$40,000  Insured. 

17 

1 

2 

2 

6 

25 

18 

4 

26 

0 

1 

1 

9.5 

2 

1 

19.5 

6 

19 

4 

27 

1 

1 

17.5 

2 

86 

7 

2 

2 

8 

15.5 

4 

3 

88.5 

s 

20 

4 

28 

3 

4 

10 

6 

25 

9 

21 

4 

29 

4 

1 

1 

7.5 

5 

2 

21 

10 

22 

4 

30 

5 
6 

7 

2 

1 

6 
6 
4 

5 
3 

15 
15  • 
10 

11 
12 
13 

23 

1 

1 

4 

4 

31 

10,12 

116.0 

17 

19 

245.5 

8 

2 

3 

4 

7 

U 

9 

1 

1 

3 

3 

15 

10 

10 

80.0 

26 

14 

185.0 

TABLE    I. 

OBSERVATIONS  ON  MALE  LIFE. 


79 


Age  at  Entry,  9  Years. 

Age  at  Entry,   11  Years. 

No.  OP  Entbants,  80. 

$58,000  Insured. 

•a 

a 

P 
bo 

< 

■si 

No.  OP  Entrants,  78. 

$148,000  Insured. 

coed 

si 

'h 

.22-5 

1  -«  . 
5  1  h2 

to 

a 

.2 

H 

".2 

5a 
Si 

no 

1    1^- 
aw 

eg 

§1  ^ 
5"  5 

If 

1 

T 

§1 
T 

$ 

T 

~$ 

$ 

T 

$ 

0 

15 

29 

9 

0 

7 

4 

37 

10 

8 

70 

11 

1 

1 

3 

28.5 

1 

4 

56 

10 

1 

2 

22 

56 

3 

30 

115 

12 

2 

7 

22.5 

5 

50.5 

11 

2 

3 

8 

39 

1  6 

13 

90.5 

13 

3 

1 

19 

2 

48 

12 

3 

3 

4 

30 

i  6 

11 

72.5 

U 

4 

1 

1 

17.5 

1 

2 

45 

13 

4 

2 

5 

22.5 

13 

9 

56.5 

15 

5 

1 

1 

15.5 

1 

1 

42.5 

n 

5 

1 

1 

17.5 

2 

3 

37.5 

16 

6 

1 

14 

2 

41 

15 

6 

1 

2 

15 

3 

5 

31.5 

17 

7 

1 

1 

12.5 

5 

1 

38.5 

16 

7 

3 

13 

8 

26 

18 

8 

3 

1 

10.5 

5 

3 

31.5 

17 

8 

2 

10 

4 

18 

19 

9 

1 

1 

6.5 

2 

1 

2-4.5 

18 

9 

1 

7.5 

1 

13.5 

20 

10 

1 

5 

1 

22 

19 

10 

1 

6.5 

4 

11 

21 

11 

2 

4 

18 

21 

20 

11 

6 

9 

22 

12 

1 

2 

1 

3 

21 

12 

6 

9 

23 

13 

1 

2 

22 

13 

6 

9 

H 

14 

1 

2 

23 

14 

1 

6 

2 

9 

25 

15 

1 

1 

1 

2 

2 

H 

15 
16 
17 
18 
19 

20 
21 

1 
1 

1 

4.5 

4 

4 

3 

2 

2 

2 
2 

1 

2' 

1 

6.5 

6 

6 

5 

3 

3 
3 
3 

26 
27 
28 
29 
30 

31 

32 
33 

15 

15 

175.5 

41 

17 

458.5 

Age  at  Entry 

,   10  Years. 

No.  OP  EM:rant8,  74. 

$157,000  Insured. 

0 

6     1; 

36.5 

19 

1 

78 

10 

AX 

22 

1 

5 

11 

61.5 

16 

21 

126.5 

11 

23 

2 

3 

Slf 

2 

3 

6 

48 

7 

19 

90.5 

12 

24 

2 

3 

35 

3 

4 

4 

4 

6 
3 

39 
30.5 

3 
2 

15 
10 

66.5 
51 

13 
U 

25 
26 

1 

2 

1 

2 

3 
1 

36 

37 

5 
6 

7 

3 

C 
2 

2^ 

3! 

24 

19.5 

13 

6 

13 

4 

1 
3 

43.5 
35.5 
21 

15 
16 
17 

27 

JL 

1 

1 

1 

38 

29  '49 

309.5 

63|85 

624.5 

8 
9 

1 

11 
11 

10 

8.5 
8 
7 
6 

1 

17 
17 

16 

13 

11 

10.5 

10 

18 
19 

20 
21 

22 
23 
24 

Age  at  Entry,  12  Years. 

10 
11 
12 
13 
14 

1 

1 

-L 

1 

4 

0 

No.  OP  Entrants,  155. 1 

'                         1 

$296,000  Insured. 

12 

17 

5 

75 

24 

7 

144.5 

2 

1 

1 
2 

3 
16 

23 
12 

1 

121.5 
100 

9 
20 

30 
30 

1 

250 
210 

13 
U 

3 

6 

12 

72 

10 

16 

167 

15 

15 

6 

10 

25 

4 

3 

7 

56.5 

5 

15 

\ 

141.5 

16 

16 

17 
18 
19 

2 

6 
4 
4 
4 

2 

10 

8 
8 
8 

26 

27 
28 
29 

5 

7 

4 

48 

6 

7 

125.5 

17 

6 

14 

1 

38.5 

19 

3 

114.5 

18 

7 
8 

9 
2 

1 

23.5 
14 

29 
37 

1 

93.5 
64 

19 

20 

20 

4 

8 

30 

9 

2 

12 

3 

27 

21 

21 
22 
23 
24 

2 
2 

4 
4 
2 
2 

2 

6 

8 
8 
6 
6 

31 
32 
33 

10 
11 
12 
13 

1 
1 

1 

1 
1 

9.5 

8     1 

7   : 
6.5 

5 
2 

3 

5 
1 

21.5 
14 
12 
11.5 

22 
23 

H 
25 

41 

33 

373.5 

82 

75 

687.0 

14 

1 

4.5 

2! 

7 

26 

80 


TABLE    I. 

OBSERVATIONS  ON  MALE  LIFE. 


Age  at  Entry,   12  Years. 


Age  at  Entry,   14  Years. 


No. 

OP  Entrants,  155. 

$396,000  INSTJBED. 

hr 

13    . 

i    fcb 

-a  .      1 

O  =! 

go 

5 

«2 

c 
$ 

O  3 

o  S 

ft" 

■SB 

Expose 
to  Risk 

$ 

$ 

15 

1 

4 

1 

6 

16 

3 

5 

17 

1 

2.5 

1 

4.5 

18 

2 

4 

19 

1 

2 

a 

4 

20 

1 

1 

21 

1 

1 

22 

1 

1 

1 

1 

83 

69 

3 

613.0 

175 

118 

3 

1,430.0 

27 
28 
29 
SO 
SI 

S2 
S3 
SJ, 


Age  at  Entry,  13  Years. 


No. 

OP  Entbants,  235. 

$458,000  INSUBED. 

0 

14 

8 

1 

113.5 

34 

17 

2 

220.5 

1 

16 

40 

2 

192 

24 

82 

1 

364 

2 

8 

18 

145 

21 

35 

280.5 

3 

11 

16 

120 

32 

38 

223 

4 

16 

16 

93 

20 

22 

161 

5 

13 

10 

1 

64 

12 

24 

4 

118 

6 

11 

6 

1 

42 

18 

16 

1 

82 

7 

5 

1 

2 

26.5 

10 

5 

3 

52.5 

8 

4 

2 

1 

18 

8 

4 

1 

35 

9 

2 

1 

11.5 

4 

1 

23.5 

10 

2 

2 

8 

2 

4 

17 

11 

1 

5 

5 

13 

12 

4 

8 

13 

1 

4 

1 

8 

14 

3 

7 

15 

3 

7 

16 

3 

7 

17 

1 

3 

3 

7 

18 

1 

2 

1 

4 

19 

1 

3 

20 

1 

3 

21 

1 

3 

22 

1 

3 

23 

1 

1 

3 

3 

105 

120 

10 

865.5 

192 

248 

18 

1,653.0 

13 

u 

15 
16 
17 

18 
19 
20 
21 

22 

23 

25 
26 
27 

28 
29 
30 
31 


No.  OP  Entrants,  722. 


0 

1 

2 
3 

4 

5 
6 
7 
8 
9 

10 
11 
12 
13 
14 

15 
16 
17 
18 
19 

20 
21 
22 
23 
24 

25 
26 
27 
28 
29 


28 
26 
38 
40 
45 

50 

38 
34 

27 
18 

8 
4 
2 
1 
3 


1^ 
375 


36 

117 

60 

44 

26 

18 
9 

10 
4 
1 


327  20 


a« 


343 

598.5 
482 
390 
314 

246 

181.5 

131 

90 

60.5 

39 

28 
23 
19 
18 

14 
14 
13 
13 
13 

12 

10 
8 
8 
4 

2 
2 
1 
1 
1 

3,079.5 


$1,491,000  Insured. 


$ 

64 
52 

62 

75 
75 

83 
51 
76 
41 

28 

25 
3 
4 
1 

11 


3 

9 

14 
9 


695 


.2 -T-  i  C.5 


$ 

64 
234 
142 
125 

68 

64 
39 
20 
12 
4 


777 


19 


1^ 
h2 


$ 

713.5 
1,244 
1,002 

802.5 

630 

487 

351.5 

270 

178 

129 

95.5 

67 

63 

58 

57 

'45 
45 
44 
44 
44 

40 
37 

27 
27 
13 

4 
4 
3 
3 
3 

6,531.0 


60 


u 

15 
16 
17 
18 

19 
20 
21 


U 
26 
26 
27 
28 

29 
30 
31 

32 
33 

S4 

35 
36 
37 
38 

39 
US 


TABLE    I. 


81 


OBSERVATIONS  ON  MALE  LIFE. 


Age  at  Entry,   15  Years. 

:i 

NUMBEB  OF 

Entbants,  1,086. 

$2,088,000  Ihsubed. 

Age 

»2S 

at 

Discon- 

Exposed to 
Bisls. 

Amounts 

Amounts 

Death 

Exposed  to 
Risk. 

Exit. 

>'^ 

Existing. 

tinued. 

Died. 

Existing. 

Discontinued. 

Claims. 

i 

$ 

$ 

$ 

0 

46 

58 

1 

514 

112 

93 

2 

997.5 

IS 

1 

44 

207 

4 

877.5 

81 

386 

7 

1,688 

16 

2 

50 

88 

7 

682 

82 

221 

6 

1,296.5 

17 

3 

46 

59 

4 

551.5 

66 

155 

6 

1,020.5 

18 

4 

67 

35 

5 

454.5 

99 

101 

16 

820.5 

19 

5 

62 

29 

1 

350.5 

94 

82 

1 

614 

20 

6 

54 

26 

2 

260 

92 

30 

2 

463 

21 

7 

41 

17 

3 

182.5 

71 

22 

7 

343 

22 

8 

32 

1 

129.5 

70 

9 

249.5 

23 

9 

30 

4 

.95 

77 

4 

173 

2^ 

10 

12 

a 

1 

62.5 

10 

2 

1 

93 

25 

11 

13 

3 

1 

47.5 

13 

2 

1 

80 

26 

12 

2 

32 

2 

65 

27 

13 

3 

1 

29.5 

7 

4 

61 

28 

14 

2 

2 

25 

6 

2 

51 

29 

15 

1 

22 

2 

44 

30 

16 

2 

21 

2 

42 

31 

17 

1 

1 

19 

4 

1 

40 

32 

18 

1 

17 

2 

35 

33 

19 

16 

33 

3J^ 

20 

.    16 

33 

35 

21 

1 

16 

3 

33 

36 

22 

1 

15 

1 

30 

37 

23 

4 

1 

14 

11 

1 

29 

38 

24 

3 

9 

11 

17 

39 

25 

5 

6 

5 

6 

UO 

26 

1 

1 

U 

27 

1 

1 

1 

1 

J^ 

524 

531 

31 

4,466.5 

924 

1,113 

51 

8,359.5 

Age  at  Entry,  16  Years. 

0 

N 

[THBEB  OF  ] 

ENTRANTe 

,  1,659. 

$3,063,000  iNStTRBD. 

16 

118 

100 

5 

779.5 

206 

174 

6 

1,444.5 

1 

93 

318 

7 

1,277 

189 

524 

12 

2,415 

17 

2 

95 

139 

7 

948.5 

193 

287 

17 

1,808.5 

18 

3 

61 

93 

5 

730.5 

112 

237 

11 

1,336.5 

19 

4 

83 

-66 

3 

585 

114 

142 

4 

1,024 

20 

5 

78 

51 

2 

440.5 

125 

110 

1 

780 

21 

6 

75 

23 

2 

323.5 

114 

61 

2 

568.5 

22 

7 

60 

15 

1 

227.5 

87 

26 

2 

409 

23 

8 

44 

7 

155.5 

68 

9 

302.5 

n 

9 

32 

2 

1 

107 

74 

5 

1 

227.5 

25 

82 


TABLE    I. 

OBSERVATIONS  ON  MALE  LIFE. 


|; 

Age  at  Entry,   16  Years. 

1     of 

NnXBER  OP 

Entrants,  1,659. 

$3,063,000  iNStJRED. 

Age 

'  Is 

at 

Dii»con- 

Exposed  to 
Risk. 

Amounts 

'    Amounts 

'     Death 

Exposed  to 
Risk. 

Exit. 

■  >"& 

Existing. 

tiuued. 

;    Died. 

Existing. 

IDiscontin'ed. 

Claims. 

$ 

$ 

$ 

$ 

10 

18 

4 

1 

.71 

30 

s 

1 

146 

26 

11 

7 

1 

49,5 

•  17 

1 

110.5 

21 

12 

5 

3 

40.5 

19 

9 

88.5 

28 

13 

8 

1 

34 

7 

1 

65 

29 

14 

1 

1 

3; 

24.5 

1 

2 

2 

56 

30 

15 

'       2 

20: 

3 

52 

■31 

16 

3 

1 

17.5 

12 

■2. 

:     48 

32 

17 

3 

i 

I 

14 

3 

35 

33 

18 

2 

; 

11: 

7 

32 

SJf 

19 

, 

' 

9! 

;  25 

■  35 

20 

[       3 

1 

a 

6 

1 

:  25 

36 

21 

! 

^ 

1 

1 

19 

37 

22 

i; 

6; 

i 

X 

19 

38 

23 

1 

» 

5; 

5 

1 

:  18 

39 

1   24 

2 

i 

1 

4^ 

11 

j 

; 

i  13 

Jfi 

25 

2 

i 

1 
2i 

1 

2 

i 

1 

!    2 

\U1 

■  796 

824 

39; 

.    5,897.5 

1,405 

1,597; 

^ 

ll]070.0 

\ 

Age  at  Ell 

try,   17  1 

1 
fears. 

! 

0 

N 

nUBBR'  OF 

ENTBAKTf 

5,  2,455. 

$4,692,000 

INSUBED. 

i 
i 

17 

137 

— ; — : — t 

14^ 

f 

9- 

1,156.5 

275 

225' 

17 

2,'233.5 

1 

134 

445 

10-: 

1,9445    I 

250 

813 

12 

3,768.5 

18 

2 

126 

23^ 

10? 

1,459       ' 

220 

554 

16 

2. 

823 

■19 

3 

'95 

142 

9 

1,133 

168 

314 

13 

2, 

153 

20 

i  4 

,  121 

88 

10: 

916;  5    1 

184 

194 

9 

1, 

718 

21 

5 

124 

70 

71 

709' 

217 

157 

I'B 

1, 

349.5 

22 

6 

134 

39 

6 

523.5    ' 

212 

98 

8 

989 

23 

7 

94 

17 

3 

355.5 

228 

30 

7 

705 

2U 

;  8 

61 

8 

1 

246 

120 

14 

6 

448 

25 

i  9 

64 

4 

1 

178 

119 

6 

1 

312 

26 

10 

30 

2 

111 

49 

4 

189 

27 

11 

11 

2 

2 

78 

20 

5 

1 

133.5 

.28 

12 

5- 

2 

63 

12 

2 

109 

29 

13 

.  8 

3 

55.5 

13 

3 

94.5 

30 

14 

4 

2 

46 

8 

4 

80 

\31 

15 

6 

1 

40 

5 

4 

.,  68 

'>32 

16 

33 

59 

,33 

17 

4 

1 

32.5 

3 

1 

I 

■  58.5 

34 

18 

1 

28 

1 

f 

' 

i  55 

35 

19 

3 

1: 

21^ 

9 

i 

i  54 

\36 

'20 

4 

1 

23 

4 

4 

44 

37 

21 

2 

18 

7 

36 

•38 

22 

16  ■ 

;  29 

39 

23 

2 

1 

16 

2 

2 

29 

Jfi 

24 

6 

13 

12 

25 

Jfl 

TABLE    I. 


83 


OBSERVATIONS  ON   MALE  LIFE. 


Age  at  Entry,   17  Years. 

!i 

Number  op 

Entrant 

3,  2,455. 

$4,692,000  Insured. 

Age 

B 

at 

Discon- 

Exposed to 

Amounts 

Amounts 

Death 

Exposed  to 
Risk. 

Exit.  1 

>"& 

Existing. 

tinued. 

Died. 

Rigli. 

Existing. 
$ 

Discontin'cd. 

Claims. 

$ 

$ 

:$ 

25 

3 

7 

4 

13 

r^ 

26 

1 

4 

5 

9 

43 

■27 

1 

2.5 

2 

3 

u 

28 

3 

2 

2 

2 

45 

1,182 

1,197 

76 

9,237.0 

2,149 

2,418 

125 

17,590.0 

Age  at  Entry,   18  Years. 

0 

N 

UMBER  OF 

Entrants 

,  3,973. 

$7,466,000  INSUKED. 

18 

288 

291 

9 

1,841 

563 

466 

14 

3,500 

1 

225 

832 

21 

2,969 

386 

1,413 

36 

5,716.5 

19 

2 

181 

329 

21 

2,142.^5 

341 

813 

42 

4,181.5 

20 

3 

175 

232 

9 

1,660 

263 

463 

14 

3,160.5 

21 

4 

178 

139 

7 

1,290.5 

292 

303. 

16 

2,500.5 

22 

:  5 

174 

113 

11 

979.5 

322 

253; 

14 

1,914.5 

23 

6 

198 

47 

5 

714.5 

362 

lor 

7 

i;398.5 

24 

!  7 

123 

30 

5 

473 

279 

50' 

14 

951 

25 

8 

111 

20 

1 

320 

194 

32 

2 

617 

26 

9 

66 

1 

2 

197.5 

129 

6 

6 

402 

27 

10 

39 

6 

2 

126 

;74 

11' 

iB 

258.5 

28 

11 

16 

4 

80 

^5 

Hi 

! 

165.5 

29 

12 

3 

1 

61.5 

;  5 

3! 

r 

123.5 

SO 

13 

5 

58 

9 

1 

i 

117 

31 

;14 

9 

1 

1 

52.5 

:21 

2' 

n 

107 

32 

15 

7 

42 

10 

84 

33 

16 

3 

2 

35 

2 

7 

74 

34 

17 

5 

1 

30 

4 

4 

65 

35 

18 

1 

24 

1 

57 

36 

19 

5 

23 

10 

56 

37 

20 

2 

18 

3 

46 

38 

21 

1 

16 

6 

43 

39 

22 

2 

15 

3 

37 

40 

23 

2 

1 

13 

6 

; 

4 

34 

Al 

24 

3 

10 

8 

24 

42 

25 

2 

7 

3 

16 

43 

26 

2 

1 

5 

3 

4 

13 

U 

27 

1 

2   ■ 

4 

6 

45 

28 

1 

1 

.     2 

2 

46 

1,827 

2,046 

100 

13,20^.5 

3,336 

3,933 

197 

25,670.5 

84 


TABLE    I 


OBSERVATIONS  ON  MALE  LIFE. 


Age  at  Entry,   19  Years. 

H 

NUMBEB  OP 

Entrant 

s,  6,365. 

$11,576,000  INSUBED. 

Age 

§§ 

at 

^3 

Existing. 

Discon- 
tinued. 

Died. 

Exposed  to 
Risk. 

Amounts 
Existing. 

Amounts 
Discontin'ed. 

Death 
Claims. 

Exposed  to 
ffisk. 

Tlxit. 

$ 

$ 

$ 

$ 

0 

387 

559 

25 

2,903 

713 

875 

37 

5,350.5 

19 

1 

363 

1,451 

39 

4,668.5 

625 

2,497 

78 

8,702.5 

20 

2 

294 

526 

26 

3,278 

521 

1,024 

65 

6,239 

21 

3 

277 

353 

13 

2,518.5 

435 

825 

24 

4,728.5 

22 

4 

273 

191 

15 

1,956.5 

419 

456 

34 

3,629 

23 

5 

298 

121 

10 

1,512.5 

478 

•      256 

39 

2,820 

n 

6 

285 

80 

20 

1,104 

498 

191 

18 

2,079.5 

25 

7 

219 

48 

11 

735 

353 

91 

30 

1,422.5 

26 

8 

146 

16 

2 

473 

304 

39 

4 

974.5 

27 

9 

102 

8 

1 

313 

218 

18 

1 

638 

28 

10 

48 

7 

2 

202.5 

94 

24 

3 

398 

29 

11 

34 

5 

1 

146.5 

65 

10 

2 

284 

30 

12 

10 

3 

1 

107.5 

24 

7 

3 

208.5 

31 

13 

11 

1 

2 

94.5 

26 

4 

1 

176 

32 

14 

6 

4 

1 

79 

12 

5 

3 

144.5 

33 

15 

8 

1 

69.5 

14 

2 

126 

S4 

18 

7 

1 

3 

60.5 

9 

5 

8 

108.5 

35 

17 

5 

50 

5 

89 

36 

18 

4 

45 

8 

84 

37 

19 

6 

1 

41 

5 

4 

76 

38 

20 

6 

1 

2 

33.5 

8 

4 

5 

65 

39 

21 

5 

1 

25 

7 

3 

50 

UO 

22 

5 

1 

1 

18.5 

4 

1 

5 

39.5 

Jfl 

23 

6 

12 

20 

30 

42 

24 

2 

6 

4 

10 

43 

25 

2 

4 

2 

6 

U 

26 

2 

2 

4 

4 

Jf5 

2,811 

3,377 

177 

20,459.0 

4,875 

6,334 

367 

38,483.0 

Age  at  En 

try,  20  1 

fears. 

0 

Ni 

JMBEB  OF  1 

Sntkants 

,  10,110. 

119,352,000  Insubsd. 

20 

704 

817 

38 

4,646.5 

1,324 

1,415 

58 

8,918.5 

1 

562 

2,297 

59 

7,402.5 

1,085 

4,232 

112 

14,339 

21 

2 

464 

790 

43 

5,238 

800 

1,769 

64 

10,141.5 

22 

3 

438 

589 

31 

4,041.5 

678 

1,359 

51 

7,713.5 

23 

4 

450 

368 

18 

3,094 

721 

954 

45 

5,828 

U 

5 

420 

191 

26 

2,346.5 

713 

421 

52 

4,374.5 

25 

6 

414 

131 

18 

1,739.5 

697 

291 

33 

3,253.5 

26 

7 

361 

81 

8 

1,201.5 

671 

141 

19 

2,307.5 

27 

8 

245 

27 

7 

778.5 

455 

58 

21 

1,518 

28 

9 

164 

22 

2 

502 

297 

39 

4 

993.5 

29 

1 

TABLE     I 


85 


OBSERVATIONS  ON  MALE  LIFE. 


Age  at  Entry,  20  Years. 

^i 

Number  op  Entbants 

,  10,110. 

$19,252,000  Insured. 

Age 

£  2 

" 

at 

►2S 

Discon- 

Exposed to 
Risk. 

Amounts 

Amounts 

Death 

Exposed  to 

Exit. 

>"& 

Existing. 

tinued. 

Died. 

Existing. 

Discontin'ed. 

Claims. 

Risk. 

$ 

$ 

% 

$ 

10 

77 

11 

3 

319.5 

161 

22 

3 

662 

SO 

11 

36 

6 

5 

231 

66 

21 

13 

476.5 

31 

12 

25 

6 

3 

184 

52 

12 

11 

381 

32 

13 

9 

1 

3 

152.5 

12 

6 

3 

309 

33 

14 

16 

2 

139 

43 

4 

289 

3U 

15 

27 

.    122 

45 

244 

35 

16 

14 

1 

94.5 

31 

4 

197 

36 

17 

15 

80 

20 

164 

37 

18 

•    2 

3 

63.5 

2 

6 

141 

38 

19 

10 

1 

59.5 

17 

1 

135.5 

39 

20 

6 

49 

13 

118 

Jfi 

21 

5 

2 

42 

15 

3 

103.5 

Jfl 

22 

5 

1 

35.5 

7 

1 

86.5 

^ 

23 

10 

30 

31 

79 

kS 

24 

4 

2 

1 

19 

11 

2 

4 

47 

u 

25 

6 

13 

8 

31 

Jt5 

26 

4 

7 

16 

23 

^6 

27 

2 

3 

.  4 

7 

Ul 

28 

1 

3 

Jt8 

29 

1 

1 

3 

3 

Jfi 

4,496 

5,349 

265 

32,636.5 

7,998 

10,761 

493 

62,887.5 

Age  at  Ee 

itry,  21  1 

fears. 

0 

Nr 

ruBEB  or  I 

Intrants 

14,896. 

130,749,000  Insured. 

21 

1,058 

1,094 

49 

6,901 

2,018 

2,125 

62 

14,312 

1 

794 

3,382 

68 

11,004 

1,628 

6,571 

115 

23,258.5 

22 

2 

672 

1,183 

70 

7,859.5 

1,428 

2,948 

184 

16,756 

23 

3 

662 

852 

42 

6,100 

1,194 

1,994 

89 

12,673 

2^ 

4 

697 

495 

40 

4,722.5 

1,170 

1,224 

68 

9,781 

25 

5 

622 

318 

24 

3,579 

1,254 

833 

40 

7,514.5 

26 

6 

638 

176 

25 

2,686 

1,179 

428 

66 

5,590 

27 

7 

503 

133 

26 

1,868.5 

1,086 

252 

54 

4,005 

28 

8 

360 

48 

13 

1,249 

777 

113 

31 

2,682.5 

29 

9 

265 

21 

5 

841.5 

546 

61 

7 

1,787.5 

30 

10 

108 

18 

2 

552 

236 

44 

4 

1,182 

31 

11 

79 

8 

2 

429 

154 

22 

8 

909 

32 

12 

28 

4 

6 

342 

66 

11 

12 

730.5 

33 

13 

40 

8 

2 

302 

95 

26 

1 

634 

SJf 

14 

33 

3 

3 

254.5 

56 

6 

8 

522 

35 

15 

28 

2 

2 

216 

62 

4 

3 

453 

36 

16 

35 

2 

1 

184 

78 

2 

1 

385 

37 

17 

26 

2 

1 

146 

41 

6 

4 

302 

38 

18 

15 

1 

1 

117.5 

29 

3 

2 

252.5 

39 

19 

23 

1 

2 

100.5 

62 

1 

5 

219.5 

UO 

86 


TABLE    I. 

OBSERVATIONS  ON  MALE  LIFE. 


Age  at  Entry,  21  Years. 


20 
21 
^2 
23 
24 

25 
26 
27 
28 
29 


Nfmbbb  op  Entbants,  14,896. 


Existing. 


13 
4 

10 
6 

21 

6 
4 
2 
1 
1. 


6,754 


Discon- 
tinued. 


DlQd. 


7,754 


388 


Exposed  to 
Risk. 


75 
61 
56 
45 
38 

17 
10 

5 

3 

1.5 


49,766,0 


$30,749,000  Insured. 


Amounts    j     Amounts         Death 
Existing.     Discontin'ed.    Claims. 


15 
8 
23 
14 
44 

14 
9 
8 
3 
3 


13,300 


16,678 


771 


Exposed  to 
Rislc. 


$ 

152 
133 
124 
100 
85 

41 

26.5 

17 

9 

4.5 


104,641.5 


Age 

at 
Exit. 


41 

4S 
U 
45 

46 
47 
48 
49 
50 


Age  at  Entry,  22  Years. 


0 

1 

2 

\Z 

|4 

is 
6 

;7 

!9 

io 
ii 
i2 

13 

14 

15 
16 
17 
18 
19 

20 
21 
22 
23 
24 

is 

26 
27 
28 
29 

io 


NuMBEB  cJf  Entrants,  19,955. 


1,263 

1,554 

57 

1,019 

4,603 

114 

913 

1,627 

75' 

812 

1,057 

58. 

895 

594 

48 

827 

437 

44 

869 

244 

32 

700 

192 

24 

515 

73 

16 

332 

28 

12 

218 

31 

8 

132 

16 

6 

41 

12 

4 

54 

6 

7 

47 

9 

56 

5 

3 

31 

3 

3 

40 

1 

2 

40 

2 

3 

13 

1 

1; 

17 

2 

10 

1; 

7 

2 

28 

1 

23 

1 

li 

16 

( 

6' 

! 

1' 

4 

! 

i 

2 

i 

i 

1 

! 

3 

1  ■ 

i 

8,934 

10,501 

520 

9,200.5 

14,779.5 

10,531.5 

8,201.5 

6,  .506 

5,047.5 

3,836 

2,717 

1,860.5 

1,279 

905.5 
.    656 
504 
450 
381.5 

327.5 

264.5 

-228.5 

185 

140.5 

125 

107 

95  i 

86;  5 

57j5 

33; 

17i 

lOi 

6' 

4 


68,546.0 


$42,124,000  Insured. 


2,690 

2,004 
1,745 
1,452 
1,749 

1,684 
1,830 
1,364 
1,240 

786 

532 

282 

94 

130 

•  96 

113 
73 
74 
90 
23 

40 
19 
16 
76 
56 

32 

17 

12 

6 

3 


18,333 


2,945 

89 

9,035 

193 

4,058 

158 

2,712 

111 

1,482 

128 

1,020 

96 

640 

72 

376 

55 

177 

31 

80 

28 

72 

19 

30 

14 

33 

9 

12 

22 

15 

7 

3 

5 

2 

4 

1 

11 

5 

1 

5 

11 

3 

7 

4 

3 

2 

5 

22,740 

1,051 

19,589.5 

31,882.5 

2S,139 

17,851 

14,191 

11,063 
8,453 
6,043 
4,347.5 
2,948 

2,058 
1,456 
1,128.5 
1,003 
837.5 

730.5 

608.5 

529 

446.5 

345.5 

311.5 

266 

240.5 

219 

139.5 

80 

:48 

26 

14 

8 


150,008.0 


23 

H 
25 
26 

27 
28 
29 
30 
31 

32 
33 

S4 

35 


37 
38 
39 

40 

^^ 

42 
43 
44 
45 
Jfi 

47 
48 
49 
50 
51 

52 


TABLE    I. 


87 


•  OBSERVATIONS  ON  MALE  LIFE. 


i 

Age  at  Entry,  23  Years. 

NUMBEB  OP  ] 

Entbants 

,  24,574. 

$54,330,000  INSUEED. 

Age 

at 
Exit. 

Discon- 

Exposed to 
Risli. 

Amounts 

Amounts 

Death 

Exposed  to 
Bisk. 

,^^ 

Existing. 

tinued. 

Died. 

Existing. 

Discontin'ed 

Claims. 

i 

$ 

■  $ 

$ 

0 

1,629 

1,748 

62 

11,413 

3,459 

3,349 

122 

25,490.5 

23 

;  I 

1,379 

5,393 

113 

18,438.5 

2,926 

10,977 

253 

41,911.5 

H 

2 

1,105 

1,897 

96 

13,301.5 

2,135 

5,367 

257 

30,560.5 

26 

3 

1,025 

1,319 

85 

10, 491 5 

2,008 

3,475 

176 

23,747.5 

26 

!   4  ■ 

1,195 

792 

55 

8,327 

2,348 

2,172 

149 

18^740 

27 

5 

1,093 

497 

52 

6,432.5 

2,283 

1,305 

136 

14.504.5 

28 

:  6 

968 

325 

42 

4,876.5 

2,001 

816 

112 

li;025 

■29 

7 

829 

243 

17 

3,582.5 

1,756 

495 

30 

8,256.5 

30 

:     8 

689 

83 

29 

2,573.5 

1,587 

206 

66 

6-120 

\81 

9 

450 

49 

16 

1,789.5 

1,008 

117 

53 

4[305:5 

'32, 

10 

280 

34 

14 

1,282 

683 

103 

37 

3,134.5 

[33 

11 

150 

31 

12 

955.5 

362 

81 

50 

2,322.5 

•Si 

12 

113 

] 

L3 

1^ 

771.5 

254 

29 

44 

1,855.5 

\35 

il3 

62 

9 

i 

634.5 

153 

14 

7 

1,536 

36 

il4 

79 

7 

f 

56(j).5 

244 

11 

f 

1;363.5 

\37 

15 

55 

8 

2 

470 

122 

It 

8 

1,096.5 

38 

16 

54 

;7 

1 

405.5 

144 

11 

:957.5 

\39 

17 

48 

■   ;3 

t 

347 

91 

^ 

3S 

i805.5 

.40 

118 

36 

3 

4 

289.5 

59 

4 

3 

;675 

M 

il9 

I 

33 

3 

t 

246.5 

78 

^ 

0 

1603 

\Jt2 

20 

34 

3 

209 

101 

7 

517 

J^3 

'21 

14 

1 

3 

171.5 

30 

5 

9 

406.5 

U 

.22 

21 

2 

4 

153 

32 

3 

16 

363.5 

¥ 

23 

33 

1 

126.5 

99 

4 

312 

46 

24 

33 

2 

93 

85 

211 

47 

25 

'■      28 

.    1 

58 

52 

5 

119 

\4S 

|26 

10 

29 

18 

.  62 

49 

27 

10 

19 

31 

.  44 

50 

,28 

7 

9 

11 

13 

51 

29 

2. 

2 

2 

2 

52 

11,464 

12,467 

643 

88,059.5 

24,162 

28,572 

1,596 

201,061.0 

* 

1 
Age  ati  En 

try,  24  1 

rears. 

j 

0 

1,967 

UBEB  OF  E 

NTB&NTS 

28,504. 

$64,563,00( 

) Insubed. 

1 

n 

1,895 

57 

13,304.5 

4,230 

3,793 

103 

30,385 

1 

1,546. 

5,871 

135 

21,649.5 

3,321 

12,504 

305' 

50,185 

■25 

2 

1,388 

2,225 

119 

15,920.5 

3,113 

6,330 

296 

37,142 

26 

3 

1,225 

1,400 

108 

12,601 

2,323 

3,768 

225 

28,684 

27 

4 

1,344 

890 

74 

10,123 

2,502 

2,456 

172 

23,024 

28 

5 

1,278 

599 

65 

7,966.5 

2,645 

1,608 

150 

18,318 

29 

i  6 

1,246 

369 

42 

6,133.5 

2,686 

981 

103 

14,228.5 

SO 

1  7 

1,012 

308 

27 

4,507 

2,167 

580 

59 

10,659 

31 

1  8 

856 

124 

15 

3,252 

2,111 

292 

44 

7,997 

,32 

!  9 

580 

63 

12 

2,287.5 

1,325 

140 

33 

5,626 

S3 

88 


TABLE    I. 

OBSERVATIONS  ON  MALE  LIFE. 


Age  at  Entry,  24  Years. 

It 

NXT3CBEB  OF 

Entkants 

i,  28,504. 

$64,563,000  IHSUBBD. 

Age 

at 

Exit. 

Existing. 

Discon- 
tinaed. 

Died. 

Exposed  to 
Risk. 

Amounts 
Existing. 

Amounts 
Discontin'ed 

Deatti 
Claims. 

Exposed  to 
Risk. 

$ 

$ 

$ 

$ 

10 

394 

57 

13 

1,635.5 

1,006 

119 

41 

4,138.5 

Si 

11 

192 

28 

10 

1,186 

495 

84 

16 

2,990 

35 

12 

108 

29 

11 

955.5 

304 

75 

29 

2,399.5 

36 

13 

89 

12 

8 

816 

233 

33 

29 

2,012.5 

37 

14 

93 

10 

13 

708 

211 

10 

33 

1,729 

38 

15 

80 

10 

5 

592 

187 

23 

15 

1,468.5 

39 

16 

63 

6 

5 

499 

191 

20 

10 

1,245 

1^0 

17 

58 

5 

2 

425.5 

126 

14 

7 

1,027 

^1 

18 

47 

2 

1 

362 

132 

5 

3 

884.5 

42 

19 

46 

1 

3 

312.5 

129 

4 

9 

745 

JfS 

20 

27 

2 

2 

262 

64 

2 

10 

604 

U 

21 

20 

1 

3 

231.5 

45 

2 

10 

528 

^ 

22 

25 

1 

207.5 

54 

3 

470.5 

J^6 

23 

31 

2 

4 

181 

72 

7 

7 

*    411.5 

47 

24 

38 

3 

145 

76 

5 

329 

Jf8 

25 

36 

1 

104 

94 

2 

248 

49 

26 

31 

2 

66 

69 

8 

148 

50 

27 

17 

1 

34 

40 

-     5 

75 

51 

28 

6 

1 

16 

14 

4 

30 

52 

29 

2 

9 

5 

12 

53 

30 

7 

7 

7 

7 

54 

13,852 

13,912 

740 

106,494.0 

29,977 

32,861 

1,725 

247,751.0 

Age  at  En 

try,  25  1 

fears. 

0 

Ni 

nCBSB  OF  I 

Cntbakts 

32,680 

$76,582,000  INSUBED. 

25 

2,209 

2,120 

84 

15,280 

4,998 

4,172 

168 

36,205 

1 

1,840 

6,496 

137 

25,019 

4,184 

14,301 

338 

60,093.5 

26 

2 

1,585 

2,396 

136 

18,596 

3,388 

6,966 

299 

44,938 

27 

3 

1,513 

1,606 

127 

14,874 

3,182 

4,307 

276 

35,614.5 

28 

4 

1,575 

964 

110 

11,949 

3,479 

2,834 

293 

28,586 

29 

5 

1,562 

688 

66 

9,438 

3,422 

1,927 

218 

22,433.5 

30 

6 

1,427 

427 

56 

7,252.5 

3,066 

1,209 

157 

17,225.5 

31 

7 

1,261 

341 

.<7 

5,385.5 

2,900 

777 

116 

13,009.5 

32 

8 

972 

149 

34 

3,832.5 

2,240 

380 

88 

9,415 

33 

9 

618 

82 

20 

2,711 

1,747 

197 

49 

6,798.5 

34 

10 

443 

49 

18 

2,007.5 

1,034 

124 

56 

4,842 

35 

11 

239 

32 

11 

1,506 

605 

66 

32 

3,657 

36 

12 

137 

28 

14 

1,226 

348 

53 

33 

2,960.5 

37 

13 

116 

22 

13 

1,050 

321 

35 

27 

2,535.5 

38 

14 

116 

19 

8 

900.5 

304 

45 

33 

2,147.5 

39 

15 

102 

15 

9 

759.5 

281 

30 

23 

1,773 

40 

16 

77 

7 

9 

637.5 

189 

23 

24 

1,442.5 

41 

17 

70 

4 

3 

546 

167 

17 

8 

1,209.5 

42 

18 

46 

4 

10 

469 

67 

14 

29 

1,019 

43 

19 

49 

3 

4 

409.5 

112 

7 

13 

912.5 

U 

TABLE    I. 


89 


OBSERVATIONS  ON  MALE  LIFE. 


Age  at  Entry,  25  Years. 

taa 

NUMBBB  OP  ] 

Entrants 

,  32,680. 

$76,582,000  Insured. 

Age 
at 

Exit. 

Discon- 

Exposed to 
Bisk. 

Amounts 

Amounts 

Deatli 

Exposed  to 
Risli. 

>*5 

Existing. 

tinued. 

Died. 

Existing. 

Discontin'ed 

Claims. 

$ 

$ 

$ 

$ 

20 

26 

1 

2 

354.5 

79 

5 

7 

781.5 

45 

21 

31 

1 

3 

325.5 

77 

1 

5 

692.5 

Jf6 

22 

27 

1 

3 

290.5 

61 

8 

4 

606 

Jf7 

23 

44 

1 

3 

259.5 

142 

1 

4 

536.5 

Jf8 

24 

46 

1 

1 

211.5 

90 

4 

1 

388 

W 

25 

66 

4 

164 

72 

16 

295 

50 

26 

47 

4 

94 

95 

17 

207 

61 

27 

22 

1 

43 

58 

5 

95 

62 

28 

15 

20 

19 

32 

53 

29 

2 

5 

4 

13 

6U 

30 

3 

3 

9 

9 

55 

16,286 

15,457 

937 

125,619.5 

36,740 

37,503 

2,339 

300,473.5 

Age  at  Ee 

itry,  26  " 

fears. 

0 

Ni 

TUBER  OI-  1 

Sntbants 

,  34,138. 

$80,336,000  Insured. 

m 

2,265 

2,182 

82 

15,978 

5,018 

4,022 

182 

38,107 

1 

1,864 

6,541 

175 

26,338.5 

4,258 

14,556 

394 

63,736 

27 

2 

1,592 

2,560 

142 

19,749 

3,498 

7,161 

348 

48,225.5 

28 

3 

1,530 

1,647 

111 

15,911.5 

3,244 

4,517 

277 

38,540.5 

29 

4 

1,561 

1,111 

115 

12,891.5 

3,538 

2,985 

280 

31,268.5 

SO 

5 

1,506 

776 

94 

10,272 

3,391 

2,194 

216 

24,861 

31 

6 

1,451 

488 

70 

8,040 

3,213 

1,353 

169 

19,480.5 

32 

7 

1,304 

396 

61 

6,077 

3,074 

931 

174 

14,956.5 

33 

8 

1,045 

181 

37 

4,423.5 

2,523 

462 

115 

11,012 

SU 

9 

750 

100 

32 

3,201 

1,813 

234 

78 

8,026 

35 

10 

498 

66 

17 

2,336 

1,213 

194 

36 

5,921 

36 

11 

318 

41 

12 

1,767.5 

755 

102 

32 

4,524 

37 

12 

126 

29 

16 

1,402.5 

327 

74 

29 

3,649 

38 

13 

124 

22 

11 

1,235 

329 

57 

25 

3,227.5 

39 

14 

170 

20 

12 

1,079 

426 

63 

29 

2,813.5 

40 

15 

130 

10 

2 

882 

359 

18 

5 

2,318 

41 

16 

72 

9 

8 

740.5 

184 

31 

23 

1,929.5 

42 

17 

90 

6 

3 

653 

208 

13 

9 

1,700.5 

43 

18 

51 

3 

3 

555.5 

126 

8 

10 

1,473 

44 

19 

65 

2 

2 

499 

209 

7 

2 

1,329.5 

45 

20 

44 

4 

2 

429 

111 

14 

4 

1,108 

46 

21 

31 

2 

5 

380 

69 

3 

17 

984.5 

47 

22 

32 

2 

6 

342 

75 

3 

17 

895.5 

48 

23 

50 

2 

4 

302 

128 

10 

4 

797 

49 

24 

65 

3 

4 

245.5 

179 

5 

12 

657.5 

60 

90 


TABLE     I 


OBSERVATIONS  ON  MALE. LIFE. 


1 

Age  at  Entry,  26  Years.                                                 i 

NcMBER  OF  Entrants 

34,1.38. 

$80,236,000  Insured. 

Age 

at 

Discon- 

Exposed to 
Bisk. 

Amounts 

Amounts 

Death 

Exposed  to 
Risk. 

>*A 

Existing. 

tinued. 

Died. 

Existing. 
$ 

Discontin'ed. 

Claims. 

$ 

$ 

$ 

25 

63 

3 

175 

135 

18 

464 

51 

26 

44 

1 

1 

108.5 

123 

1 

5 

310.5 

52 

27 

29 

1 

1 

62.5 

76 

4 

4 

180 

53 

28 

17 

1 

32 

46 

5 

98 

'  H 

29 

9 

14 

24 

• 

47 

55 

30 

5 

i 

;  5 

23 

t 
i 

23 

56 

16,901 

16,205 

1,032 

136,127.5 

38,695 

39,022 

2,519 

332,664.0 

i       Age  at  Entry,  27  Years.              « 

0 

Nt 

rHBER  OF  I 

! 
Intrants 

,  36,221. 

1 

$87,030,000  Insured. 

27 

2,274 

2,050 

81 

17,085.5  ' 

5,478 

4,344 

189 

41,343 

1 

2,019 

6,753 

201 

28,439.5 

4,678 

15,314 

479 

69,362 

28 

2 

1,660 

2,877 

150 

21,404.5  1 

3,687 

8,413 

367 

52,341.5 

29 

3 

1,689 

1,672 

128 

17,320     i 

3,604 

4,741 

306 

41.710.5 

30 

4 

1,703 

1,168 

126 

14,083     ; 

3,634 

3,360 

307 

33,750 

31 

5 

1,651 

776 

90  . 

11,282 

3,578 

2,224 

247 

27,017 

32 

6 

1,658 

473 

63 

8,916.5 

3,781 

1,270 

188 

21,445 

33 

7 

1,413 

431 

53 

6,743.5  ' 

3,225 

984 

118 

16,349 

3U 

8 

1,213 

201 

36 

4,961.5 

2,883 

489 

94 

12,269.5 

35 

9 

873 

120 

32 

3,552     ; 

2,133 

300 

77 

8,898 

36 

10 

559 

77 

15 

2,548.5  ! 

1,343 

222 

50 

6,427 

37 

11 

347 

45 

22 

1,913.5 

814 

118 

63 

4,864 

38 

12 

150 

35 

19 

1,504.5 

371 

81 

43 

3,887.5 

39 

13 

140 

33 

15 

1,301.5 

381 

86 

31 

3,390 

40 

14 

161 

23 

12 

1,118.5 

410 

74 

31 

2,898 

Ul 

15 

99 

11 

8 

928.5 

239 

20 

22 

2,410 

J^ 

16 

78 

11 

7 

810.5 

196 

24 

17 

2,127 

US 

17 

74 

4 

7 

718 

154 

5 

24 

1,899.5 

u 

18 

63 

11 

5 

629.5 

179 

28 

8 

1,705 

Jf5 

19 

55 

\  3 

3 

554.5 

1         158 

11 

13 

1,498.5 

46 

20 

42 

5 

1 

492.5 

132 

17 

2 

1,313.5 

47 

21 

41 

3 

5 

445.5 

100 

5 

10 

1,168.5 

48 

22 

41 

3 

4 

396.5 

1         104 

6 

10 

1,053 

49 

23 

47 

3 

4 

348.5 

111 

15 

11 

928.5 

50- 

24 

79 

1 

2 

295.5 

174 

4 

7 

797 

51 

25 

71 

1 

4 

213.5 

188 

3 

9 

612.5 

52 

26 

58 

3 

138 

164 

2 

414 

53 

27 

36 

4 

77 

118 

17 

248 

54 

28 

16 

1 

37 

38 

1 

113 

55 

29 

9 

20 

24 

74 

56 

30 

9 

2 

11 

44 

6 

50 

57 

18,328 

16,790 

1,103 

148,290.5 

42,123 

42,158 

2,749 

362,364.0 

TABLE    I. 


91 


OBSERVATIONS  ON  MALE  LIFE. 


Age  at  Entry,  28  Years,  i 

Number  of 

Enthanm 

,  41,636. 

$93,734,000  Insured 

Age 

at 
Exit. 

Discon- 

Exposed to 

Amounts 

Amounts 

Death 

Exposed  to 

>*A 

Existing. 

tinued. 

Died. 

Risk. 

Existing. 

Discontin'ed. 

Claims. 

Risli. 

$ 

$ 

$ 

$ 

0 

2,457 

2,052 

91 

19,792 

5,979 

4,193 

165 

44,770.5 

28 

1 

2,078 

7,044 

178 

33,514 

5,178 

16,133 

415 

75,330.5 

29 

2 

4,905 

2,917 

153 

26,277.5 

3,940 

8,513 

423 

57,414.5 

SO 

3 

1,696 

1,797 

143 

18,862.5 

3,631 

5,175 

318 

46,207.5 

31      : 

4 

1,834 

1,210 

132 

15,520 

3,972 

3,598 

258 

37,872 

32  i 

5 

1,705 

815 

113 

12,541.5 

3,695 

2,382 

285 

30,652 

33  \ 

6 

1,691 

527 

97 

10,052.5 

3,701 

1,458 

228 

24,752 

3J^  \ 

7 

1,565 

478 

80 

7,762 

3,759 

1,281 

187 

19,453.5 

35 

8 

1,330 

210 

50 

5,773 

3,299 

557 

128. 

14,588.5 

36 

9 

983 

129 

43 

4,223.5 

2,392 

339 

114 

10,713.5 

37 

10 

685 

78 

31 

3,094 

1,670 

212 

69 

7,932 

38 

11 

407 

45 

19 

2,316.5 

986 

156 

42 

6,009 

39 

12 

223 

37 

21 

1,849.5 

565 

117 

49 

4,844.5 

40 

13 

164 

30 

12 

1,572 

459 

89 

34 

4,127.5 

U 

14 

182 

26 

14 

1,368 

488 

65 

38 

3,557.5 

42 

15 

143 

is' 

12 

1,151.5 

381 

33 

23 

2,982.5 

43 

16 

98 

16 

10 

981 

239 

34 

38 

2,545 

U 

17 

100 

7 

7 

861.5 

219 

34 

20 

2,234 

4^ 

18 

102 

7 

8 

747.5 

260 

18 

26 

1,969 

46 

19 

65 

5 

7 

631.5 

197 

4 

20 

1,672 

47 

20 

48 

4 

8 

555 

120 

13 

26 

1,446.5 

48 

21 

40 

6 

3 

494 

84 

15 

5 

1,286.5 

49 

22 

45 

3 

7 

446.5 

118 

7 

21 

1,186.5 

60 

23 

54 

1 

6 

392.5 

146 

4 

10 

1,042 

51 

24 

94 

4 

4 

330 

243 

7 

15 

880.5 

52 

25 

74 

2 

5 

229 

167 

12 

20 

613 

53 

26 

63 

3 

1 

147.5 

187 

1 

6 

419.5 

54 

27 

38 

2 

82 

119 

.   9 

226 

55 

28 

24 

1 

42 

66 

f   1 

98 

56 

29 

11 

17 

8 

31 

57 

30 

5 

6 

18 

23 

58 

31 

5 

59 

32 

5 

60 

33 

5 

61 

34 

5 

62 

35 

5 

63 

36 

5 

64 

37 

5 

65 

38 

5 

66 

39 

1 

-5 

5 

67 

22,909 

17,468 

1,259 

171,642.0 

46,286 

44,450 

2,998 

406,925.0 

92 


TABLE    I. 

OBSERVATIONS  ON  MALE  LIFE. 


Age  at  Entry,  29  Years 

J*  5 

NlTMBBB  OP  ] 

3NTHANT8 

,  38,787. 

$96,811,000  Iksubed. 

Age 

at 

Discon- 

Exposed  to 
Risk. 

Amounts 

Amounts 

Death 

Exposed  to 
Risk. 

>'A 

Existing. 

tinaed. 

Died. 

Existing. 

Discontin'ed. 

Claims. 

ri  ft  1  ti 

$ 

S 

$ 

$ 

0 

2,483 

2,017 

86 

18,385 

6,013 

3,356 

217 

46,727.5 

29 

1 

2,119 

6,783 

181 

30,809.5 

5,078 

15,605 

470 

79,422.5 

SO 

2 

1,829 

2,959 

147 

23,638.5 

4,258 

8,724 

388 

61,710 

31 

3 

1,557 

1,842 

124 

19,262 

3,940 

5,801 

326 

49,801.5 

32 

4 

1,821 

1,228 

111 

16,046 

4,189 

3,614 

306 

40,828 

33 

5 

1,770 

884 

133 

13,058 

4,154 

3,082 

360 

32,985 

Si 

6 

1,765 

592 

79 

10,417 

4,321 

1,848 

241 

26,006 

35 

7 

1,631 

476 

59 

8,039 

4,005 

1,151 

141 

19,944.5 

36 

8 

1,399 

204 

53 

6,009 

3,398 

599 

121 

14,923.5 

37 

9 

1,081 

135 

34 

4,387.5 

2,574 

343 

69 

10,933.5 

38 

10 

734 

88 

22 

3,161 

1,779 

239 

56 

7,999.5 

39 

11 

448 

55 

16 

2,333.5 

1,133 

146 

35 

5,972 

40 

12 

193 

40 

17 

1,822 

444 

103 

37 

4,679.5 

U 

13 

158 

22 

13 

1,581 

398 

43 

35 

4,125.5 

J^ 

14 

184 

36 

16 

1,381 

459 

86 

30 

3,628 

JfS 

15 

130 

12 

7 

1,157 

356 

33 

14 

3,079.5 

u 

16 

94 

10 

9 

1,009 

229 

28 

47 

2,679 

45 

17 

91 

12 

8 

895 

247 

23 

14 

2,377.5 

46 

18 

78 

6 

6 

787 

188 

5 

9 

2,102.5 

47 

19 

59 

6 

6 

697 

210 

18 

14 

1,894 

48 

20 

50 

9 

7 

624.5 

127 

14 

21 

1,654 

49 

21 

44 

6 

4 

560 

111 

17 

14 

1,490.5 

50 

22 

44 

5 

5 

506.5 

127 

17 

28 

1,348.5 

51 

23 

71 

2 

8 

454 

163 

6 

14 

1,182 

52 

24 

90 

1 

8 

373.5 

246 

4 

13 

1,000 

53 

25 

109 

3 

1 

273.5 

268 

4 

4 

737 

54 

26 

57 

1 

2 

161.5 

162 

3 

8 

461.5 

55 

27 

58 

2 

101 

167 

1 

289.5 

56 

28 

17 

1 

42 

50 

3 

122 

57 

29 

15 

1 

23.5 

41 

4 

67 

58 

30 

8 

8 

24 

24 

59 

20,187 

17,437 

1,163 

168,003.0 

48,859 

44,917 

3,035 

430,195.0 

Age  at  Ee 

itry,  30  1 

fears. 

0 

Ni 

nCBEB  OF  ] 

Sntramts 

,  42,300. 

$105,978,000  Insubbd. 

30 

2,663 

2,184 

89 

20,058 

6,517 

4,702 

218 

50,638 

1 

2,279 

7,141 

226 

33,793.5 

5,266 

17,016 

593 

86,033 

31 

2 

1,952 

2,998 

176 

26,219 

4,622 

9,145 

466 

67,093.5 

32 

3 

1,855 

1,937 

163 

21,623.5 

4,052 

5,665 

437 

54,600.5 

33 

4 

2,125 

1,317 

150 

17,978.5 

4,528 

4,158 

398 

45,200 

34 

5 

1,931 

995 

92 

14,547.5 

4,774 

2,974 

271 

36,708 

35 

6 

1,862 

650 

119 

11,702 

4,748 

1,926 

293 

29,213 

36 

7 

1,802 

616 

80 

9,138 

4,358 

1,347 

241 

22,535.5 

37 

8 

1,648 

228 

45 

6,884 

3,834 

672 

136 

16,927 

38 

9 

1,264 

155 

45 

4,999.5 

2,896 

371 

131 

12,435.5 

39 

TABLE    I. 

OBSERVATIONS   ON  MALE  LIFE. 


98 


Age  at  Entry,  30  Years. 

it 

Number  op  ] 

Entrants 

,  42,300. 

1105,978,000  Insured. 

Age 

at 

'Rrit 

Discon- 

Exposed to 
Risk. 

Amounts 

Amounts 

Death 

Exposed  to 
Risk. 

>'A 

ExiBting. 

tinued. 

Died. 

Existing. 

Discontin'ed 

Claims. 

$ 

$ 

$ 

$ 

10 

805 

118 

33 

3,554 

1,868 

293 

90 

9,076.5 

40 

11 

547 

60 

21 

2,627 

1,284 

150 

52 

6,897 

41 

12 

215 

41 

19 

2,008.5 

544 

122 

40 

5,425 

42 

13 

179 

25 

14 

1,741.5 

460 

69 

43 

4,745.5 

43 

14 

182 

33 

20 

1,519.5 

486 

90 

50 

4,163 

44 

15 

160 

21 

12 

1,290.5 

468 

66 

37 

3,549 

45 

16 

102 

10 

12 

1,103 

302 

36 

52 

2,993 

46 

17 

95 

12 

9 

978 

263 

40 

35 

2,601 

47 

18 

69 

8 

7 

864 

175 

19 

10 

2,273.5 

48 

19 

72 

5 

7 

781.5 

174 

12 

19 

2,073 

49 

20 

65 

4 

4 

698 

163 

22 

13 

1,863 

50 

21 

49 

2 

4 

626 

139 

4 

/      9 

1,674 

51 

22 

57 

2 

5 

571 

138 

7 

23 

1,520.5 

52 

23 

98 

4 

8 

506 

243 

6 

23 

1,353 

53 

24 

116 

2 

6 

397 

286 

11 

12 

1,078.5 

54 

25 

93 

1 

6 

273.5 

241 

4 

23 

773 

55 

26 

73 

3 

174 

219 

10 

507 

56 

27 

45 

1 

1 

97.5 

152 

4 

1 

276 

57 

28 

29 

2 

50 

67 

2 

120 

58 

29 

13 

20 

33 

52 

59 

30 

7 

7 

19 

19 

60 

22,452 

18,472 

1,376 

186,831.0 

53,319 

48,933 

3,726 

474,416.5 

Age  at  Ee 

itry,  31  ^ 

fears. 

0 

Ni 

TKBEB  OF  I 

Sntbants 

,  39,923. 

$100,042,000  Insured. 

31 

*  2,450 

1,857 

90 

19,033 

6,132 

4,048 

253 

47,997 

1 

2,197 

6,386 

196 

32,333 

5,549 

14,806 

476 

82,206 

32 

2 

1,870 

2,747 

175 

25,373.5 

4,235 

8,270 

517 

64,643 

33 

3 

1,872 

1,851 

162 

21,029.5 

4,198 

5,522 

447 

52,995 

3^. 

4 

1,813 

1,276 

149 

17,432 

4,300 

3,858 

438 

43,660 

35 

5 

1,867 

917 

125 

14,373.5 

4,657 

2,842 

348 

35,572 

36 

6 

1,862 

622 

105 

11,612 

4,499 

1,818 

225 

28,237 

37 

7 

1,625 

532 

84 

9,068 

3,908 

1,331 

216 

21,938.5 

38 

8 

1,578 

206 

52 

6,990 

3,696 

646 

150 

16,826 

39 

9 

1,229 

132 

36 

5,191 

2,938 

338 

114 

12,488 

40 

10 

1,142 

103 

28 

3,808.5 

2,040 

273 

81 

9,130.5 

41 

11 

479 

63 

24 

2,555.5 

1,139 

155 

58 

6,795.5 

42 

12 

228 

38 

21 

2,002 

591 

104 

51 

5,469 

43 

13 

152 

24 

26 

1,722 

540 

67 

77 

4,741.5 

44 

14 

207 

27 

15 

1,518.5 

613 

75 

35 

4,053.5 

45 

15 

150 

18 

15 

1,274 

374 

39 

40 

3,348.5 

46 

16 

119 

18 

17 

1,091 

334 

40 

50 

2,895 

47 

17 

99 

8 

15 

942 

234 

29 

49 

2,476.5 

48 

18 

88 

7 

8 

820.5 

222 

14 

22 

2,172 

49 

19 

63 

8 

10 

717 

165 

14 

25 

1,914 

50 

94 


TABLE    I. 

OBSERVATIONS  ON  MALE  LIFE. 


Age  at  Entry,  31  Years. 

li 

Ndmbeb  of 

Entrants 

,  39,9-23. 

! 

$100,042,000  Insured. 

Age 

S3 

1 

at 

Existing. 

Discon- 
tinued. 

Died. 

Exposed  to 
Risk. 

Amounts 
Existing. 

Amounts 
Discontin'ed. 

Death 
Claims. 

Exposed  to 
Bisk. 

Exit. 

i           $ 

$ 

$ 

$ 

20 

66 

4 

4 

638 

i         199 

8 

14 

1,713 

51 

21 

44 

2 

11 

565 

1         124 

4 

26 

1,494 

52 

22 

42 

5 

10 

506.5 

111 

9 

27 

1,337.5 

53 

23 

85 

4 

8 

450 

205 

11 

32 

1,189.5 

5J, 

24 

95 

9 

355 

230 

26 

947 

55 

25 

82 

1 

2 

250.5 

201 

3 

10 

689.5 

56 

26 

80 

2 

166 

214 

5 

477 

57 

27 

43 

3 

84 

122 

5 

258 

58 

28 

.      20 

38 

95 

131 

59 

29 

11 

18 

26 

36 

60 

30 

7 

7 

10 

10 

61 

21,665 

16,856 

1.402 

181,964.5 

51,901 

44,324 

3,817 

457,841.0 

Age  at  Entry,  32  Years. 

0 

Nt 

7XBBR  OF  I 

5NTRANT8 

,  40,069. 

j                             $101,772,000  Insured. 

32 

2,428 

1,868 

95 

19,110.5 

■      6,080 

4,061 

244 

48,855.5 

1 

2,037 

6,409 

187 

32,493.5 

5,163 

15,640 

459 

83,567 

33 

2 

1,916 

2,813 

189 

25,658.5 

4,583 

8,484 

543 

65,883 

SJ^ 

3 

1,805 

1,776 

168 

21,259 

4,000 

5,326 

434 

53,852 

35 

4 

1,943 

1,316 

139 

17,740 

4,488 

3,985 

368 

44,762.5 

36 

5 

1,856 

905 

118 

14,547.5 

4,742 

2,556 

288 

36,636 

37 

6 

1,860 

589 

125 

11,826.5 

4,435 

1,742 

339 

29,457 

38 

7 

1,841 

486 

100 

9,304 

4,332 

1,273 

297 

23,175.5 

39 

8 

1,582 

230 

61 

7,005 

4,084 

644 

156 

17,588 

Jfi 

9 

1,288 

.    161 

48 

5,166.5 

2,997 

410 

133 

12,821 

U 

10 

833 

91 

30 

3,704.5 

2,055 

224 

87 

9,374 

Jt2 

11 

504 

87 

23 

2,752.5 

1,104 

159 

77 

7,040.5 

JfS 

12 

261 

38 

21 

2,163 

626 

115 

56 

5,722.5 

U 

13 

187 

24 

19 

1,850 

456 

72 

57 

4,947 

45 

14 

197 

28 

16 

1,618 

494 

81 

36 

4,357.5 

i6 

15 

145 

13 

14 

1,384.5 

389 

33 

37 

3,770.5 

^7 

16 

105 

9 

16 

1,214.5 

262 

7 

44 

3,324.5 

J,8 

17 

90 

12 

18 

1,083     i 

237 

43 

32 

2,993.5 

Jfi 

18 

82 

10 

11 

964 

252 

31 

33 

2,687.5 

50 

19 

61 

9 

8 

861.5 

159 

24 

27 

2,375 

51 

20 

93 

3 

9 

786.5 

313 

21 

36 

2,166.5 

52 

21 

47 

6 

12 

680 

127 

11 

30 

1,801.5 

53 

22 

59 

3 

10  . 

616.5 

162 

8 

20 

1,635 

5U 

23 

65 

1 

1,3 

545.5 

130 

4 

39 

1,447 

55 

24 

117 

2 

3 

466 

310 

6 

6 

1,273 

56 

25 

129 

1 

3 

344.5 

299 

1 

10 

953.5 

57 

26 

99 

2 

4 

211 

279 

10 

14 

639 

58 

27 

62 

1 

106.5 

176 

3 

339.5 

59 

28 

25 

1 

54 

84 

4 

162 

60 

29 

11 

28 

23 

74 

61 

30 

17 

17 

51 

51 

62 

21,735 

16,893 

1,461 

185,562.0 

52,892 

44,974 

3,906 

473,732.0 

TABLE    I. 

OBSERVATIONS  ON  MALE  LIFE. 


,05 


Age  at  Entry,  33  Years. 


eta 


0 

1 

2 
3 

4 

5 
6 

7. 

8 

9 

10 
11 
12 
13 
14 

15 
16 
17 
18 
19 

20 
21 
22 
23 
24 

25 
26 
27 
28 
29 

30 


Number  of  Entbants,  40,498. 


„  .  . .  Discou-       T»j„j  Exposed  to 

Existing.       tinned.        Died.  ^^g^ 


2,349 

2,181 
1,776 
1,843 
2,000 

1,866 
1,958 
1,920 
1,676 
1,282 

756 
524 
240 
161 
187 

130 

86 

80 

109 

79 

57 
63 
41 
77 
117 

127 

83 

38 

34 

4 


21,848 


1,872 
6,484 
2,845 
1,856 
1,292 

900 
577 
525 
232 
142 

108 
63 
32 
30 
31 

9 

12 

10 

6 

4 

4 
4 
5 
2 
6 

1 
1 


17,052 


108 
219 
218 
173 
161 

132 
97 
95 
73 
53 

51 
26 
19 
25 
15 

21 
13 
17 

7 
14 

9 

7 

14 

10 

4 

6 
5 
4 

2 


1,598 


19,313 
32,927 

25,862.5 

21,518 

17,928 

14,671 
11,934.5 

9,328.5 

6,935 

4,999 

3,539 

2,646.5 

2,049 

1,759 

1,542.5 

1,320.5 
1,159 
1,049 
944.5 

824 

727 

657 

582.5 

524 

433 

309 
175.5 

86.5 

44 


«104,474,000  INSXTRBD. 


185,800.0 


Amonnts 
Existing. 


6,073 
5,438 
4,580 
4,327 
4,821 

4,652 
4,900 
4,549 
4,057 
3,117 

1,793 

1,262 

522 

433 

543 

359 
223 

171 
280 
216 

136 
151 

99 
180 
269 

286 
223 
126 
100 
13 

20 


Amounts 
Discontinued 


I  53,919 


$ 
4,107 
15,517 

8,877 
5,817 
3,966 

2,815 

1,824^ 

1,252 

668 

385 

261 

157 

84 

82 

91 

48 
49 
22 
6 
16 

11 
19 
21 
11 
11 

2 
4 


Deatli 
Claims. 


$ 

232 

584 
604 
511 
502 

385 
264 
223 
197 
131 

118 
102 

49 
75 
55 

69 
35 
39 
41 
30 

26 
30 
33 
43 
10 

14 

13 

15 

2 


Exposed  to 
Bislc. 


46,123  I  4,432 


50,183.5 
86,303.5 
68,084.5 
55,553.5 

45,824 

37,110.5 

29,754 

23,052 

17,320 

12,539.5 

8,968.5 

6,848.5 

5,364 

4,710 

4,115.5 

3,448 

2,971.5 

2,678 

2,454 

2,122 

1,862.5 
1,685.5 
1,484.5' 
1,336.5 
1,102.5 

818 
517 
278 
135 
33 

20 


478,677.5 


Age 

at 

Exit. 


33 
34 
35 
36 

37 

38 
39 
J,0 

U 
42 

43 

U 
45 
46 

47 

48 
49 
50 
51 

52 

53 
54 

55 
56 

57 

58 
59 
60 
61 

62 

63 


Age  at  Entry,  34  Years. 


NuMBBB  OF  Entrants, 

2,491 

1,669 

99 

2,026 

6,097 

192 

1,828 

2,895 

163 

1,813 

1,791 

174 

1,864 

1,258 

169 

1,976 

836 

139 

1,977 

574 

109 

1,975 

476 

85 

1,599 

249 

62 

1,237 

144 

49 

18,977.5 
32,316.5 
25,602.5 
21,268.5 

17,757 

14,677 

11,857 

9,246 

6,823.5 

4,966 


$102,664,000  Insubbd. 


6,401 

5,508 
4,435 

4,285 
4,395 

4,849 
5,160 
4,937 
4,025 
2,967 


3,469 

262 

14,753 

497 

8,303 

494 

5,707 

481 

3,899 

446 

2,729 

402 

1,696 

305 

1,224 

223 

683 

155 

422 

118  i 

49,597.5 
85,155.5 
67,622.5 
55,688.5 
46,119.5 

37,964.5 

30,501 

23,576 

17,462.5 

12,730 


34 
35 
36 
37 
38 

39 
40 

41 
42 
43 


TABLE    I. 


OBSERVATIONS  ON  MALE  LIFE. 


Age  at  EnU7,  34  Years. 

9 

NUMBEB  OP 

Bntbants 

,  39,624. 

•    1103,664,000  Inscbed. 

Age 

at 
Exit. 

Existing. 

Discon- 
tinued. 

Died. 

Exposed  to 
Risk. 

Amounts 
Existing. 

Amounts 
Discontin'ed. 

Death 
Claims. 

Exposed  to 
Risk. 

$ 

$ 

$ 

s 

10 

789 

98 

45 

3,559 

1,972 

290 

105 

9,289 

U 

11 

458 

74 

25 

2,639 

1,079 

213 

76 

6,960.5 

45 

12 

277 

36 

29 

2,101 

722 

134 

107 

5,632 

46 

13 

160 

27 

21 

1,763.5 

430 

88 

55 

4,692 

47 

14 

169 

27 

12 

1,555.5 

425 

67 

37 

4,129.5 

48 

15 

161 

19 

16 

1,351.5 

423 

39 

49 

3,614.5 

49 

16 

111 

16 

13 

1,157 

298 

40 

40 

3,103 

60 

17 

89 

11 

14 

1,019;  5 

208 

14 

48 

2,738 

51 

18 

96 

10 

8 

906 

263 

37 

27 

2,456.5 

52 

19 

61 

7 

14 

793.5 

183 

25 

42 

2,135.5 

53 

20 

49 

8 

9 

711 

124 

6 

21 

1,895 

54 

21 

52 

6 

12 

646 

147 

14 

30 

1,740 

55 

22 

59 

7 

6 

575.5 

152 

25 

17 

1,543.5 

56 

23 

80 

5 

11 

504.5 

216 

13 

37 

1,355.5 

57 

24 

119 

8 

411 

287 

29 

1,096 

58 

25 

86 

1 

3 

283.5 

245 

1 

10 

779.5 

69 

26 

87 

2 

9 

193 

229 

4 

14 

522 

60 

27 

45 

2 

96 

153 

4 

277 

61 

28 

29 

2 

49 

84 

6 

120 

62 

29 

10 

18 

15 

31 

63 

30 

8' 

8 

16 

16 

64 

21,781 

16,343 

1,500 

183,832.5 

54,633 

43,895 

4,136 

480,543.5 

Age  at  En 

try,  35  ^ 

fears. 

0 

Ni 

FHBEB  OP  I 

Sntbants 

39,759. 

$103,782,000  iNaCBEB. 

36 

2,192 

1,826 

94 

18,966.5 

5,722 

3,955 

231 

49,913.5 

1 

2,023 

6,257 

209 

32,518.5 

5,292 

15,063 

633 

86,342.5 

36 

2 

1,738 

2,673 

203 

25,821.5  1 

4,423 

8,570 

597 

68,601 

37 

3 

1,833 

1,761 

190 

21,663.5  ' 

4,324 

5,703 

519 

56,444.5 

38 

4 

1,993 

1,252 

187 

18,134 

4,887 

4,157 

517 

46,671.5 

39 

5 

1,967 

891 

153 

14,882.5 

5,120 

2,684 

426 

37,847 

40 

6 

2,034 

605 

126 

12,014.5 

4,923 

1,760 

311 

30,079 

41 

7 

1,923 

520 

87 

9,292 

4,358 

1,325 

255 

23,302.5 

42 

8 

1,577 

233 

67 

6,905.5 

3,905 

662 

178 

17,696 

43 

9 

1,254 

155 

48 

5,067.5 

3,079 

440 

120 

13,062 

U 

10 

835 

97 

47 

3,639.5 

1,899 

262 

119 

9,512 

45 

11 

500 

59 

27 

2,679.5 

1,142 

184 

80 

7,271 

46 

12 

249 

37 

28 

2,104.5 

724 

105 

73 

5,904.5 

47 

13 

189 

23 

26 

1,797.5 

496 

94 

71 

5,008 

48 

14 

183 

33 

12 

1,554.5 

509 

114- 

31 

4,337 

49 

15 

139 

16 

19 

1,335 

351 

54 

56 

3,713 

60 

16 

115 

11 

15 

1,163.5 

332 

25 

40 

3,266.5 

61 

17 

79 

8 

13 

1,024 

235 

14 

32 

2,875 

62 

18 

69 

9 

13 

923.5 

151 

14 

33 

2,594 

53 

19 

72 

6 

12 

834 

245 

16 

43 

2,395 

54 

TABLE    I. 

OBSERVATIONS  ON  MALE  LIFE. 


97' 


* 

Age  at  Entry,  35  Years. 

If 

NlTHBEB  OF  EKTBAltTS, 

39,759. 

$103,782,000  Insubed. 

Age 

at 
Exit. 

Discon- 

Exposed to 
Risk. 

Amounts 

Amounts 

Death 

Exposed  to 
Risk. 

>'A 

Existing. 

tinued. 

Died. 

Existing. 

Discontin'ed. 

Claims. 

$ 

$ 

$ 

$ 

20 

54 

6 

17 

744 

146 

9 

51 

2,094.5 

55- 

21 

50 

9 

10 

665.5 

156 

24 

31 

1,881 

56 

22 

32 

5 

12 

598.5 

70 

19 

31 

1,672.5 

67 

23 

91 

3 

10 

550.5 

195 

7 

35 

1,558.5 

68 

24 

93 

1 

7 

447.5 

213 

2 

20 

1,324 

69 

25 

120 

1 

7 

346.5 

293 

2 

17 

1,089 

60 

26 

101 

4 

4 

217 

423 

5 

15 

775.5 

61 

27 

63 

1 

110 

178 

1 

335 

62 

28 

28 

2 

46 

90 

1 

156 

63 

29 

11 

1 

15.5 

39 

4 

63 

64 

30 

2 

2 

4 

7 

15 

22 

66 

21,609 

16,502 

1,648 

186,066.5 

53,927 

45,273 

4,582 

487,806.5 

Age  at  En 

try,  36  1 

fears. 

0 

Nt 

rUBEB  07  £ 

Intbasts 

38,034. 

$102,433,000  Insubed. 

36 

2,233 

1,632 

103 

18,201 

6,295 

3,859 

279 

49,287 

1 

1,973 

5,731 

231 

31,200.5 

5,509 

14,327 

1,120 

84,836.5 

37 

2 

1,734 

2,564 

206 

24,849 

4,343 

8,256 

656 

66,916 

38 

3 

1,757 

1,675 

198 

20,789.5 

4,279 

5,440 

505 

55,069 

39 

4 

1,850 

1,176 

174 

17,409 

4,348 

4,151 

454 

45,489.5 

JfO 

5 

1,885 

841 

148 

14,376.5 

4,849 

2,799 

496 

37,212.5 

U 

6 

1,844 

575 

110 

11,635.5 

4,985 

1,745 

346 

29,595.5 

Jf2 

7 

1,845 

507 

97 

9,140.5 

4,806 

1,279 

206 

22,752.5 

Jf3 

8 

1,588 

260 

89 

6,815 

4,034 

792 

214 

16,705 

U 

9 

1,234 

146 

39 

4,935 

2,867 

345 

110 

11,888.5 

46 

10 

888 

78 

31 

3,550 

1,754 

204 

97 

8,637 

46 

11 

556 

58 

36 

2,563 

1,315 

170 

115 

6,599 

47 

12 

206 

40 

18 

1,922 

514 

84 

56 

5,042 

48 

13 

165 

29 

19 

1,663.5 

423 

99 

54 

.    4,380.5 

49 

14 

188 

28 

17 

1,451 

496 

68 

66 

3,820 

60 

15 

147 

11 

12 

1,226.5 

401 

49 

28 

3,199.5 

61 

16 

94 

11 

19 

1,056.5 

236 

24 

65 

2,734 

62 

17 

65 

5 

14 

935.5 

138 

16 

35 

2,413 

63 

18 

78 

7 

8 

850.5 

185 

30 

17 

2,217 

64 

19 

64 

9 

12 

756.5 

217 

18 

31 

1,991 

66 

20 

44 

6 

7 

673 

.     109 

23 

32 

1,722.5 

66 

21 

51 

4 

11 

617 

135 

10 

27 

1,565 

67 

22 

38 

4 

10 

551 

106 

10 

41 

1,393 

68 

23 

62 

3 

9 

499.5 

129 

9 

30 

1,236.5 

69 

24 

107 

1 

10 

426.5 

156 

3 

27 

1,071.5 

60 

25 

109 

1 

12 

308.5 

279 

3 

33 

885.5 

61 

26 

69 

2 

4 

186 

198 

20 

5 

562 

62 

27 

56 

1 

4 

111.5 

181 

3 

19 

347.5 

63 

28 

23 

2 

51 

89 

6 

146 

64 

29 

13 

26 

1           13 

51 

66 

98 


TABLE     I. 

OBSERVATIONS  ON   MALE   LIFE. 


i 

1 

Age  at  Entry,  36  Years. 

'' 

Kj  d 

NUMBEK  OP 

ENTBANTf 

5,  38,034. 

$102,433,000  INSUBBD. 

Age 

at 

Eiit 

Discon- 

Exposed to 
Risk. 

Amounts 

Amounts 

Death 

Exposed  to 

94  H 

Existing. 

tinued. 

Died. 

Existing. 

Discontin'cd. 

Claims. 

$ 

$ 

1 

$ 

-30 

11 

, 

13 

35 

38 

66 

31 

2 

3 

67 

32 

1 

2 

1 

3 

68 

33 

2 

69 

34 

2 

70 

35 

2 

71 

36 

2 

72 

37 

2 

73 

38 

1 

2 

2 

U 

20,977 

15,405 

1,652 

178,799.5 

53,424 

43,836 

5,173 

469,821.5 

Age  at  Entry,  37  Years. 

0 

Number  of  I 

ilTBANTS 

,  35,363. 

$94,029,000  INSXJKED. 

37 

2,074 

1,462 

73 

16,950.5 

5,468 

3,584 

178 

45,222.5 

1 

1,731 

5,294 

222 

29,107 

4,549 

13,034 

623 

78,282 

38 

2 

1,624 

2,432 

188 

23,291 

4,090 

7,308 

594 

62,939 

39 

3 

1,572 

1,506 

171 

19,510 

3,413 

5,215 

454 

51,993.5 

40 

4 

1,753 

1,160 

162 

16,434 

4,357 

3,602 

462 

43,718 

U 

5 

1,782 

814 

139 

13,532 

4,684 

2,866 

426 

35,665 

42 

6 

1,690 

536 

113 

10,936 

4,644 

1,688 

319 

28,278 

JfS 

7 

1,687        472 

96 

8,629 

4,185 

1,338 

264 

21,802 

U 

8 

1,538         258 

63 

6,481 

3,881 

716 

152 

16,326 

45 

9 

1,212 

129 

48 

4,686.5 

2,792 

362 

107 

11,754 

46 

10 

785 

92 

35 

3,316 

1,905 

292 

82 

8,528 

47 

11 

465 

66 

32 

2,417 

1,112 

160 

109 

6,315 

48 

12 

221 

37 

28 

1,868.5 

593 

107 

93 

4,960.5 

49 

13 

165 

28 

23 

1,587 

429 

68 

59 

4,187 

50 

14 

168 

25 

23 

1,372.5 

441 

74 

58 

3,628 

51 

15 

117 

.    12 

18 

1,163 

329 

29 

50 

3,077.5 

52 

16 

116 

15 

14 

1,014.5 

360 

33 

33 

2,667.5 

53 

17 

87 

5 

13 

874.5 

201 

28 

42 

2,244 

54 

18 

64 

6 

16 

769 

156 

7 

42 

1,983.5 

55 

19 

60 

6 

8 

683 

173 

22 

24 

1,771 

56 

20 

57 

4 

7 

610     ! 

164 

22 

17 

1,552 

57 

21 

28 

2 

8 

543 

61 

6 

26 

1,357 

58 

22 

39 

6 

9 

503 

92 

21 

33 

1,256.5 

59 

23 

60 

3 

11  1 

450.5 

135 

8 

26 

1,117 

60 

24 

93 

2 

10 

377 

191 

3 

42 

950.5 

^1 

25 

82 

5 

273      ■ 

198 

15 

716 

62 

26 

61 

6 

186     ' 

179 

25 

503 

63 

27 

58 

4 

119 

164 

14 

299 

64 

28 

28 

1 

57 

71 

5 

121 

65 

29 

14 

1 

28     1 

22 

1 

45 

66 

30 

12 

1 

13     i 

21 

1 

22 

67 

19,443 

14,372 

1,548 

167,781.5 

49,060 

40,593 

4,376 

443,281.0 

TABLE    I. 

OBSERVATIONS  ON  MALE  LIFE. 


99 


1 

Age  at  Entry,  38  Years.                                                  1 

Number  op  Entbants 

,  34,7r2. 

$93,522,000  INSUBED. 

Age  1 
at 
Exit 

Discon- 

r 

Exposed  to 
Risk. 

1 

!     Amounts 

Amounts 

Death 

Exposed  to 
Risk. 

Existing. 

tinued. 

Died. 

i    Existing. 

Discontin'ed. 

Claims. 

$ 

$ 

$ 

$ 

0 

2,110 

1,427 

92 

16,672.5 

5,262 

3,130 

240 

45,196 

S8 

1 

1,746 

5,169 

224 

28,558.5 

4,751 

12,952 

591 

78,414 

39 

2 

1,650 

2,301 

186 

22,853.5 

4,304 

7,316 

515 

62,938 

¥> 

3 

1,545 

1,608 

176 

19,063 

1      3,879 

5,226 

468 

51,848 

41 

4 

1,816 

1,120 

138 

15,978 

1      4,492 

3,724 

468 

43,026 

J^ 

5 

1,542 

747 

141 

13,090.5 

4,422 

2,400 

334 

35,004 

J,B 

6 

1,796 

509 

125 

10,779.5 

4,860 

1,657 

308 

28,219.5 

U 

7 

1,743 

432 

84 

8,388 

4,499 

1,188 

242 

21,629 

J^o 

8 

1,591 

212 

64 

6,239 

4,062- 

582 

170 

16,003 

m 

9 

1,158 

143 

47 

4,406.5 

2,829 

362 

103 

11,299 

Jf7 

10 

711 

91 

38 

3,084.5 

1,625 

243 

96 

8,064.5 

Jt8 

11 

457 

58 

31 

2,261 

1,080 

174 

91 

6,135 

Jf9 

12 

231 

34 

25 

1,727 

537 

112 

53 

4,821 

50 

13 

149 

24 

15 

1,442 

447 

60 

45 

4,145 

51 

14 

195 

23 

12 

1,254.5 

610 

64 

49 

3,591 

52 

15 

101 

13 

14 

1,029.5 

295 

37 

34 

2,881.5 

.  53 

16 

88 

13 

14 

901.5 

238 

34 

35 

2,517 

5k 

17 

64 

7 

13 

789.5 

163 

24 

43 

2,215 

55 

18 

69 

7 

12 

705.5 

187 

15 

39 

1,989.5 

56 

19 

47 

2 

11 

620 

120 

10 

29 

1,751 

57 

20 

38 

4 

9 

559 

108 

11 

20 

1,591.5 

58 

21 

35 

3 

6 

508.5 

115 

16 

24 

1,450 

59 

22 

33 

3 

11 

464.5 

88 

3 

31 

1,301.5 

60 

23 

45 

2 

9 

418 

113 

11 

39 

1,175.5 

61 

24 

102 

1 

10 

362.5 

234 

4 

25 

1,016 

62 

25 

85 

10 

250 

237 

37 

755 

63 

26 

60 

1 

4 

154.5 

182 

10 

7 

476 

6U 

27 

48 

1 

90 

167 

i 

1 

282 

65 

28 

22 

2 

41 

74 

1 

114 

66 

29 

6 

1 

1 

16.5 

18 

3 

3 

37.5 

67 

30 

^8 
19,291 

1 

9 

12 

3 

15 

68 

13,955 

1,526 

162,717.5 

50,010 

39,368 

4,144 

439,901.0 

Age  at  Ed 

try,  39  1 

fears. 

0 

Nt 

rHBEB  OF  I 

Entrants 

32,206. 

$88,592,000  Insured. 

39 

1,839 

1,307 

79 

15,449.5 

4,986 

2,922 

258 

42,835 

1 

1,636 

4,705 

201 

26,628.5 

4,765 

11,866 

588 

74,493 

Jfi 

2 

1,550 

2,030 

195 

21,424     1 

4,133 

6,324 

579 

60,045 

Jfl 

3 

1,521 

1,417 

190 

17,955.5 

3,629 

4,767 

518 

49,787.5 

1^ 

4 

1,547 

1,029 

172 

15,021.5 

4,034 

3,385 

510 

41,564.5 

43 

5 

1,624 

753 

146 

12,411.5  ! 

4,488 

2,360 

410 

34,148 

U 

6 

1,633 

493 

108 

10,018.5  : 

4,605 

1,596 

273 

27,272 

45 

7 

1,649 

412 

75 

7,825      : 

4,507 

1,173 

302 

21,009.5 

46 

8 

1,513 

197 

53 

5,796.5 

3,773 

591 

139 

15,318.5 

47 

9 

1,042 

130 

47 

4,067 

2,645 

384 

118 

10,920 

48^ 

100 


TABLE    I. 

OBSERVATIONS   ON  MALE  LIFE. 


Age  at  Entry,  39  Years. 

»2S 

Number  op 

Entrants 

,  32,206. 

$88,592,000  iNsmiED. 

1 
Age 
at 
Fixit 

Discon- 

Exposed to 
Risk. 

Amounts 

Amounts 

Death 

Exposed  to 
Bisk. 

^►3 

Existinff. 

tinued. 

Died. 

Existing. 

Discontin'ed. 

Claims. 

$ 

$ 

$ 

$ 

10 

698 

80 

31 

2,873 

1,759 

182 

110 

7,874 

J^o 

11 

403 

65 

37 

2,071.5 

996 

155 

108 

5,836.5 

50 

12 

191 

26 

29 

1,586 

523 

85 

89 

4,612.5 

51 

13 

139 

19 

17 

1,343.5 

433 

72 

51 

3,922 

52 

14 

148 

19 

15 

1,168.5 

393 

80 

46 

3,362 

53 

15 

112 

10 

14 

991 

356 

17 

31 

2,874.5 

5^ 

16 

102 

7 

14 

856.5 

275 

22 

50 

2,468 

55 

17 

63 

4 

9 

735 

192 

7 

20 

2,128.5 

56 

18 

70 

4 

15 

659 

171 

27 

55 

1,899.5 

57 

19 

53 

4 

11 

570 

141 

6 

28 

1,657 

58 

20 

39 

5 

8 

501.5 

93 

10 

34 

1,480 

59 

21 

32 

3 

12 

450.5 

91 

9 

46 

1,343.5 

60 

22 

34 

2 

9 

404 

166 

5 

22 

1,199.5 

61 

23 

48 

2 

5 

359 

107 

5 

16 

1,006.5 

62 

24 

66 

9 

305 

145 

30 

881 

63 

25 

75 

2 

5 

229 

160 

1 

22 

705.5 

6U 

26 

68 

6 

148 

227 

24 

523 

65 

27 

30 

3 

74 

123 

13 

272 

66 

28 

21 

1 

3 

40.5 

61 

3 

11 

134.5 

67 

29 

4 

3 

16 

12 

4 

61 

68 

30 

9 

9 

45 

45 

69 

17,959 

12,726 

1,521 

151,988.0 

48,033 

36,054 

4,505 

421,679.0 

Age  at  En 

try,  40  ^ 

fears. 

0 

Ni 

JHBEB  OP  1 

Sntbants 

.  33,003. 

$90,364,000  Insured. 

Jfi 

1,883 

1,346 

90 

15,828.5 

5,034 

3,001 

271 

43,681.5 

1 

1,712 

4,760 

222 

27,304 

4,910 

11,946 

668 

76,085 

Jil 

2 

1,534 

2,114 

204 

21,933 

3,276 

7,046 

564 

61,011 

J^ 

3 

1,449 

1,447 

193 

18,414.5 

3,332 

4,951 

594 

51,172.5 

JfP 

4 

1,639 

1,045 

173 

15,526.5 

3,850 

3,490 

560 

43,026 

U 

5 

1,758 

735 

121 

12,824.5 

5,273 

2,560 

330 

35,591 

Jf5 

6 

1,950 

478 

109 

10,339 

5,219 

1,534 

307 

27,941 

Jf6 

7 

1,736 

386 

101 

7,848 

4,520 

1,082 

289 

21,107 

Jf7 

8 

1,387 

208 

55 

5,714 

3,808 

650 

170 

15,432 

U8 

9 

1,043 

138 

45 

4,099 

2,702 

398 

135 

10,930 

49 

10 

713 

85 

38 

2,899.5 

1,811 

216 

132 

7,786 

50 

11 

436 

53 

30 

2,079.5 

1,103 

136 

86 

5,667 

51 

12 

191 

25 

22 

1,574.5 

491 

72 

66 

4,374 

52 

13 

120 

21 

12 

1,338.5 

390 

49 

44 

3,756.5 

53 

14 

160 

23 

26 

1,184.5 

486 

71 

83 

3,262.5 

5U 

15 

122 

9 

13 

982.-5 

361 

32 

36 

2,642 

55 

16 

84 

8 

21 

839 

259 

32 

78 

2,213 

56 

17 

66 

7 

■    17 

726.5 

155 

35 

46 

1,842.5 

57 

18 

54 

2 

15 

639 

126 

1 

40 

1,623.5 

58 

19 

37 

5 

12 

566.5 

88 

13 

26 

1,450.5 

59 

TABLE     I. 

OBSERVATIONS  ON  MALE  LIFE. 


101 


Age  at  Entry,  40  Years. 

11 

NUMBEB  OP  ] 

Entrants 

,  33,003. 

$90,364,000  Insubbd. 

Age 

at 
Exit. 

Discon- 

Exposed to 
Risk. 

Amounts 

Amounts 

Death 

Exposed  to 

>'A 

Existing. 

tinued. 

Died. 

Existing. 

Discontin''ed. 

Claims. 

Eisk. 

$ 

$ 

$ 

20 

37 

5 

11 

512.5 

110 

13 

23 

1,323.5 

60 

21 

41 

4 

14 

460 

93 

17 

55 

1,175.5 

61 

22 

43 

2 

13 

402 

96 

4 

34 

1,017 

62 

23 

54 

2 

10 

344 

119 

3 

32 

•883.5 

63 

24 

65 

6 

279 

149 

20 

731 

6J, 

25 

89 

9 

208 

208 

33 

562 

65 

26 

45 

1 

2 

109.5 

138 

3 

4 

319.5 

66 

27 

30 

62 

89 

176 

67 

28 

19 

1 

32 

48 

1 

87 

68 

29 

9 

12 

35 

38 

69 

30 

3 

3 

3 

3 

70 

18,509 

12,909 

1,585 

155,085.0 

48,282 

37,355 

4,727 

426,910.5 

Age  at  Er 

itry,  41  ^ 

fears. 

0 

Nt 

THBKB  OF  I 

Sntbants 

,  27,981. 

$79,495,000  Insubbd. 

U 

1,711 

1,076 

84 

13,452.5 

4,784 

2,382 

257 

38,556.5 

1 

1,399 

3,943 

202 

23,138.5 

4,102 

10,345 

577 

66,899.5 

42 

2 

1,275 

1,824 

178 

18,654 

3,111 

6,085 

519 

54,005.5 

43 

3 

1,366 

1,251 

159 

15,663.5 

3,262 

4,196 

417 

45,235 

U 

4 

1,386 

872 

133 

13,077 

3,561 

3,106 

369 

37,905 

45 

5 

1,494 

631 

123 

10,806.5 

4,454 

2,164 

355 

31,340 

46 

6 

1,519 

434 

101 

8,657 

4,552 

1,769 

356 

24,564.5 

47 

7 

1,412 

360 

76 

6,640 

3,937 

1,012 

216 

18,266 

48 

8 

1,298 

171 

68 

4,886.5 

3,599 

508 

162 

13,353 

49 

9 

827 

98 

39 

3,386 

2,139 

306 

96 

9,185 

50 

10 

602 

68 

27 

2,437 

1,594 

222 

60 

6,686 

51 

11 

369 

32 

23 

1,758 

937 

83 

62 

4,879.5 

52 

12 

179 

23 

18 

1,338.5 

490 

86 

74 

3,796 

53 

13 

122 

19 

10 

1,120.5 

373 

64 

23 

3,157 

54 

14 

132 

17 

14 

970,5 

427 

72 

36 

2,693 

55 

15 

92 

12 

11 

810 

261 

48 

32 

2,170 

56 

16 

64 

6 

13 

698 

182 

33 

48 

1,836.5 

57 

ar 

38 

5 

9 

615.5 

106 

22 

24 

1,579 

58 

18 

50 

6 

9 

563 

152 

19 

22 

1,428.5 

59 

19 

47 

4 

13 

499 

130 

4 

25 

1,243 

60 

20 

31 

2 

10 

436 

68 

4 

27 

1,084 

61 

21 

19 

3 

9 

392.5 

56 

2 

19 

986 

62 

22 

39 

1 

12 

362.5 

87 

4 

30 

908 

63 

23 

35 

2 

9 

310- 

79 

5 

27 

786.5 

64 

24 

71 

1 

10 

264.5 

108 

3 

35 

676.5 

65 

25 

63 

6 

183 

152 

23 

532 

66 

26 

37 

1 

4 

113.5 

100 

3 

17 

355.5 

67 

27 

34 

3 

72 

113 

7 

237 

68 

28 

17 

1 

35 

70 

4 

117 

69 

29 

7 

1 

17 

22 

1 

43 

70 

103 


TABLE    I. 


OBSERVATIONS  ON  MALE  LIFE. 


Age  at  Entry,  41 

YesLTs. 

■a  c3 

NlTHBBR  OF 

Entbants,  27,981. 

$79,495,000  Insured. 

Age 

at 

"Exit. 

Discon- 

j    Exposed  to 
1          Risk. 

Amounts 

Amounts 

Deatli 

Exposed  to 
Bislc. 

^5 

Existing. 

tinued. 

Died. 

Existing. 

Discontin'ed 

Claims. 

$ 

$ 

$ 

$ 

30 

6 

1 

9 

18 

1 

20 

71 

31 

2 

1 

72 

32 

2 

1 

73 

33 

2 

1 

7Jf 

34 

2 

1 

1 

.5 

75 

15,741 

10,864 

1,376 

131,373.5 

43,026 

32,548 

3,921 

374,527.5 

Age  at  Entry,  42  Years. 

0 

Ni 

JMBEB  OP  ] 

Entrants 

,  36.450. 

j                             $76,522,000  Insured. 

1 

42 

1,538 

965 

92 

12,742.5 

1 

4,399 

2,396 

263 

37,063 

1 

1,295 

3,703 

191 

22,003.5 

3,950 

9,795 

511 

64,566.5 

A3 

2 

1,265 

1,712 

173 

17,810 

3,388 

5,643 

510 

52,386.5 

U 

3 

1,217 

1,141 

122 

14,945.5 

3,123 

4,110 

339 

43,612 

J,5 

4 

1,372 

823 

141 

12,624.5 

3,637 

3,009 

462 

36,590.5 

Jf6 

5 

1,310 

608 

137 

10,396 

3,910 

2,133 

389 

29,920.5 

Jf7 

6 

1,413 

389 

89 

8,450.5 

4,058 

1,398 

279 

23,856 

48 

7 

1,452 

345 

58 

6,581.5  1 

4,150 

1,030 

167 

18,305 

49 

8 

1,205 

176 

70 

4,811      i 

3,391 

506 

195 

13,220 

50 

9 

929 

90 

59 

3,403 

2,405 

293 

147 

9,234.5 

51 

10 

553 

71 

26 

2,334.5 

1,394 

205 

59 

6,433.5 

52 

11 

350 

47 

25 

1,696.5 

903 

168 

59 

4,794 

58 

12 

156 

25 

20 

1,285.5 

465 

58 

52 

3,719 

54 

13 

120 

20 

15 

1,087 

352 

62 

47 

3,142 

55 

14 

113 

14 

13 

935 

285 

43 

40 

2,690.5 

56 

15 

63 

8 

12 

798 

177 

18 

43 

2,335 

57 

16 

57 

5 

12 

716.5 

175 

26 

36 

2,093 

58 

17 

55 

8 

11 

641 

155' 

27 

44 

1,855.5 

59 

18 

49 

2 

10 

570 

148 

3 

46 

1,641.5 

60 

19 

39 

3 

9 

508.5 

121 

8 

20 

1,442 

61 

20 

18 

4 

12 

457 

53 

20 

31 

1,287 

62 

21 

25 

4 

14 

423 

83 

19 

27 

1,183.5 

63 

22 

29 

3 

10 

380.5  , 

51 

13 

36 

1,057.5 

64 

23 

57 

2 

15 

339 

159 

4 

58 

962 

65 

24 

81 

3 

13 

264.5 

226 

5 

46 

740.5 

66 

25 

68 

5 

169 

189 

11 

466 

67 

26 

44 

3 

96 

102 

15 

266 

68 

27 

29 

2 

2 

48 

101 

2 

10 

148 

69 

28 

11 

1 

16 

27 

5 

36 

70 

29 

i 

4 

4 

4 

4 

71 

14,917 

10,173 

1,360 

126,537.5 

41,581 

30,994 

3,947 

365,051.0 

TABLE    I. 

OBSERVATIONS  ON  MALE  LIFE. 


103 


1                                                 Age  at  Entry,  43  Years. 

ji 

Number  op  Entbants 

24,402. 

$69,852,000  IKSUBKD. 

Age 

at 

Exit. 

Discon- 

Exposed to 
Bisk. 

Amounts 

Amounts 

Deatli 

Exposed  to 
Risk. 

>'S 

Existing. 

tinued. 

Died. 

Existing. 

Discontinued. 

Claims. 

1 

$ 

$ 

$ 

0 

1,384 

937 

90 

11,733.5 

3,938 

3,170 

235 

33,841 

4S 

1 

1,340 

3,382 

187 

20,300 

3,731 

8,783 

548 

59,128 

u 

2 

1,344 

1,529 

172 

16,317.5 

3,334 

5,404 

497 

47,756 

^ 

3 

1,205 

1,030 

166 

13,622 

3,171 

3,511 

503 

39,567.5 

46 

4 

1,344 

723 

146 

11,374.5 

3,378 

2,691 

434 

32,792.5 

47 

5 

1,266 

518 

136 

9,364 

3,589 

1,880 

434 

26,705 

It8 

6 

1,259 

392 

85 

7,507 

3,444 

1,304 

293 

21,090 

49 

7 

1,329 

281 

92 

5,826.5 

3,639 

858 

289 

1'6,373 

50 

8 

1,012 

152 

60 

4,189 

3,835 

533 

155 

11,663.5 

51 

9 

806 

88 

49 

3,997 

3,157 

364 

107 

8,280 

52 

10 

466 

49 

32 

2,073.5 

1,196 

170 

91 

5,799 

53 

11 

359 

32 

23 

1,535 

976 

135 

77 

4,364.5 

54 

12 

134 

26 

19 

1,124 

385 

68 

43 

3,215 

55 

13 

105 

14 

15 

951 

333 

58 

48 

2^724 

56 

14 

108 

8 

16 

820 

352 

38 

48 

2,395 

57 

15 

85 

6 

13 

689 

335 

13 

39 

1,870 

58 

16 

43 

7 

10 

584.5 

131 

30 

22 

1,585 

59 

17 

41 

6 

8 

525 

138 

15 

27 

1,419.5 

60 

18 

40 

5 

470.5 

115 

16 

20 

1,249 

61 

19 

23 

3 

15 

419.5 

49 

8 

43 

1,102 

62 

20 

34 

6 

8 

377 

74 

15 

22 

998.5 

63 

21 

23 

3 

15 

340.5 

48 

8 

48 

891 

64 

22 

30 

8 

301 

73 

35 

791 

65 

23 

50 

1 

13 

263.5 

138 

3 

35 

681.5 

66 

24 

62 

1 

8 

198.5 

149 

1 

26 

506.5 

67 

25 

31 

3 

5 

137 

77 

4 

17 

329 

68 

26 

33 

1 

3 

89.5 

85 

6 

8 

230 

69 

27 

24 

2 

53 

69 

3 

134 

70 

28 

13 

2 

3 

36 

40 

1 

9 

61.5 

71 

29 

-'.2' 

1 

1 

8.5 

6 

3 

1 

10.5 

72 

30 

5 

5 

2 

2 

73 

13,790 

9,205 

1,407 

114,310.5 

37,737 

37,968 

4,147 

327,354.0 

Age  at  En 

try,  44  1 

fears. 

0 

Ni 

THBBB  OF  ] 

Sntbants 

22,431. 

$64,953,000  Inscbsd.- 

4U 

1,374 

830 

73 

10,800.5 

3,956 

1,911 

187 

31,521 

1 

1,076 

3,072 

163 

18,618 

2,999 

7,803 

432 

54,998 

Jt5 

2 

1,083 

1,477 

186 

15,104.5 

2,921 

4,943 

563 

45,194,5 

46 

3 

1,135 

987 

150 

13,603.5 

2,793 

3,583 

445 

37,448 

47 

4 

1,202 

679 

119 

10,485.5 

3,155 

3,531 

404 

31,153.5 

48 

5 

1,124 

535 

103 

8,557.5 

3,291 

1,676 

305 

25,491 

49 

6 

1,256 

354 

102 

6,886     1 

3,823 

1,350 

294 

20,432 

50 

7 

,  1,097 

284 

72 

5,309     1 

3,409 

811 

207 

15,285.5 

51 

8 

933 

132 

59 

3,833 

3,765 

415 

186 

11,056.5 

52 

9 

691 

78 

47 

3.735 

1.887 

371 

130 

7,762.5 

53 

104 


TABLE    I. 

OBSERVATIONS  ON  MALE  LIFE. 


Age  at  Entry,  44  Years. 

1 

i 

!i 

NUMBEB  OF  EnTB&NTS 

22,431. 

$64,9.53,000  Ihsdbbd. 

Age 
at 

S33 

£3 

. 

Discon- 

Exposed to 
Bisk. 

Amounts 

Amounts 

Death 

Exposed  to 

Exit 

>*A 

Existing. 

tinued. 

Died. 

Existing. 

Discontin'ed. 

Claims. 

Risk. 

$ 

$ 

f 

$ 

10 

447 

56 

33 

1,930 

1,198 

179 

90 

5,520.5 

H 

11 

266 

34 

28 

1,405 

686 

93 

88 

4,096.5 

55 

12 

141 

28 

17 

1,080 

438 

73 

52* 

3,239.5 

56 

13 

106 

10 

16 

903 

320 

35 

58 

2,695.5 

57 

14 

101 

8 

17 

772 

292 

19 

46 

2,290.5 

58 

15 

77 

4 

13 

648 

218 

32 

.     43 

1,927 

59 

16 

51 

7 

20 

552.5 

153 

19 

56 

1,640.5 

60 

17 

33 

4 

13 

476 

93 

4 

54 

1,420 

61 

18 

28 

4 

13 

426 

76 

8 

33 

1,267 

62 

19 

30 

2 

10 

382 

84 

24 

30 

1,142 

63 

20 

20 

2 

9 

340 

55 

7 

49 

1,012.5 

6Jf 

21 

26 

1 

14 

309.5 

91 

3 

51 

903.5 

65 

22 

15 

13 

269 

37 

92 

760 

66 

23 

61 

3 

16 

239.5 

159 

7 

42 

627.5 

67 

24 

50 

11 

161 

117 

25 

423 

68 

25 

38 

5 

100 

98 

19 

281 

69 

26 

25 

1 

2 

56.5 

58 

3 

10 

162.5 

70 

27 

19 

29 

64 

93 

71 

28 

7 

10 

16 

29 

72 

29 

1 

3 

3 

13 

73 

30 

2 

2 

10 

' 

10 

7^ 

12,515 

■  8,592 

1,324 

104,925.5 

35,264 

25,698 

3,991 

309,896.5 

Age  at  En 

try,  45  1 

fears.    * 

0 

Nt 

THBBB  OF  I 

Sntbants 

21,980. 

$63,491,000  iKSTTBXt). 

45 

1,241 

859 

69 

10,560.5 

3,441 

1,947 

222 

30,772 

1 

1,137 

3,043 

180 

18,289.5 

3,319 

8,169 

537 

53,796.5 

46 

2 

1,076 

1,361 

170 

14,770.5 

2,724 

4,349 

455 

43,681.5 

47 

3 

1,055 

906 

158 

12,391 

3,034 

3,277 

450 

36,689.5 

48 

4 

1,217 

657 

131 

10,396.5 

3,136 

2,223 

418 

3(r,455.5 

49 

5 

1,135 

482 

96 

8,479 

3,329 

1,624 

286 

24,978 

50 

6 

1,193 

339 

104 

6,837.5 

3,635 

1,145 

279 

19,978.5 

51 

7 

1,101 

274 

79 

5,234 

3,312 

897 

246 

15,043.5 

52 

8 

949 

113 

55 

3,860.5 

2,732 

406 

169 

10,834 

53 

9 

745 

95 

42 

2,752.5 

2,054 

330 

91 

7,565 

54 

10 

490 

56 

30 

1,890 

1,266 

176 

73 

5,167 

55 

11 

289 

38 

16 

1,323 

773 

104 

37 

3,688 

56 

12 

112 

17 

13 

990.5 

336 

44 

43 

2,804 

57 

13 

90 

6 

20 

854 

250 

35 

52 

2,385.5 

58 

14 

81 

14 

23 

734 

252 

35 

59 

2,048.5 

59 

15 

58 

6 

20 

620 

164 

14 

46 

1,713 

60 

16 

38 

6 

11 

536 

120 

17 

38 

1,487.5 

61 

17 

45 

3 

10 

482.5 

99 

10 

30 

1,316 

62 

18 

44 

5 

12 

423.5 

120 

6 

34 

1,179 

63 

19 

15 

4 

7 

363 

39 

11 

13 

1,016.5 

64 

TABLE    I. 

OBSERVATIONS  ON  MALE  LIFE. 


105 


Age  at  Entry,  45  Years. 

<b5 

Ntjhber  op  Entbants 

21,980. 

$63,491,000  Iksxtbed. 

Age 
at 

FiTlt 

Discon- 

Exposed to 
Risk. 

Amounts 

Amounts 

Death 

Exposed  to 
Risk. 

>'A 

Existing. 

tinued. 

Died. 

Existing. 

Discontin'ed 

Claims. 

$ 

$ 

$ 

$ 

20 

19 

3 

11 

337.5 

68 

4 

23 

957 

65 

21 

22 

4 

14 

304 

54 

11 

35 

858.5 

66 

22 

31 

1 

11 

265.5 

68 

8 

38 

760 

67 

23 

32 

2 

6 

222 

86 

6 

50 

647 

68 

21 

52 

13 

183 

146 

32 

508 

69 

25 

42 

8 

118 

104 

15 

330 

70 

26 

21 

2 

68 

75 

13 

211 

71 

27 

25 

2 

45 

71 

4 

123 

72 

28 

11 

1 

1 

17.5 

33 

3 

3 

46.5 

73 

29 

2 

5 

6 

9 

7A 

30 

3 

3 

3 

3 

75 

12,371 

8,295 

1,314 

103,356.5 

34,849 

24,851 

3,791 

301.052.0 

Age  at  Er 

Ltry,  46  ^ 

fears. 

0 

Nt 

TMBEB  OF  I 

Entrants 

19,350. 

$57,757,000  Insubbd. 

J,6 

1,135 

711 

6V 

9,319.5 

3,449 

1,638 

155 

28,059.5 

1 

959 

2,613 

156 

16,130.5 

3,146 

6,791 

481 

49,119.5 

Jf7 

2 

900 

1,221 

137 

13,098.5 

1      2,507 

4,299 

486 

39,947.5 

^ 

3 

937 

816 

122 

11,043 

2,607 

2,843 

421 

33,383.5 

^9 

4 

1,002 

573 

126 

9,289.5 

2,825 

2,202 

385 

27,833 

50 

5 

1,053 

417 

107 

7,666.5 

3,102 

1,554 

327 

22,745 

51 

6 

1,093 

282 

89 

6,157 

3,301 

1,082 

256 

17,998 

52 

7 

1,002 

259 

78 

4,704.5 

3,054 

807 

247 

13,496.5 

53 

8 

891 

125 

54 

3,432.5 

2,547 

432 

141 

9,576 

51, 

9 

711 

76 

41 

2,387 

1,837 

245 

108 

6,549.5 

55 

10 

408 

51 

26 

1,571.5 

1,106 

134 

79 

4,415 

56 

11 

262 

24 

11 

1,100 

638 

59 

37 

3,133.5 

57 

12 

123 

18 

16 

806 

352 

49 

70 

2,404.5 

58 

13 

67 

10 

11 

653 

210 

60 

63 

1,928 

59 

14 

69 

8 

17 

566 

236 

22 

45 

1,614 

60 

15 

62 

2 

5 

475 

187 

6 

22 

1,319 

61 

16 

28 

5 

6 

404.5 

73 

21 

30 

1,096.5 

62 

17 

43 

2 

11 

367 

128 

10 

12 

978 

63 

18 

15 

1 

15 

311.5 

62 

4 

40 

831 

6A 

19 

19 

3 

11 

279.5 

41 

6 

22 

724 

65 

20 

20 

1 

12 

247.5 

46 

8 

35 

654 

66 

21 

14 

3 

8 

213.5 

50 

10 

24 

564 

67 

22 

30 

1 

9 

189.5 

75 

3 

31 

483.5 

68 

23 

27 

2 

6 

149 

57 

11 

15 

370.5 

69 

24 

30 

2 

3 

114 

68 

4 

8 

291 

70 

25 

26 

5 

80 

58 

21 

213 

71 

26 

20 

3 

49 

61 

7 

134 

72 

27 

16 

2 

26 

27 

2 

66 

73 

28 

4 

1 

8 

21 

3 

37 

74 

29 

2 

3 

10 

13 

75 

30 

1 

1 

3 

3 

76 

, . 

10,969 

7,226 

1,155 

90,843.0 

31,884 

22,300 

3,573 

269,980.5 

106 


TABLE     I. 


OBSERVATIONS  OX   MALE  LIFE. 


r 

1 
i 

Age  at  Entry,  47  Years. 

;  -si 

NUJfitBB  OF 

EnTBANT! 

i,  16,859. 

151,924,000  Ihsurbd. 

Age 

{SS 

at 
Exit. 

Existing. 

Discon- 
tinued. 

i    Died. 

1 

Exposed  to 
Risk. 

[      Amonnts 
Existing. 

Amoants 
Discontin'ed 

j     Death 
Claims. 

Exposed  to 
Risk. 

$ 

$ 

$ 

$ 

0 

955 

634 

61 

8,112.5 

2,704 

1,528 

178 

25,198 

47 

1 

788 

2,246 

173 

14,086 

2,394 

6,252 

546 

44,388 

4-8 

2 

781 

1,082 

133 

11,461 

2,185 

3,860 

369 

36,392 

49 

3 

853 

703 

96 

9,654.5 

2,231 

2,608 

317 

30,604 

50 

4 

863 

479 

120 

8,114.5 

2,450 

1,903 

358 

25,800.5 

51 

5 

953 

368 

66 

6,708    " 

2,829 

1,409 

214 

21,336.5 

52 

6 

1,019 

252 

77 

5,379 

3,137 

950 

210 

17,114 

53 

7 

938 

206 

65 

4,054 

2,936 

644 

210 

12,970 

H 

8 

765 

118 

53 

2,889 

3,341 

391 

150 

9,306.5 

55 

9 

572 

64 

43 

1,980 

1,528 

160 

94 

5,540 

56 

10 

341 

35 

22 

1,315.5 

937 

'      102 

87 

3,787 

57 

11 

187 

27 

14 

921.5 

454 

60 

39 

2,682 

58 

12 

107 

9 

17 

702.5 

275 

53 

54 

2,132.5 

59 

13 

56 

8 

7 

570      i 

168 

25 

18 

1,764.5 

60 

14 

45 

8 

10 

499 

119 

21 

32 

1,555.5 

61 

15 

41 

1 

8 

439.5 

136 

2 

17 

1,393 

62 

16 

37 

3 

13 

388.5 

113 

10 

55 

1,234 

63 

17 

23 

3 

11 

335.5 

47 

17 

20 

052.5 

64 

18 

32 

3 

8 

298.5 

123 

7 

119 

973.5 

65 

19 

18 

2 

12 

256 

116 

4 

35 

726 

66 

20 

13 

2 

7 

224 

25 

8 

23 

569 

67 

21 

14 

1 

9 

202.5 

48 

3 

20 

515.5 

68 

22 

13 

1 

7 

178.5  i 

37 

4 

15 

444. 

69 

23 

20 

2 

6 

157      i 

53 

4 

17 

388 

70 

24 

31 

6 

130 

73 

14 

316 

71 

25 

27 

1 

4 

92.5 

69 

3 

17 

227*5 

72 

26 

28 

2 

61      1 

66 

3 

140 

73 

27 

18 

4 

31 

43 

7 

71 

74 

28 

2 

2 

9 

7 

7 

21 

76 

29 

2 

1 

5 

2 

1 

7 

76 

30 

2 

2 

4 

4 

77 

9,544 

6,258 

1,057 

79,257.5 

28,650 

20,028 

3,246 

248,653.0 

Age  at  En 

try,  48  1 

rears. 

0 

Nt 

rXBBB  OF  I 

Intrants 

15,825. 

$47,985,000 

Insubbo. 

48 

905 

582 

72 

7,621.5 

2,555 

1,775 

175 

23,105 

1 

785 

1,986 

152 

13,273 

2,466 

5,366 

535 

40,797 

49 

2 

810 

987  ! 

121 

10,849.5 

2,426 

3,274 

358 

33,476 

50 

3 

758 

720 

112 

9,065 

1,888 

2,844 

362 

27,633 

51 

4 

849 

431 

108 

7,619.5 

2,342 

1,729 

373 

23,096.5 

52 

5 

838 

381 

95' 

6,256.5 

2,634 

1,499 

313 

18,767.5 

53 

6 

920 

251 

80 

5,007.5 

2,795 

879 

202 

14,631.5 

54 

7 

854 

163 

48 

3,800.5  i 

2,576 

540 

154 

10,925 

55 

8 

801 

93 

58 

2,770.5 

2,412 

297 

203 

7,776.5 

56 

9  1 

540 

49 

31 

1,840.5 

1,442 

149 

80 

4,938.5 

67 

TABLE    I. 


107 


OBSERVATIONS  ON  MALE  LIFE. 


Age  at  Entry,  48  Yfears. 

"1 

NUMBEB  OF  ] 

EKTBANTe 

,  15,825. 

$47,985,000  iHsxiBED. 

Age  I 

Js 

at 

Discon- 

T\Jnjl 

Exposed  to 
Risk. 

Amounts 

.  Amounts 

Death 

Exposed  to 

ETit  1 

^& 

Existing. 

tinued. 

Uiea. 

Existing. 

Discontin'ed. 

Claims. 

Rislc. 

$ 

1 

$ 

$ 

10 

278 

31 

22 

1,229.5 

646 

115 

68 

3,284.5 

58 

11 

227 

19 

13 

904.5 

575 

68 

40 

2,479 

59 

12 

83 

13 

16 

648.5 

208 

37 

56 

1,811.5 

60 

13 

60 

10 

10 

538 

157 

31 

27 

1,513.5 

61 

14 

62 

9 

8 

458.5 

173 

23 

31 

1,302.5 

62 

15 

50 

3 

11 

382.5 

184 

8 

40 

1,083 

63    \ 

16 

22 

3 

8 

318.5 

62 

11 

23 

849.5 

6J^    i 

17 

19 

8 

287 

63 

19 

759 

65    \ 

18 

23 

3 

9 

258.5 

65 

4 

20 

675 

66 

19 

18 

3 

11 

223.5 

48 

5 

31 

585.5 

67 

20 

9 

3 

11 

191.5 

27 

8 

33 

500 

68 

21 

11 

1 

8 

169.5 

33 

5 

18 

433.5 

69 

22 

17 

1 

7 

149.5 

47 

3 

23 

378.5 

70 

23 

26 

1 

5 

124.5 

51 

2 

8 

306 

'   71 

24 

37 

11 

93 

81 

35 

246 

■  72 

25 

13 

3 

45 

28 

9 

130 

73 

26 

10 

4 

29 

29 

11 

93 

7A 

27 

6 

15 

14 

53 

75 

28 

4 

9 

21 

39 

76 

29 

2 

5 

11 

18 

77 

30 

2 

3 

2 

1 

78 

31 

1 

5 

79 

32 

1 

5 

80 

33 

1 

1 

5 

5 

81 

9,039 

5,743 

1,043 

74,190.0 

26,061 

18,672 

3,252 

221,708.5 

Age  at  En 

try,  49  1 

fears. 

0 

Nt 

rHBER  OP  I 

Sntrants 

13,873. 

143,119,000  Insured. 

Jf9 

795 

456 

57 

6,708.5 

2,405 

1,090 

181 

21,014.5 

1 

686 

1,776 

128 

11,677 

2,155 

4,937 

356 

36,974.5 

50 

2 

680 

841 

125 

9,554.5 

2,071 

2,887 

383 

30,551.5 

51 

3 

725 

614 

118 

8,022 

1,973 

2,204 

383 

25,552 

52 

4 

758 

394 

90 

6,675 

1,907 

1,594 

277 

21,297 

63 

5 

854 

291 

96 

5,484.5 

2,594 

1,993 

289 

17,319.5 

H 

6 

826 

219 

86 

4,279.5 

2,545 

851 

295 

13,014.5 

55 

7 

774 

148 

63 

3,184 

2,350 

481 

173 

9,508.5 

56 

8 

588 

82 

38 

2,232 

1,874 

296 

120 

6,597 

57 

9 

411 

54 

38 

1,538 

1,163 

150 

120 

4,380 

58 

10 

261 

30 

32 

1,047 

715 

72 

81 

2,986 

59 

11 

146 

18 

17 

730 

419 

53 

54 

2,127.5 

60 

12 

71 

7 

10 

554.5 

206 

35 

36 

1,610.5 

61 

13 

45 

8 

10 

466 

134 

29 

26 

1,336.5 

62 

14 

51 

4 

10 

405 

166 

9 

25 

1,157.5 

63 

108 


TABLE    I. 

OBSERVATIONS   ON  MALE  LIFE. 


Age  at  Entry,  49  Years. 

^1 

Number  of 

Entrants 

,  13,87.3. 

143,119,000  Insured. 

Age 

at 

Discon- 

Exposed to 
Rislc. 

Amounts 

Amounts 

Deatti 

Exposed  to 
Risk. 

FrTit 

Existing. 

tinued. 

Died. 

Existing. 

Discontin'ed. 

Claims. 

$ 

s 

$ 

$ 

15 

39 

2 

11 

341 

107 

10 

39 

957 

6i 

16 

32 

18 

290 

114 

55 

806 

66 

17 

10 

1 

16 

239.5 

30 

1 

40 

636.5 

66 

18 

21 

2 

6 

212 

67 

3 

15 

564.5 

67 

19 

10 

2 

11 

183 

25 

3 

22 

479.5 

68 

20 

17 

1 

9 

160.5 

53 

11 

17 

425.5 

69 

21 

9 

1 

8 

133.5 

18 

1 

34 

349.5 

70 

22 

14 

12 

116 

30 

28 

297 

71 

23 

9 

6 

90 

19 

12 

239 

72 

24 

17 

6 

75 

43 

28 

208 

73 

25 

15 

2 

4 

51 

28 

1 

9 

136.5 

n 

26 

13 

3 

31 

50 

6 

99 

75 

27 

4 

1 

15 

10 

4 

43 

76 

28 

5 

10 

14 

29 

77 

29 

2 

5 

4 

15 

78 

30 

1 

1 

1 

2.5 

3 

3 

5 

9.5 

79 

7,889 

4,954 

1,030 

64,512.5 

23,292 

16,714 

3,113 

200,721.5 

Age  at  En 

try,  50  ' 

JTears. 

0 

Ni 

TMBKB  OP  I 

Entrants 

,  13,650. 

$41,776,000  Insured. 

50 

857 

491 

85 

6,579.5 

2,445 

1,110 

280 

20,333 

1 

667 

1,796 

163 

11,319 

1,949 

4,860 

581 

35,511 

51 

2 

652 

836 

147 

9,173 

1,893 

3,108 

487 

28,997 

52 

3 

673 

575 

132 

7,668.5 

1,875 

1,986 

467 

24,070 

53 

4 

831 

382 

104 

6,385 

2,266 

1,447 

340 

20,011.5 

5^ 

5 

823 

252 

93 

5,133 

2,707 

1,032 

298 

16,166 

55 

6 

768 

177 

62 

4,002.5 

2,393 

615 

209 

12,337.5 

56 

7 

784 

150 

72 

3,009 

2,541 

558 

287 

9,149 

57 

8 

575 

66 

44 

2,045 

1,725 

254 

131 

5,915 

58 

9 

364 

36 

29 

1,375 

1,020 

100 

86 

3,882 

59 

10 

236 

38 

26 

945 

603 

188 

59 

2,632 

60 

11 

120 

14 

17 

657 

320 

43 

54 

1,854.5 

61 

12 

63 

5 

16 

510.5 

142 

29 

57. 

1,444.5 

62 

13 

52 

8 

11 

425 

176 

19 

19 

1,221.5 

63 

14 

53 

6 

9' 

355 

153 

23 

25 

1,005.5 

H 

15 

34 

4 

12 

288 

119 

12 

28 

810 

65 

16 

19 

3 

6 

238.5 

56 

16 

11 

649 

66 

17 

18 

2 

6 

211 

53 

5 

22 

571.5 

67 

18 

15 

10 

185.5 

33 

1 

55 

493.5 

68 

19 

11 

4 

159.5 

26 

4 

13 

403 

69 

20 

16 

10 

143.5 

49 

6 

27 

359 

70 

21 

6 

3 

116.5 

17 

3 

7 

278.5 

71 

22 

13 

7 

106.5 

30 

1 

19 

252.5 

72 

23 

10 

3 

86 

21 

8 

203 

73 

24 

19 

5 

73 

42 

8 

174 

7Jt 

TABLE    I. 


109 


OBSERVATIONS  ON  MALE  LIFE. 


Age  at  Entry,  50  Years. 

•si 

n  d 

>2S 

NUMBKR  OF 

Entbantb 

,  13,650. 

$41,776,000  Insubkd. 

Age 
at 

Discon- 

Exposed to 
Rislv. 

Amounts 

Amounts 

Deatli 

Exposed  to 
Bislf. 

Exit. 

>"& 

Existing. 

tinued. 

Died. 

Existing. 

Discontin'ed. 

Claims. 

$ 

$ 

$ 

$ 

25 

17 

4 

49 

46 

10 

124 

75 

26 

7 

2 

3 

27 

15 

2 

7 

67 

76 

27 

8 

1 

16 

18 

1 

44 

77 

28 

3 

1 

7 

8 

2 

25 

78 

29 

3 

15 

79 

30 

3 

3 

15 

15 

80 

7,717 

4,848 

1,085 

61,295.0 

22,756 

15,422 

3,598 

189,014.0 

Age  at  Entry,  51  Years. 

0 

Ni 

JMBEB  OP  ] 

Sntrants 

,  10,458. 

$32,807,000  Insukbd. 

61 

619 

406 

56 

5,026 

1,703 

1,067 

177 

15,870 

1 

546 

1,381 

135 

8,686.5 

1,565 

3,899 

445 

27,910.5 

52 

2 

556 

607 

95 

7,011.5 

1,642 

2,373 

362 

22,764.5 

5S 

3 

513 

423 

90 

5,845.5 

1,510 

1,641 

359 

18,753.5 

5U 

4 

626 

317 

83 

4,872.5 

1,847 

1,266 

285 

15,431 

55 

5 

607 

225 

83 

3,892.5 

2,035 

918 

260. 

12,207 

56 

6 

591 

155 

61 

3,012.5 

1,924 

654 

215 

9,176 

57 

7 

557 

127 

41 

2,219.5 

1,683 

426 

132 

6,547 

68 

8 

398 

44 

49 

1,536 

1,149 

140 

141 

4,449 

59 

9 

254 

31 

29 

1,051.5 

837 

159 

95 

3,009.5 

60 

10 

171 

12 

25 

747 

422 

33 

55 

1,981. "5 

61 

11 

91 

9 

22 

540.5 

234 

31 

63 

1,472.5 

62 

12 

58 

5 

7 

420.5 

162 

18 

12 

1,151 

68 

13 

35 

5 

11 

350.5 

126 

18 

29 

959 

6Jf 

14 

47 

3 

6 

300.5 

134 

6 

16 

792 

65 

15 

31 

1 

8 

245.5 

109 

8 

18 

635 

66 

16 

26 

1 

10 

205.5 

70 

3 

17 

502.5 

67 

17 

22 

3 

3 

167.5 

67 

8 

7 

410 

68 

18 

17 

2 

7 

140 

64 

7 

9 

328.5 

69 

19 

7 

1 

4 

114.5 

16 

2 

8 

251 

70 

20 

3 

1 

5 

102.5 

5 

2 

9 

^25 

71 

21 

8 

1 

4 

93.5 

6 

1 

10 

209.5 

72 

22 

19 

6 

81 

22 

11 

193 

73 

23 

12 

9 

56 

28 

23 

160 

74 

24 

14 

2 

35 

33 

1 

109 

75 

25 

5 

4 

19 

48 

9 

75 

76 

26 

1 

10 

.       5 

18 

77 

27 

2 

2 

9 

4 

1 

13 

78 

28 

3 

5 

6 

8 

79 

29 

2 

2 

2 

2 

80 

5,841 

3,760 

857 

46,799.0 

17,458 

12,580 

2,769 

145,613.5 

110 


TABLE    I. 


OBSERVATIONS  ON  MALE  LIFE. 


Age  at  Entry,  53  Years. 

NUMBBB  OF 

Entrant 

3,  9,452. 

$29,239,000  Insured. 

Age 

at 

Discon- 

T\fy^.l 

Exposed  to 
Risk. 

Amounts 

Amounts 

Death 

Exposed  to 

BLli 

Exit. 

>*& 

Eristing. 

tinued. 

JJiecl. 

Existing. 

Discontin'ed. 

Claims. 

Risk. 

$ 

$ 

$ 

0 

566 

299 

42 

4,576.5 

1,745 

694 

162 

14,272.5 

52 

1 

476 

1,222 

104 

7,934 

1,372 

3,329 

286 

24,973.5 

53 

2 

529 

551 

113 

6,467.5 

1,507 

1,959 

325 

20,671.5 

5Jf 

3 

497 

354 

92 

5,373 

1,375 

1,531 

303 

17,094.5 

55 

4 

566 

263 

83 

4,475.5 

1,719 

1,025 

246 

14,138.5 

66 

5 

561 

178 

62 

3,606 

1,736 

730 

199 

11,296 

57 

6 

546 

100 

65 

2,844 

1,747 

405 

223 

8,793.5 

58 

7 

503 

90 

75 

2,138 

1,741 

272 

181 

6,485 

69 

8 

444 

44 

33 

1,493 

1,336 

208 

91 

4,323 

60 

9 

266 

19 

21 

984.5 

833 

62 

67 

2,761 

61 

10 

166 

11 

21 

682.5 

464 

45 

58 

1,807.5 

62 

11 

111 

8 

18 

486 

303 

17 

47 

1,254.5 

63 

12 

44 

5 

10 

350.5 

75 

14 

25 

889 

64 

13 

28 

1 

5 

293.5 

75 

6 

18 

779 

65 

14 

25 

2 

6 

259 

48 

21 

17 

672.5 

66 

15 

31 

3 

7 

225.5 

72 

9 

26 

592.5 

67 

16 

25 

1 

7 

185.5 

92 

3 

19 

488.5 

68 

17 

13 

2 

6 

152 

46 

5 

10 

373.5 

69 

18 

2 

1 

10 

131.5 

6 

2 

22 

314 

70 

19 

9 

.  1 

4 

118.5 

25 

2 

4 

284 

71 

20 

6 

8 

105 

16 

16 

254 

72 

21 

10 

1 

3 

90.5 

14 

3 

5 

220.5 

73 

22 

5 

1 

4 

76.5 

11 

2 

9 

199 

n 

23 

14 

1 

7 

66.5 

39 

1 

20 

177.5 

75 

24 

13 

3 

45 

28 

8 

118 

76 

25 

10 

1 

6 

28.5 

23 

3 

18 

80.5 

77 

26 

3 

4 

12 

7 

16 

38 

78 

27 

3 

5 

10 

15 

79 

28 

2 

5 

80 

29 

2 

5 

81 

30 

1 

2 

3 

5 

82 

31 

1 

2 

83 

32 

1 

2 

8U 

33 

1 

2 

85 

34 

. 

1 

1 

2 

2 

86 

5,473 

3,159 

820 

43,215.5 

16,468 

10,348 

2,423 

133,389.5 

Age  at  Ei 

itry,  53  ^ 

fears. 

0 

N 

UMBER  OF  ] 

Entrants 

,  8,213. 

125,055,000  Insured. 

53 

537 

301 

32 

3,956 

1,306 

579 

130 

12,238 

1 

477 

1,061 

74 

6,812.5 

1,336 

3,145 

218 

21,467.5 

5If 

2 

412 

493 

99 

5,484.5  i 

1,070 

1,963 

384 

17,359.5 

55 

3 

415 

306 

93 

4,574 

1,187 

1,222 

294 

14,313 

56 

4 

432 

219 

89 

3,803.5 

1,276 

835 

273 

11,803.5 

57 

TABLE    I. 


Ill 


OBSERVATIONS  ON  MALE  LIFE. 


Age  at  Entry,  53  Years. 

ill 

Number  of 

Entrants,  8,213. 

$25,055,000  Insured. 

' 

Age 

11 

►•5 

at 

Existing. 

Discon- 

Died. 

Exposed  to 

Amounts 

Amounts 

Death 

Exposed  to 

Exit. 

tinued. 

Risk. 

Existing. 

Discontin'ed 

Claims. 

Risk. 

1 

$ 

$ 

$ 

$ 

5 

457 

173 

63 

3,086.5 

1,465 

714 

172 

9,480 

58 

6 

530 

101 

47 

2,429.5 

1,555 

399 

122 

7,286.5 

59 

7 

393 

82 

36 

1,761 

1,353 

255 

.     89 

5,282.5 

60 

.     8 

358 

41 

39 

1,270.5 

1,135 

137 

120 

3,644.5 

61 

9 

226 

26 

20 

840 

645 

74 

53 

2,284 

62 

10 

117 

10 

14 

576 

303 

40 

26 

1,529 

63 

11 

92 

7 

16 

436.5 

172 

37 

46 

1,161.5 

64 

12 

38 

2 

14 

324 

98 

6 

44 

922 

65 

13 

28 

4 

10- 

269 

110 

14 

24 

770 

66 

14 

32 

1 

5 

228.5 

97 

3 

11 

627.5 

67 

15 

26 

1 

10 

190.5 

85 

3 

24 

516.5 

68 

16 

13 

2 

7 

153 

53 

6 

22 

403 

69 

17 

9 

3 

7 

130.5 

20 

3 

12 

323.5 

70 

18 

15 

3 

113 

45 

8 

290 

71 

19 

9 

2 

6 

94 

34 

2 

15 

236 

72 

20 

5 

1 

5 

77.5 

7 

4 

16 

184 

73 

21 

4 

6 

67 

2 

24 

159 

n 

22 

5 

2 

57 

17 

4 

133 

75 

23 

4 

4 

50 

5 

7 

112 

76 

24 

16 

6 

42 

47 

3 

100 

77 

25 

5 

1 

20 

16 

2 

50 

78 

26 

4 

2 

14 

7 

10 

32 

79 

27 

8 

8 

15 

15 

80 

4,667 

2,836 

710 

36,868.5 

13,461 

9,441 

2,153 

112,723.0 

- 

Age  at  En 

tv^  54  1 

rears. 

0 

N 

aMBER  OF 

Entrants 

,  7,146.                 i 

122,521,000  Insured. 

H 

495 

241 

50 

3,452.5  i 

1,657 

467 

160 

11,027 

1 

356 

898 

88 

5,911 

1,040 

2,624 

283 

18,925 

55 

2 

403 

412 

87 

4,812      i 

1,243 

1,541 

308 

15,519.5 

56 

3 

361 

272 

81 

3,980    : 

964 

1,194 

302 

12,601 

57 

4 

370 

197 

83 

3,303.5  1 

1,097 

789 

206 

10,343.5 

58 

6 

440 

141 

64 

2,681.5 

1,447 

549 

263 

8,371.5 

59 

6 

386 

94 

50 

2,060      i 

1,155 

380 

141 

6,197 

60 

7 

351 

61 

51 

1,546.5  ! 

1,237 

201 

161 

4,610.5 

61 

8 

343 

28 

20 

1,100 

971 

71 

79 

3,076.5 

62 

9 

203 

15 

25 

715.5 

540 

56 

79 

1,963 

63 

10 

117 

11 

12 

474.5 

285 

49 

24 

1,291.5 

6Jf 

11 

51 

6 

12 

337 

158 

22 

26 

947 

65 

12 

20 

1 

12 

270.5 

65 

1 

18 

751.5 

66 

13 

25 

3 

4 

236.5 

75 

6 

11 

665 

67 

14 

25 

3 

11 

205 

69 

4 

15 

574 

68 

113 


TABLE    I. 


OBSERVATIONS  ON  MALE  LIFE. 


Age  at  Entry,   54  Years. 

NCHBEB  OF 

Entbante 

,  7,146. 

$22,521,000  Insured. 

Age 

|h 

at 

£S 

Discon- 

, 

Exposed  to 
Risk. 

Amounts 

Amounts 

Deatii 

Exposed  to 

Exit. 

>"& 

Existing. 

tinued. 

Died. 

Existing, 

Discontin'ed. 

Claims. 

Risk. 

" 

$ 

$ 

$ 

$ 

15 

24 

3 

11 

166.5 

74 

17 

25 

479.5 

69 

16 

8 

1 

5 

129.5 

35 

1 

9 

371.5 

70 

17 

10 

1 

5 

115.5 

34 

1 

23 

326.5 

71 

18 

3 

2 

3 

99 

11 

2 

7 

268 

72 

19 

5 

6 

92 

25 

14 

249 

73 

20 

8 

1 

5 

80.5 

21 

.  3 

6 

208.5 

u 

21 

3 

5 

67 

8 

14 

180 

75 

22 

6 

6 

59 

13 

13 

158 

76 

23 

13 

1 

1 

46.5 

29 

2 

1 

131 

77 

24 

7 

2 

32 

15 

5 

100 

78 

25 

9 

2 

1 

22 

25 

4 

2 

78 

79 

26 

4 

1 

3 

10.5 

12 

3 

13 

47.5 

80 

27 

1 

3 

3 

21 

.81 

28 

1 

2 

8 

18 

82 

29 

1 

4,048 

1 

10 

10 

83 

2,394 

704 

32,012.0 

12,323 

7,987 

2,211 

99,510.0 

Age  at  Er 

itry,  55  "5 

fears. 

0 

N 

UMBER  OF 

Entrants 

i,  5,963. 

$18,980,000  Insttbkd. 

55 

384 

193 

49 

2,885 

1,190 

478 

214 

9,230.5 

1 

319 

770 

76 

4,952 

1,018 

2,255 

241 

15,929.5 

56 

2 

285 

348 

74 

3,998 

906 

1,264 

231 

12,911 

57 

3 

325 

227 

65 

3,351.5 

1,009 

1,079 

198 

10,602.5 

58 

4 

308 

172 

59 

2,762 

926 

721 

160 

8,495.5 

59 

5 

349 

111 

64 

2,253.5 

^  1,114 

443 

170 

6,827.5 

60 

6 

343 

61 

43 

1,754.5 

'  1,172 

308 

120 

5,168 

61 

7 

333 

44 

31 

1,316 

958 

150 

128 

3,647 

62 

8 

249 

26 

23 

917 

674 

98 

59 

2,437 

68 

9 

193 

15 

20 

624.5 

540 

47 

59 

1,631.5 

6^ 

10 

108 

10 

7 

399 

278 

23 

29 

997.5 

65 

11 

75 

2 

7 

278 

175 

6 

14 

676 

66 

12 

33 

4 

5 

193 

80 

15 

15 

476.5 

67 

13 

13 

2 

5 

152 

49 

4 

16 

372 

68 

14 

19 

2 

4 

132 

43 

5 

13 

302.5 

69 

15 

10 

1 

5 

107.5  * 

25 

2 

9 

243 

70 

16 

10 

4 

7 

90 

20 

4 

21 

206 

71 

17 

7 

7 

71 

21 

24 

163 

72 

18 

4 

1 

1 

56.5 

11 

1 

1 

117.5 

73 

19 

5 

4 

51 

8 

6 

105 

U 

20 

8 

3 

42 

24 

3 

91 

75 

21 

2 

31 

5 

64 

76 

22 

1 

29 

1 

59 

77 

23 

2 

2 

28 

4 

2 

68 

78 

24 

9 

4 

24 

15 

9 

52 

79 

TABLE    I.  • 


113 


OBSERVATIONS  ON  MALE  LIFE. 


Age  at  Entry,  55  Years. 

!i 

Number  op 

Entrants,  5,963. 

$18,939,000  iNstJBED. 

Age 

ei0 

at 

a>  CO 

Discon- 

Exposed to 
Risk. 

Amounts 

Amounts 

Death 

Exposed  to 
Risk. 

Exit. 

>'A 

Existing. 

tinued. 

Died. 

Existing. 

Discontin'ed 

Claims. 

$ 

$ 

$ 

$ 

25 

1 

11 

1 

28 

80 

26 

7 

10 

19 

27 

81 

27 

2 

1 

3 

6 

2 

8 

82 

3,403 

1,993 

567 

26,522.0 

10,291 

6,903 

1,745 

80,926.0 

Age  at  Entry,  56  Years. 

0 

N 

TTMBEB  07 

ENTBANTf 

i,  4,978. 

$16,256,000  Insubed. 

56 

335 

155 

38 

2,411.5 

1,056 

409 

117 

7,923.5 

1 

220 

634 

77 

4,1.33 

686 

1,837 

288 

13,755.5 

57 

2 

231 

284 

68 

3,377 

726 

999 

244 

11,363.5 

58 

3 

230 

194 

64 

2,839 

829 

808 

266 

9,490 

59 

4 

243 

140 

69 

2,378 

857 

538 

201 

7,722 

60 

5 

299 

86 

59 

1,953 

1,008 

450 

160 

6,170 

61 

6 

328 

48 

40 

1,528 

942 

180 

160 

4,687 

62 

7 

285 

43 

32 

1,114.5 

929 

127 

113 

3,431.5 

63 

8 

212 

18 

22 

767 

710 

77 

67 

2,287.5 

6Jf 

9 

159 

8 

14 

520 

443 

20 

50 

1,462 

65 

10 

74 

8 

13 

339 

217 

23 

41 

947.5 

66 

11 

56 

2 

8 

247 

130 

9 

40 

673.5 

67 

12 

23 

5 

11 

179.5 

76 

8 

28 

495 

68 

13 

20 

2 

10 

142 

72 

4 

25 

385 

69 

14 

19 

2 

8 

110 

50 

4 

24 

284 

70 

15 

5 

1 

82 

19 

3 

208 

71 

16 

3 

7 

76 

15 

14 

186 

72 

17 

6 

1 

6 

65.5 

9 

1 

27 

156.5 

73 

18 

4 

1 

1 

52.5 

8 

1 

1 

119.5 

7^ 

19 

2 

5 

47 

2 

13 

110 

75 

20 

3 

3 

40 

11 

7 

95 

76 

21 

2 

1 

4 

33.5 

5 

2 

7 

76 

77 

22 

3 

3 

27 

8 

8 

63 

78 

23 

3 

1 

21 

9 

1 

47 

79 

24 

8 

2 

17 

20 

2 

37 

80 

25 

1 

1 

7 

3 

1 

15 

81 

26 

2 

1 

5 

7 

1 

11 

82 

27 

1 

2 

2 

3 

83 

28 

1 

1 

8J, 

29 

1 

1 

i             1 

1 

85 

2,778 

1,632 

568 

22,516.0 

8,850 

5,497 

1,909 

72,206.5 

114 


TABLE    I. 


OBSERVATIONS  ON  MALE  LIFE. 


Age  at  Entry,  57  Years. 

i 

Number  of 

Entrants,  4,212. 

$13,878,000  Insured. 

Age 

at 

Discou- 

Exposed  to 

Amounts 

Amounts 

Death 

Exposed  to 
Risk. 

£zit. 

^.2 

Existinor. 

tinacd. 

Died. 

Risk. 

Existing. 

Discontined. 

Claims. 

% 

f 

$ 

$ 

0 

290 

126 

28 

2,043 

1,042 

296 

82 

6,791 

57 

1 

199 

464 

66 

3,536 

579 

1,406 

184 

11,755 

58 

2 

275 

244 

54 

2,917 

795 

871 

224 

9,853.5 

59 

3 

200 

139 

60 

2,396.5 

655 

mb 

162 

8,081.5 

60 

4 

238 

119 

57 

2,007.5 

758 

456 

250 

6,719 

61 

5 

297 

53 

47 

1,626.5 

923 

265 

158 

5,350.5 

62 

6 

2G4 

42 

35 

1,235 

974 

243 

209 

4,015.5 

63 

7 

230 

38 

37 

896 

801 

127 

113 

2,647.5 

6^ 

8 

171 

12 

22 

604 

548 

36 

59 

1,652 

65 

9 

122 

10 

13 

400 

328- 

32 

30 

1,011 

66 

10 

63 

11 

7 

254.5 

144 

27 

25 

623.5 

67 

11 

42 

3 

6 

177.5 

60 

6 

21 

438 

68 

12 

13 

2 

8 

127 

44 

2 

15 

353 

69 

13 

11 

8 

105 

33 

28 

293 

70 

14 

10 

1 

1 

85.5 

28 

1 

1 

231.5 

71 

15 

5 

1 

5 

73.5 

23 

1 

10 

201.5 

72 

16 

9 

2 

2 

62 

40 

2 

1 

167 

73 

17 

6 

2 

50 

18 

4 

125 

U 

18 

3 

1 

42 

9 

1 

103 

75 

19 

2 

4 

38 

3 

7 

93 

76 

20 

2 

6 

32 

9 

12 

83 

77 

21 

3 

24 

8 

62 

78 

22 

1 

4 

20.5 

3 

15 

52.5 

79 

23 

1 

16 

5 

36 

80 

24 

8 

1 

15 

13 

1 

31 

81 

25 

1 

1 

5.5 

3 

3 

15.5 

82 

26 

2 

1 

4 

7 

3 

11 

83 

27 

1 
2,466 

1 

1 

1 

8Jf 

1,269 

477 

18,794.5 

7,843 

4,412 

1,623 

60,797.0 

Age  at  Eb 

try,  58  1 

fears. 

0 

N 

ITUBEB  OF 

ENTRANTa 

,  3,605. 

$11,429,000  Insured. 

58 

243 

100 

16 

1,752.5 

715 

220 

77 

5,604.5 

1 

212 

375 

62 

3,058.5 

609 

1,171 

166 

9,831.5 

59 

2 

183 

167 

54 

2,513.5 

486 

675 

165 

8,133.5 

60 

3 

171 

117 

59 

2,134.5 

501 

546 

225 

6,872 

61 

4 

242 

72 

42 

1,810 

716 

336 

125 

5,705 

62 

5 

294 

58 

43 

1,461 

1         920 

219 

143 

4,586.5 

63 

6 

228 

43 

36 

1,073.5 

^81 

173 

118 

3,327.5 

H 

7 

197 

31 

28 

772.5 

668 

99 

90 

2,392.5 

65 

8 

156 

7 

20 

528.5 

517 

28 

44 

1,571 

66 

9 

100 

8 

10 

345 

299 

19 

38 

986.5 

67 

TABLE     I. 


US- 


OBSERVATIONS   ON  MALE  LIFE. 


i 

Age  at  Entry,  58  Years. 

A 

H 

NUMBBB  OP 

Entbants,  3,605. 

1 

111,429,000  Insubed. 

Age 

►2s 

1 

at 

1    Discon- 

1 

Exposed  to 
Kisli. 

Amounts 

Amounts 

Deatli 

Exposed  to 
Risk. 

Exit. 

>'A 

Existing. 

tinued. 

1    Died. 

Existing. 

Discontin'ed. 

Claims. 

1 

$ 

$ 

$ 

10 

65 

4 

12 

229 

206 

10 

37 

635 

68 

11 

36 

1 

5 

149.5 

99 

8 

12 

383 

69 

12 

9 

3 

8 

106.5 

34 

6 

17 

265 

70 

13 

10 

1 

6 

87.5 

34 

1 

19 

210.5 

71 

14 

13 

1 

3 

70.5 

42 

1 

5 

156.5 

72 

15 

3 

2 

54 

3 

5 

109 

73 

16 

6 

3 

49 

6 

6 

101 

7A 

17 

3 

3 

40 

7 

7 

89 

75 

18 

2 

2 

34 

5 

4 

75 

76 

19 

2 

5 

30 

6 

7 

66 

77 

20 

4 

23 

10 

53 

78 

21 

1 

1 

19 

4 

1 

43 

79 

22 

1 

3 

17 

3 

3 

38 

80 

23 

2 

2 

13 

11 

4 

32 

81 

24 

4 

2 

9 

6 

4 

17 

82 

25 

1 

3 

1 

7 

83 

26 

2 

6 

8J, 

27 

1 

2 

3 

6 

85 

28 

1 

3 

86 

29 

1 

1 

3 

3 

87 

2,186 

988 

431 

16,389.5 

6,585 

3,512 

1,332 

51,308.5 

Age  at  En 

try,   59  ^ 

fears. 

0 

N 

tIMBKB  OF 

Entbants 

,  2,933. 

$9,413,000  Insubed. 

59 

190 

110 

20 

1,411.5 

581 

252 

73 

4,580.5 

1 

154 

330 

76 

2,448 

504 

1,007 

250 

8,003.5 

60 

2 

144 

133 

56 

1,986.5 

476 

498 

162 

6,497 

61 

3 

151 

94 

42 

1,673 

492 

400 

117 

5,410 

62 

4 

180 

65 

38 

1,400.5 

611 

330 

145 

4,436 

63 

5 

197 

41 

37 

1,129.5 

644 

175 

88 

3,427.5 

64- 

6 

176 

29 

31 

860.5 

589 

91 

135 

2,562.5 

65 

7 

169 

17 

33 

630.5 

528 

64 

60 

1,761 

66 

8 

137 

7 

19 

416.5 

361 

19 

38 

1,131.5 

67 

9 

59 

3 

10 

255.5 

195 

14 

38 

716 

68 

10 

38 

1 

13 

184.5 

120 

6 

29 

473 

69 

11 

27 

1 

14 

132.5 

63 

3 

25 

319.5 

70 

12 

8 

1 

6 

90.5 

34 

1 

17 

229.5 

71 

13 

10 

1 

7 

75.5 

32 

3 

16 

176.5 

72 

14 

13 

1 

2 

57.5 

41 

3 

7 

125.5 

73 

15 

5 

1 

1  , 

41.5 

8 

1 

1 

75.5 

74 

16 

1 

35 

6 

66 

75 

17 

1 

1 

3 

33.5 

2 

1 

4 

59.5 

76 

18 

29 

53 

77 

19 

1 

5 

29 

3 

4 

53 

78 

116 


TABLE    I. 


OBSERVATIONS  ON  MALE  LIFE. 


Age  at  Entry,  59  Years. 

NUMBBB  OP 

Entrants,  2,93a 

$9,413,000  Insured. 

Age 

U 

at 

£S 

Discon- 

Exposed to 

Amonnts 

Amounts 

Death 

Exposed  to 
Risk. 

Exit. 

>"& 

Existing. 

tinued. 

Died. 

Risk. 

Existing. 

Discontin'ed. 

Claims. 

$ 

$ 

$ 

$ 

20 

1 

1 

22.5 

1 

1 

45.5 

79 

21 

1 

1 

2 

20.5 

7 

2 

5 

43 

80 

22 

2 

2 

17 

5 

2 

30 

81 

23 

2 

4 

13 

8 

4 

23 

82 

24 

5 

1 

7 

8 

1 

11 

83 

25 

1 

2 

8h 

26 

1 

1 

2 

2 

85 

1,672 

838 

423 

13,002.5 

5,320 

2,871 

1,222 

40,313.0 

Age  at  Ee 

Ltry,  60  1 

fears. 

0 

N 

CniBEB  OF 

Entrants 

,  2,682. 

$8,497,000  Insuked. 

60 

179 

81 

32 

1,300.5 

619 

165 

103 

4,166 

1 

147 

282 

55 

2,249 

456 

747 

191 

7,236.5 

61 

2 

144 

147 

55 

1,832.5 

485 

516 

147 

5,958 

62 

3 

152 

82 

50 

1,519 

446 

345 

187 

4,895.5 

63 

4 

132 

53 

49 

1,249.5 

386 

271 

138 

3,954.5 

61, 

5 

165 

50 

34 

1,017 

535 

167 

115 

3,211.5 

65 

6 

187 

27 

27 

779.5 

562 

144 

99 

2,406 

66 

7 

139 

18 

20 

543 

409 

55 

59 

1,645.5 

67 

8 

117 

7 

10 

371.5 

402 

55 

25 

1,122.5 

68 

9 

74 

6 

10 

238 

202 

18 

23 

659 

69 

10 

39 

4 

3 

149 

94 

23 

7 

413.5 

70 

11 

26 

1 

6 

104.5 

61 

4 

11 

299 

71 

12 

8 

1 

5 

71.5 

26 

4 

18 

223 

72 

13 

3 

2 

5 

57 

10 

17 

16 

168.5 

73 

14 

5 

1 

2 

47.5 

15 

3 

3 

132.5 

7^ 

15 

6 

2 

1 

39 

12 

6 

4 

110 

75 

16 

2 

2 

31 

7 

2 

91 

76 

17 

1 

3 

27 

5 

11 

82 

77 

18 

2 

23 

5 

66 

78 

19 

21 

61 

79 

20 

1 

1 

21 

5 

5 

61 

80 

21 

3 

19 

8 

51 

81 

22 

1 

4 

16 

1 

3 

43 

82 

23 

1 

1 

11 

12 

7 

39 

83 

24 

1 

9 

1 

20 

8Jf 

25 

4 

1 

1 

7.5 

11 

1 

1 

18.5 

85 

26 

1 

2 

3 

6 

86 

27 

1 

3 

87 

28 

1 

3 

88 

29 

1 

1 

3 

3 

89 

1,536 

765 

381 

11,758.5 

4,769 

2,541 

1,187 

37,149.0 

TABLE    I. 


117 


OBSERVATIONS  ON   MALE   LIFE. 


Age  at  Entry,  61 

years. 

•si 

Number  OF 

Entrants,  1,683. 

$5,239,000  Insured. 

Age 

at 

Exit. 

Existing. 

Discon- 
tinued. 

Died. 

Exposed  to 
Risk. 

Amounts 
Existing. 

Amounts 
Discontin'ed. 

Deatli 
Claims. 

Exposed  to 
Rislc. 

$ 

$ 

$ 

$ 

0 

90 

53 

20 

815 

219 

117 

77 

2,561 

61 

1 

74 

187 

24 

1,426.5 

207 

591 

80 

4,530.5 

62 

2 

73 

68 

29 

1,201 

277 

257 

89 

3,819.5 

63 

3 

121 

54 

32 

1,038 

291 

266 

90 

'      3,192 

6J, 

4 

128 

46 

27 

835 

342 

228 

125 

2,564 

65 

5 

109 

35 

23 

639.5 

250 

171 

77 

1,897.5 

66 

6 

118 

8 

15 

486 

401 

30 

40 

1,470 

67 

7 

101 

15 

20 

341.5 

306 

28 

67 

1,000 

68 

8 

61 

5 

10 

210.5 

180 

9 

35 

608.5 

69 

9 

30 

3 

10 

135.5 

72 

11 

37 

383.5 

70 

10 

18 

1 

6 

93.5 

53 

1 

12  . 

268.5 

71 

11 

11 

2 

4 

68 

58 

9 

12 

198.5 

72 

12 

4 

2 

1 

51 

4 

6 

5 

121 

73 

13 

4 

1 

2 

44.5 

11 

2 

1 

108 

U 

14 

4 

2 

38 

8 

8 

95 

75 

15 

1 

2 

32 

1 

5 

79 

76 

16 

1 

2 

29 

4 

1 

73 

77 

17 

2 

1 

5 

25.5 

5 

3 

12 

66.5 

78 

18 

2 

18 

12 

48 

79 

19 

1 

16 

3 

36 

80 

20 

1 

15 

3 

33 

81 

21 

1 

1 

1 

13.5 

2 

2 

3 

29 

82 

22 

1 

11 

3 

23 

83 

23 

1 

1 

10 

4 

'       1 

20 

8^ 

24 

3 

8 

4 

15 

85 

25 

2 

1 

5 

6 

2 

11 

86 

26 

1 

2 

2 

3 

87 

27 

1 

1 

88 

28 

1 

1 

89 

29 

1 

1 

1 

1 

90 

957 

482 

244 

7,611.5 

2,705 

1,731 

803 

23,257.0 

Age  at  En 

try,  62  1 

fears. 

0 

Ni 

JMBER  OF 

Entrants 

,  1,206. 

$4,188,000  Insured. 

62 

89 

27 

20 

589.5 

341 

71 

38 

2,058.5 

1 

52 

118 

33 

1,011 

213 

333 

115 

3,571.5 

63 

2 

55 

42 

21 

846 

185 

181 

71 

2,986.5 

6J, 

3 

64 

48 

29 

725 

157 

161 

114 

2,559.5 

65 

4 

95 

25 

27 

595.5 

305 

186 

79 

2,115 

66 

5 

62 

16 

18 

453 

239 

155 

33 

1,560.5 

67 

6 

89 

6 

11 

362 

330 

19 

28 

1,201.5 

68 

7 

78 

13 

19 

252.5 

329 

33 

55 

817.5 

69 

8 

46 

4 

6 

147 

131 

8 

16 

413 

70 

9 

28 

1 

--- 

6 

92.5 

76 

14 

12 

255 

71 

118 


TABLE    I. 


OBSERVATIONS  ON  MALE  LIFE. 


Age  at  Entry,  62  Years. 

!i 

Number  op 

Entrants,  1,306. 

$4,188,000  Insured. 

Age 

!3b 

at 

Existing. 

Discon- 
tinued. 

Died. 

Exposed  to 
Risli. 

Amounts 

Existing. 

Amounts 
Discontin'ed. 

Death 
Claims. 

Exposed  to 
Risli. 

Exit. 

$ 

$ 

$ 

$ 

10 

5 

2 

58 

20 

3 

160 

72 

11 

8 

1 

4 

50.5 

23 

3 

6 

135.5 

73 

12 

3 

1 

1 

37.5 

5 

1 

5 

104.5 

u 

13 

•     1 

2 

33 

6 

6 

94 

75 

14 

1 

1 

30 

3 

1 

82 

76 

15 

3 

"       1 

4 

27.5 

9 

2' 

9 

77 

77 

16 

1 

3 

21 

10 

7 

58 

78 

17 

1 

17 

1 

41 

79 

18 

1 

1 

16 

5 

1 

40 

80 

19 

1 

2 

14 

2 

3 

34 

81 

20 

1 

11 

4 

29 

82 

21 

1 

10 

3 

25 

88 

22 

1 

1 

9 

6 

3 

22 

8J^ 

23 

4 

7 

9 

13 

85 

24 

3 

4 

86 

25 

3 

4 

87 

26 

1 

1 

3 

2 

1 

4 

88 

27 

1 

1 

1 

1 

89 

687 

303 

216 

5,425.5 

2,406 

1,167 

615 

18,466.5 

Age  at  Entry,  63  Years. 

0 

> 

fUMBER  OF 

Entrant 

8,  957. 

$2,897,000  Insured. 

63 

52 

24 

9 

466.5 

159 

62 

24 

1,417.5 

1 

47 

116 

23 

814 

171 

316 

60 

2,494 

6J^ 

2 

56 

52 

24 

660 

192 

143 

79 

2,033.5 

65 

3 

37 

37 

18 

535.5 

92 

107 

74 

1,637.5 

66 

4 

64 

32 

.    15 

446 

181 

106 

42 

1,365 

67 

5 

62 

15 

12 

343.5 

161 

144 

48 

1,017 

68 

6 

54 

10 

14 

257 

172 

30 

43 

721 

69 

7 

47 

6 

6 

181 

166 

17 

16 

482.5 

70 

8 

46 

2 

5 

124 

99 

8 

13 

288 

■71 

9 

15 

2 

6 

71 

31 

5 

14 

169.5 

72 

10 

9 

1 

3 

48.5 

34 

1 

5 

121.5 

73 

11 

5 

1 

4 

35.5 

6 

3 

6 

80.5 

U 

12 

3 

1 

4 

25.5 

10 

2 

2 

66 

75 

13 

4 

1 

1 

17.5 

22 

1 

5 

52.5 

76 

14 

1 

-2 

12 

1 

2 

25 

77 

15 

1 

9 

1 

22 

78 

16 

8 

21 

79 

17 

1 

8 

5 

21 

80 

18 

1 

1 

7 

6 

3 

16 

81 

19 

.      1 

4.5 

3 

5.5 

82 

TABLE     I 


119 


OBSERVATIONS  ON  MALE  LIFE. 


Age  at  Entry,  63  Years. 

Number  op 

Entrants,  957. 

$2,897,000  Insured. 

Age 

^u 

at 

«m 

,    , 

Discon- 

, 

Exposed  to 
Risk. 

Amounts 

Amounts 

Death 

Exposed  to 

Exit. 

>'A 

Existing. 

tinued. 

Died. 

Existing. 

Discontin'ed. 

Claims. 

Kisk. 

$ 

$ 

$ 

$ 

20 

1 

4 

1 

4 

83 

21 

3 

3 

84 

22 

3 

3 

85 

23 

1 

3 

1 

3 

86 

24 

2 

2 

87 

25 

2 

2 

2 

2 

88 

506 

301 

150 

4,091.0 

1,506 

948 

443 

12,073.5 

Age  at  Entry,  64  Years. 

0 

1^ 

lUMBBB  OF 

Entrant 

8,  770. 

12,381,000  Insured. 

64 

56 

18 

6 

376 

179 

32 

19 

1,174.5 

1 

35 

75 

23 

652.5 

101 

189 

58 

2,056.5 

65 

2 

34 

39 

13 

537.5 

105 

127 

51 

1,739.5 

66 

3 

39 

33 

12 

454.5 

114 

93 

49 

1,473.5 

67 

4 

50 

7 

12 

383.5 

179 

64 

39 

1,232 

68 

5 

63 

13 

14 

311.5 

159 

99 

42 

932.5 

69 

6 

50 

10 

12 

223 

134 

25 

47 

669.5 

70 

7 

27 

4 

11 

154 

102 

29 

41 

461.5 

71 

8 

41 

2 

10 

113 

140 

3 

34 

302:5 

72 

9 

16 

3 

3 

59.5 

37 

7 

5 

123.5 

73 

10 

11 

2 

1 

38 

20 

3 

1 

76.5 

74 

11 

1 

25 

4 

54 

75 

12 

1 

2 

24 

2 

6 

50 

76 

13 

2 

3 

20 

1 

7 

41.5 

77 

14 

2 

2 

16 

2 

4 

34 

78 

15 

1 

12 

2 

28 

79 

16 

2 

1 

11 

1 

3 

26 

80 

17 

8 

22 

81 

18 

1 

3 

•      7.5 

3 

13 

20.5 

82 

19 

1 

4 

3 

6 

83 

20 

2 

3 

2 

3 

84 

21 

1 

1 

85 

22 

1. 

1 

86 

23 

1 

1 

1 

1 

87 

427 

209 

134 

3,436.5 

1,275 

675 

431 

10,530.0 

120 


TABLE    I. 

OBSERVATIONS  ON  MALE  LIFE. 


Age 

at  Entry,  65  Years. 

Age 

at  Entry,  66  Years. 

^a" 

No.  OF  Entrants,  592. 

$1,780,000  Insubed. 

■i-> 

•a 

« 
bo 

< 

No.< 

3F  Entrants,  801. 

■$858,000  Insured. 

•a 

bo 

< 

a>c3 

a 

11 
3*" 

i 
s 

1^ 
^2 

1 
S 

W 

§1 
5*^ 

H2 

1 

1 

1 -a 

C  o  1 

5*"  5 

73     . 

ion 

c 

1 
$ 

S  2 

T 

5i 
S3 

$ 

on 

^2 

$ 

$ 

$ 

$ 

0 

46 

17 

6 

287.5 

53 

22 

36 

852 

65 

15 

3 

7 

5 

12 

81 

1 

20 

66 

11 

490 

37 

192 

32 

1,519 

66 

16 

1 

4 

2 

7 

82 

2 

24 

42 

12 

405 

71 

110 

43 

1,299 

67 

17 

3 

5 

83 

3 

27 

17 

15 

339.5 

77 

79 

41 

1,090.5 

68 

18 

3 

5 

8J, 

4 

34 

11 

10 

283.5 

97 

43 

27 

911.5 

69 

19 

1 

2.5 

3 

3.5 

85 

5 

44 

14 

13 

227 

127 

123 

39 

704.5 

70 

20 

2 

2 

86 

6 

31 

8 

10 

159 

95 

39 

27 

457.5 

71 

21 

1 

2 

1 

2' 

87 

7 

45 

6 

5 

111 

111 

31 

9 

300.5 

72 

22 

88 

8 

21 

5 

58 

56 

23 

165 

73 

23 

89 

9 

12 

1 

4 

31.5 

33 

9 

12 

81.5 

U 

24 

90 

10 

3 

15 

12 

32 

75 

25 

91 

11 
12 
13 
14 

1 

1 
1 
2 

12 
12 
11 

9 

3 

1 
2 

2 

20 
20 
19 
14 

76 

77 
78 
79 

26 

1 

130 

1 

92 

94 

77 

1,363.5 

397 

259 

202 

4,215.5 

15 

1 

7 

1 

12 

80 

Age 

at  Entry,  67 

Years. 

16 
17 
18 
19 

1 

1 

5.5 
4 
4 
4 

.1 

2 

10.5 
8 
8 
8 

81 
'82 
83 
8J, 

0 

No. 

OF  Entrj 

INTS,  229. 

$597,000  Insured. 

67 

11 

8 

8 

110.5 

22 

14 

45 

291.5 

20 

1 

1 

4 

3 

1 

8 

85 

1 

8 

22 

8 

191 

12 

64 

25 

484 

68 

21 

1 

2 

3 

4 

86 

2 

4 

13 

7 

157.5 

11 

22 

25 

404 

69 

22 

1 

1 

87 

3 

8 

11 

3 

134.5 

17 

44 

9 

335 

70 

23 

1 

1 

88 

4 

18 

8 

3 

114 

47 

12 

9 

281 

71 

24 

1 

1 

89 

5 

11 

6 

4 

86 

25 

15 

7 

211.5 

72 

25 

1 

1 

775 

649 

1 

1 

90 

6 

7 
8 

18 
9 
9 

3 
2 
3 

4 

2 

66.5 
42 

28  5 

66 
13 
39 

12 

5 

2 

4 

6 
4 

169.5 
94 

74 
33 

73 

74 
75 
76 

309 

183 

100 

2,485.5 

302 

7,548.0 

A 

Ke  . 

it  Entry,  66  Year 

s. 

9 

6 

18 

10 
11 

2 

1 

1  j- 

12 
9 

7 

21 
13 

77 
78 

No.  OP  E 

■ntba 

NTS,  301. 

$858,000  In 

5UBED. 

12 

8 

12 

7Q 

0 

9 

11 

5 

145 

37 

25 

11 

416.5 

66 

13 

1 

8 

12 

80 

1 

23 

29 

8 

261.5 

5 

69 

14 

750.5 

67 

14 

7 

11 

81 

2 

11 

20 

11 

206 

29 

58 

29 

668 

68 

15 

1 

7 

11 

82 

3 

7 

17 

8 

165.5 

42 

50 

32 

556 

69 

16 

1 

6 

10 

83 

4 

10 

3 

8 

140.5 

44 

4 

25 

455 

70 

17 

1 

5 

8 

8J, 

5 

21 

6 

9 

118 

64 

28 

16 

370 

71 

18 

4 

7 

85, 

6 

12 

2 

5 

84 

47 

8 

18 

272 

72 

19 

^ 

4 

4 

7 

66 

7 

13 

3 

2 

64.5 

36 

2 

4 

202 

73 

20 

1 

3 

3 

87 

8 

13 

1 

2 

47.5 

32 

11 

4 

155.5 

n 

21 

1 

2 

2 

88.' 

9 

6 

1 

2 

31.5 

20 

1 

9 

113.5 

75 

22 

1 

1 

89 

10 

2 

8 

23 

20 

7 

84 

76 

23 

1 

1 

90 

11 

2 

3 

18 

20 

3 

57 

77 

24 

1 

1 

91 

12 
13 

3 
3 

13 
10 

6 
16 

34 

28 

78 

79 

25 

1 

1 

1 

1 

92 

14 

7 

12 

80 

105 

76 

48 

1,027.5 

275 

182 

140 

2,498.5 

TABLE    I. 


121 


OBSERVATIONS  ON  MALE  LIFE. 


Age  at  Entry,  68  Years. 


Age  at  Entry,  70  Years. 


0 
1 
2 
3 

4 

5 
6 
7 
8 
9 

10 
11 
12 
13 
14 

15 
16 
17 
18 
19 

20 
21 
22 


0 
1 
2 
3 

4 

5 
6 
7 
8 
9 

10 
11 
12 
13 


No. 

OF  Entrants,  151. 

si's 

O  13 

13 

1^* 

6 

5 

1 

73 

3 

16 

2 

131 

1 

6 

5 

115 

5 

7 

102.5 

6 

6 

1 

91 

16 

3 

8 

79.5 

11 

1 

5 

53.5 

4 

2 

3 

36 

8 

3 

28 

3 

1 

2 

16.5 

1 

1 

2 

10.5 

1 

6.5 

1 

6 

1 

1 

4.5 

1 

3 

2 

2 
2 
2 

2 

2 

1 

2 

' 

1 

.5 

64 

51 

36 

771.0 

3,000  Insdbed. 


17 
5 

14 
19 

50 
22 
15 
36 
16 


202  83 


93 


h: 


$ 

188 
357 
320.5 

287.5 
262 

233.5 

165 

120.5 

94 

42 

20.5 
10 
9 

7.5 
4 

3 
3 
3 
3 
3 

3 
3 
.5 


2,142.5 


Age  at  Entry,  69  Years. 


68 
69 

70 
71 

72 

73 
7U 

75 
76 
77 

78 
79 
80 
81 
82 

83 
8J, 
85 
86 
87 

88 
89 
90 


No, 

OF  Entrants,  92. 

$284,000  Insured. 

1 

46 

1 

132 

3 

6 

5 

88 

8 

24 

12 

251 

1 

7 

1 

73.5 

1 

34 

1 

202 

4 

0 

0 

65.5 

9 

14 

6 

176 

6 

1 

2 

53.5 

17 

3 

3 

152.5 

9 

3 

2 

43.5 

36 

14 

3 

124 

8 

2 

5 

30 

19 

2 

10 

77 

6 

1 

16 

15 

4 

47 

1 

9 

10 

28 

2 

7 

4 

16 

2 

1 

6 

2 

1 

14 

2 

3 
1 

10 

11 

1 

1 

1 

1 

1 

42 

26 

24 

443.0 

127 

95 

42 

1,232.5 

69 

70 
71 

72 
73 

75 
76 
77 
78 

79 
80 
81 

82 


Cm  <0 


0 

1 

2 
3 

4 

5 
6 

7 
8 
9 

10 
11 
12 
13 
14 

15 
16 
17 
18 
19 


No.  OF  Entrants,  58. 


23 


22  13 


25.5 
43.5 
34.5 
29.5 
24 

19.5 
15 
9 


3 
3 
3 
3 
2.5 

1 
1 
1 
1 
1 


233.0 


$120,000  Insured. 

o  a 
5'^ 

5s 

W2 

$ 

% 

1 

$ 

4 

8 

3 

56 

1 

11 

5 

99.5 

1 

9 

4 

83.5 

10 

5 

1 

71.5 

15 

58 

7 

1 

1 

42.5 

10 

6 

34 

2 

18 

6 

16 

1 

1 

10 

8 
8 
8 
8 

1 

5 

7.5 

2 
2 
2 
2 

2 

2 

55 

35 

30 

538.5 

Age  at  Entry,  71  Years. 


Age  at  Entry,  72- Years. 


No.  OF  Entrants,  84. 

$59,000  Insurbd. 

1 

1 

11.5 

2 

1 

1 

29 

3 

1 

20.5 

7 

1 

1 

54.5 

1 

15.5 

3 

1 

45.5 

1 

13.5 

3 

4 

40.5 

1 

1 

11.5 

5 

1 

4 

34.5 

bo 
< 


70 
71 

72 
73 
7Jt 

75 
76 
77 
78 
79 

80 
81 
82 
83 
81f 

85 
86 
87 
88 
89 


No. 

OF  Entrants,  31. 

$79,000  Insured. 

1 

15.5 

2 

39.5 

1 

5 

2 

27.5 

1 

8 

9 

73 

4 

2 

2 

21 

1 

3 

8 

57.5 

3 

1 

14 

11 

1 

47 

1 

1 

10 

1 

1 

35 

1 

8 

1 

33 

2 

1 

6 

6 

5 

29 

3 

1 

3.5 

20 

1 

20.5 

14 

10 

7 

105.5 

37 

18 

24 

334.5 

71 

72 
73 

u 

75 

76 
77 
78 


72 
73 
71^ 
75 
76 


132 


TABLE     I. 

OBSERVATIONS  ON  MALE  LIFE. 


Age  at  Entry,  72  Years 


Age  at  Entry,  75  Years. 


0 

1 

2 
3 
4 

5 
6 

7 
8 
9 

10 
11 
12 
13 
14 


11 

No. 

OP  Entrants,  24. 

$59,000  Insubed. 

to 

a 

a  Q 
1.3 

5^ 

■t 

•o    . 

§.2 

h2 

si 

a 

1 

1.1 
T 

si 

ax 

w2 
1 

5 

1 

1 

8.5 

2 

2 

24 

6 

1 

1 

6.5 

2 

5 

20 

7 

1 

1 

5 

1 

5 

14 

8 

1 

1 

3 

2 

1 

8 

9 

1 

5 

10 

1 

5 

11 

1 

5 

12 

1 

5 

13 

1 

"9" 

7 

8, 

1 
100.5 

5 
25 

11 

5 

23 

295.0 

Age  at  Entry,  73  Years. 


Age  at  Entry,  74  Years. 


No.  OF  Entrants,  11. 

1 

1 

5 

1 

8.5 

1 

7.5 
7 

3 

1 

7 

3 
3 

1 

1 

2.5 

1 

6 

4 

1 

50.5 

$22,000  Insubed. 


10.5 
19.5 
18.5 
18 
18  • 


8 

5.5 
1 
1, 

1 
1 
1 
1 
1 

113.0 


77 
78 
79 
80 
81 


83 
8Jf 
85 


No. 

OF  ENTBANT8,  19. 

$44,000  Insured. 

1 

1 

9.5 

3 

1 

22 

2 

16 

9 

35^ 

2 

3 

13.5 

2 

8 

27 

1 

1 

9.5 

1  ^ 

1 

18.5 

1 

8 

1 

15 

2 

7 

1 

14 

2 

5 

2 

13 

2 

2 

6 

8 

1 

1 

5 

5 

4 

8 

7 

71.5 

10 

28 

6 

158.0 

73 

u 

75 
76 
77 

lO 

79 
80 
81 


u 

75 
76 
77 
78 

79 
80 
81 
82 
83 

8^ 
85 

86 
87 


Is 

(D  ^ 


0 

1 

2 
3 

4 

5 
6 

7 
8 
9 

10 
11 
12 
13 
14 

15 
16 
17 
18 
19 

20 


No.  OF  Entrants,  11. 


§1    .• 

u  a    % 


1     2 


$19,000  Insured. 


1? 
W2 


5.5 
11 
10 

9 

< 

6.5 

2 

1 

1 

1 

1 
1 
1 
1 
1 

1 
1 
1 
1 
1 


65.0 


.2I  1-3 


14 


$  '  $ 

2 


w2 


$ 

9.5 
19 
17 
16.5 
15 

14.5 
4 
1 
1 
1 

1 
1 
1 
1 
1 

1 
1 
1 
1 
1 


109.5 


Age  at  Entry,  76  Years. 


Age  at  Entry,  77  Years. 


to 

< 


75 
76 
77 
78 
79 

80 

81  \ 

82  \ 

83  \ 
Sh 

85 
86 
87 
88 
89 

90 
91 
92 
93 
9A 

95 


No. 

OF  Entrants,  2. 

$a,000  Insured. 

1 

1.5 

2 

3 

2 

3 

\ 

2 

3 

1 

2 
1 

2 

3 
1 

1 

.5 

1 

.5 

1 

1 

10.5 

2 

1 

15.0 

76 
77 
78 
79 
80 

81 

82 


No. 

OF  Entrants,  1. 

$2,0X)  Insured. 

.5 

1 

1 

2 

1 

1 

2 
2 

2 

1 

2.5 

5.0 

77 
78 
79 


TABLE    I. 


123 


OBSERVATIONS  ON  MALE  LIFE. 


Age  at  Entry,  78  Years. 

Age  at  Entry,  82  Years. 

"1 
^1 

No.  OF  Entrants,  4. 

15,000  Insured. 

is" 

No.  OP  Entrants,  1. 

$1,000  Insured. 

a 
1 

Died. 

Exposed 
to  Risk. 

be 

B  a) 

i.5 

«5 

14 
is 

si 

g 

hi 
1.1 

5*" 

i 

1^- 
w2 

bi) 

% 
1 

1.1 

5'^ 

51 
§•5 

as 

0 
1 
2 
3 

4 

1 
1 

1 

1 

2 

3.5 
1.5 
1 
.5 

$ 

$ 

1 
1 

2 

$ 
1 

$ 

2.5 

4.5 

2.5 

2 

1 

7<f? 
7-9 
80 
81 
82 

0 

1 

.5 

I 

$ 

$ 

.5 

<9^ 

Age 

at  Entry,  83,  84,  85,  86,  and  87 

Years. 

3 

1 

8.5 

4 

1 

12.5 

No.  OP  Entrants,  0. 

$0,000  Insured. 

A^ 

res  at  Entry,  79  and  80  Years. 

r 

Age  at  Entry,  88  Years. 

No.  OP  Entbantb,  0. 

$0,000  Insured. 

0 
1 
2 
3 
4 

5 

No.  OF  Entrants,  1. 

$1,000  Insured. 

5<? 

90 
91 
92 

93 

Age  at  Entry,  81  Years. 

1 

.5 

1 
1 
1 
1 

1 

1 

.5 
1 
1 
1 
1 

1 

0 
1 

No.  OP  Entrants,  2. 

$2,000  Insured. 

81 

82 

1 

1 

1 
.5 

1 

1 

1 
.5 

1 

1 

1 

1.5 

1 

1 

1.5 

1 

5.5 

1 

5.5 

134 


TABLE    II. 


FEMALE  LIFE.     SUMMARY  (A).    OBSERVATIONS  CLASSIFIED  ACCORDING  TO  THE  AGE 

AT  EXIT  OR  EXPOSURE. 


Age 

Whole  Number  of  Entbants,  44,795. 

88,452  Thousand  Dollars  Insured. 

Age  at 

at 

£zit  or 

Ut\t 

Exit. 

Existing. 

Discon- 
tinued. 

Died. 

Exposed  to 
Risk. 

Amounts 
Existing. 

Amounts 
Diecontin'ed. 

Death 
Claims. 

Exposed  to 
Risk. 

Exposure. 

0 
1 

2.5 

3 

0-     i 

i-  H 

2 

1 

5.5 

1 

6.5 

H-  n 

3 

1 

7 

1 

8 

2^-  3} 

If 

1 

9 

1 

10 

Si-  U 

5 

1 

2 

9.5 

2 

2 

10.5 

H-  H 

6 

1 

1 

8 

1 

1 

8 

5i-  6i 

7 

2 

8 

2 

8 

6i-  U 

8 

2 

10.5 

2 

10.5 

n-  H 

9 

3 

2 

14.5 

7 

2 

21.5 

^-  H 

10 

1 

2 

22 

5 

2 

34 

9i-10i 

11 

4 

5 

1 

39 

9 

6 

X 

56 

10^-11^ 

12 

3 

2 

56.5 

16 

2 

93 

lli-12^ 

13 

5 

11 

74 

17 

8 

124 

12i-13^ 

u 

13 

15 

2 

112.5 

28 

28 

3 

175 

m-ui 

15 

17 

28 

187 

30 

31 

283.5 

m-iH 

16 

19 

48 

1 

282 

22 

60 

1 

426.5 

15i-16i 

17 

39 

74 

2 

387.5 

48 

95 

2 

608.5 

16i-17i 

18 

39 

107 

8 

546.5 

56 

131 

15 

939 

17^-18^ 

19 

60 

178 

3 

791 

91 

363 

5 

1,362 

18^-19^ 

20 

103 

251 

7 

1,134 

162 

408 

14 

1,939.5 

19^-20^ 

21 

137 

326 

20 

1,548 

211 

561 

28 

2,696.5 

20^-21i 

22 

183 

448 

16 

2,014.5 

276 

819 

28 

3,534.5 

21^-221 

23 

248 

500 

28 

2,544 

417 

939 

63 

4,478.5 

22^-23 i 

U 

329 

610 

34 

3,044.5 

480 

1,133 

46 

5,398 

23i-2J4 

25 

365 

661 

31 

3,519 

592 

1,229 

40 

6,552 

2^-25^ 

26 

403 

745 

45 

4,025.5 

621 

1,471 

92 

7,655.5 

251-26 i 

27 

455 

719 

52 

4,489.5 

720 

1,481 

118 

8,609.5 

26i-27i 

28 

489 

768 

47 

4,977 

773 

1,653 

88 

9,551.5 

27i-28i 

29 

572 

845 

47 

5,417 

904 

1,838 

117 

10,436 

28^-29^ 

30 

644 

826 

56 

5,791 

1,082 

1,799 

115 

11,275 

29i-30i 

31 

631 

778 

64 

6,098 

1,080 

1,611 

149 

12,073 

30^-31^ 

32 

741 

769 

64 

6,348 

1,248 

1,771 

114 

12,770 

31i-32^ 

33 

744 

816 

80 

6,524.5 

1,192 

1,912 

157 

13,137.5 

32^-331 

3Ji. 

795 

811 

68 

6,623.5 

1,363 

1,915 

143 

13,283 

33^-341 

35 

825 

780 

74 

6,661.5 

1,471 

1,838 

151 

13,384 

S4i-35i 

36 

783 

724 

68 

6,638.5 

1,399 

1,809 

158 

13,250.5 

35^-36% 

37 

822 

722 

59 

6,614 

1,554 

1,737 

128 

12,944 

S6i-37i 

38 

843 

725 

66 

6,537.5 

1,432 

1,646 

148 

12,636 

37i-38^ 

39 

807 

648 

60 

6,361 

1,393 

1,393 

113 

12,470.5 

38l-39l 

40 

792 

632 

59 

6,241 

1,442 

1,554 

89 

12,326 

39^-40^ 

U 

821 

614 

60 

6,027.5 

1,377 

1,555 

118 

11,823 

m-4H 

J^ 

746 

588 

58 

5,634.5 

1,323 

1,350 

127 

11,135 

jfH-m 

m 

692 

509 

62 

5,323 

1,122 

1,246 

140 

10,540.5 

m-m 

U 

716 

444 

58 

5,046 

1,340 

1,119 

145 

10,064 

m-m 

TABLE    II. 


135 


FEMALE  LIFE.     SUMMARY  (A).     OBSERVATIONS  CLASSIFIED  ACCORDING  TO  THE  AGE 

AT  EXIT  OR  EXPOSURE. 


Age 

Whole  Nttmbbb  op  Entrants,  44,795. 

88,452  Thousand  Dollars  Insured. 

Age  at 

at 

Exit  or 

Exit. 

Existing. 

Discon- 
tinued. 

Died. 

Exposed  to 
Risk. 

Amounts 

Existing. 

Amounts 
Discontin'ed 

Death 
Claims. 

Exposed  to 
Risk. 

Exposure. 

J,5 

638 

407 

57 

4,770 

1,150 

1,014 

119 

9,350 

m-4s^ 

j,6 

610 

390 

44 

4,539 

1,073 

865 

79 

8,847.5 

4H-46i 

h7 

586 

356 

43 

4,330.5 

1,148 

877 

83 

8,378 

m-m 

J^8 

541 

331 

41 

3,979.5 

1,033 

740 

75 

7,699 

U7^m 

W 

573 

381 

36 

3,763 

1,048 

621 

89 

7,394 

m-Jfii 

50 

634 

279 

39 

3,445.5 

986 

615 

78 

6,714 

Jf9i-50^ 

51 

435 

262 

38 

3,138.5 

782 

654 

82 

6,070 

50^2-51^ 

52 

411 

216 

37 

3,865.5 

706 

543 

67 

5,511.5 

51^-52^ 

53 

420 

169 

45 

3,601.5 

765 

413 

89 

5,038 

52^-53^2 

5Jf 

394 

164 

26 

3,393.5 

731 

438 

65 

4,403.5 

53I-5U 

55 

344 

151^ 

25 

3,038 

631 

398 

54 

3,845 

5^-55^ 

56 

293 

137 

35 

1,776.5 

517 

337 

62 

3,360 

55^-56^ 

57 

328 

109 

34 

1,538.5 

421 

346 

80 

3,965.5 

56^-57^ 

58 

241 

93 

29 

1,366 

400 

215 

73 

3,663.5 

57i-58^ 

59 

170 

76 

18  • 

1,169 

338 

152 

27 

3,333.5 

58^-59^ 

60 

138 

63 

20 

1,039.5 

260 

153 

50 

3,050 

59^-60^ 

61 

170 

42 

15 

935    . 

323 

118 

39 

1,809.5 

60l-61^- 

62 

105 

43 

17 

779.5 

199 

115 

36 

1,484 

61^-621- 

63 

111 

34 

16 

676.5 

188 

74 

35 

1,380 

62^-63^ 

6U 

87 

29 

20 

573.5 

151 

54 

40 

1,115 

63^-64^ 

65 

64 

33 

31 

486.5 

138 

38 

44 

973 

6U-65i- 

66 

67 

31 

9 

409.5 

141 

64 

17 

810 

65^-66^ 

67 

49 

14 

15 

332 

100 

30 

46 

641.5 

66^-67^  1 

68 

47 

13 

9 

264.5 

68 

23 

36 

483 

67i-68l 

69 

38 

12 

15 

303 

62 

26 

30 

380 

68^-69^ 

70 

23 

1 

5 

149.5 

36 

1 

10 

391 

69lr-70^ 

71 

10 

4 

5 

131 

14 

6 

15 

245 

70l-7ll 

72 

10 

3 

3 

103.5 

31 

9 

10 

210 

71i-72^ 

73 

12 

3 

5 

88.5 

18 

4 

13 

174 

72^-731 

7If 

10 

4 

2 

68.5 

33 

10 

3 

136.5 

73^-7U 

75 

4 

3 

9 

55 

6 

8 

19 

105 

Ui-75^ 

76 

6 

1 

1 

42 

7 

1 

3 

78 

75i-76i 

77 

3 

6 

35.5 

5 

10 

70 

76^-77^ 

78 

2 

4 

27 

3 

7 

56 

77i-78^^ 

79 

2 

2 

5 

20 

6 

3 

10 

44.5 

78i-79i 

80 

2 

12.5 

7 

27.5 

79i-80^ 

81 

6 

11.5 

10 

21.5 

80l-81i 

82 

1 

6 

1 

12 

81^-82ly 

83 

1 

5 

6 

11 

82i-83l 

8J, 

1 

4 

1 

5 

831-8 ^ 

85 

3 

4 

8U-85^ 

86 

3 

3 

4 

85}-86i 

87 

2 

3 

86^-871 

88 

1 

2 

1 

3 

87i-88\ 

89 

1 

1 

88\-89^ 

90 

1 

1 

38,813 

1 
4,359 

1 

89^90^ 

22,261 

20,476 

3,058 

177,710.5 

45,380 

345,038.0 

126 


TABLE     II. 


FEMALE  LIFE.    SUMMARY  (B). 


OBSERVATIONS  CLASSIFIED  ACCORDING  TO  YEARS  OF 
INSURANCE. 


Years  of 
Insurance. 

Whole  Number  op  Entrants,  44,795. 

88,452  Thousand  Dollars  Insured. 

Duration 

of 
Insurance. 

Existing. 

Discon- 
tinued. 

Died. 

Exposed  to 
Bisk. 

AmonntB 
Existing. 

Amounts 
Discontin'd. 

Death 
Claims. 

Exposed  to 
llisk. 

0 

2,266 

2,040 

184 

21,377.5 

4,057 

3,397 

397 

42,527.5 

0-    i 

1 

1,986 

8,253 

391 

36,178.5 

3,539 

15,798 

814 

72,702 

f-  H 

2 

2,604 

3,410 

297 

27,970 

4,447 

8,442 

612 

56,229 

If-  2i 

3 

2,193 

2,471 

252 

22,128.5 

3,557 

6,603 

556 

43,647.5 

2i-  3i 

4 

2,537 

1,611 

204 

17,642.5 

4,283 

4,351 

450 

34,057.5 

3i-4i 

5 

2,411 

1,010 

174 

13,591 

4,063 

2,849 

369 

25,724.5 

^-  5i 

6 

2,383 

580 

143 

10,211 

4,233 

1,436 

295 

19,150 

H-  H 

7 

2,080 

511 

95 

%139.5 

3,806 

1,193 

180 

13,307.5 

6i-  7i 

8 

1,490 

211 

49 

4,803.5 

2,762 

544 

98 

8,453 

7i-  H 

9 

793 

124 

50 

2,897 

1,362 

260 

80 

5,191 

8|-9i 

10 

391 

77 

27 

1,953.5 

659 

176 

48 

3,531 

9i-10i 

11 

207 

50 

22- 

1,472 

404 

90 

43 

2,691 

lOi-lli 

12 

61 

29 

16 

1,203.5 

114 

55 

26 

2,171.5 

lli-12^ 

13 

31 

14 

17 

1,105 

75 

27- 

.    42 

1,990.5 

12i-13i 

14 

54 

17 

11 

1,041.5 

133 

28 

17 

1,846 

13|-14^ 

15 

45 

12 

11 

962 

89 

24 

30 

1,670 

141-15i 

16 

37 

6 

15 

897 

98 

14 

42 

1,532 

15i-16i 

17 

32 

10 

11 

837 

61 

21 

20 

1,374.5 

16^-171 

18 

26 

12 

17 

783 

54 

14 

21 

1,276 

17^-18i 

19 

27 

10 

11 

729 

49 

20 

19 

1,184 

18^-19i 

20 

41 

4 

13 

684 

72 

8 

31 

1,102 

19i-20i 

21 

45 

4 

18 

626 

68 

13 

28 

988.5 

20i-21i 

22 

60 

7 

5 

557.5 

98 

12 

5 

880 

21i-22^ 

23 

122 

2 

12 

488 

175 

3 

15 

769.5 

22i-23i 

24 

147 

1 

11 

352.5 

240 

2 

19 

577 

23i-24i 

25 

122 

2 

194 

197 

2 

317 

24^-25i 

26 

59 

70 

94 

118 

25^26i 

27 

8 

11 

20 

24 

26|-27i 

28 

2 

3 

3 

/ 

4 

27i-28i 

29 

1 

1 

28^-29^ 

30 

1 

1 

1 

1 

29|-30i 

22,261 

20,476 

2,058 

177,710.5 

38,813 

45,380 

4,259 

345,038.0 

TABLE    II. 

OBSERVATIONS  ON  FEMALE  LIFE. 


m 


Excepting  the  first  Aggregates,  the  Amounts  Insured  are  stated  in  Thousand  Dollaks  in  the 
columns  $,  where  1  denotes  $1000,  etc. 


Age  at  Entry,   1  Year. 

Age  at  Entry,  4  Years. 

«"§ 

No.  OF  Entbants,  5. 

$6,000  INSUBBD. 

i 

««§ 

No.  OF  Entrants,  3. 

$3,000  Insured. 

'9 

®§ 

» 

«>§ 

f^2 

M  1  ,     •! 

•o 

6b 

.  -^             "»  • 

2S 

M 

-a   . 

bb   1  .    _! 

13    . 

&U 

.S    tPo' 

w^ 

a 

=^     »;     s-^ 

03 

.a 

o'li^ 

^x 

c 

a% 

ui 

^M 

03 

1 

1 1|.|  i 

H    fi     1  ft 

©•2 

h2 

o  - 

5" 

q5 

M 

bo 
< 

{Si 

1 

(5" 

5 

h2 

ig'-s 

OS 

if 

MS 

« 

bo 

< 

$ 

$ 

$ 

$ 

$ 

% 

1 

$ 

0 

2.5 

3 

1 

0 

1 

1 

1 

1 

•4 

1 

1 

4.5 

1 

5.5 

2 

1 

1 

1.5 

1 

1.5 

5 

2 

4 

5 

3 

2 

1 

1 

6 

3 

4 

5 

Jf 

3 

1 

1 

7 

4 

1 

4 

2 

5 

5 

4 

1 

1 

8 

5 

1 

2.5 

1 

2.5 

6 

5 

1 

.5 

1 

.5 

9 

6 

7 
8 

1 

2 
2 

2 

1 

2 
2 
2 

V 
8 
9 

3 

6.0 

3 

6.0 

9 
10 

1 

1 

1 

1 

1' 
1 

10 
11 

Age  at  Entry,  5  Years. 



— 

— 

No.  OF  Entrants,  1. 

$1,000  Insubed. 

3 

2 

29.5 

4 

2 

34.0 

0 

■ 

.5 

.5 

5 

Age  at  Entry,  2  Years. 

1 
2 

1 

1 
.5 

1 

1 
.5 

6 
7 

0 

No.  OF  Ektbants,  2. 

$2,000  Inscbbd. 

2 

■ 

1 

2.0 

1 

2.0 

1 

1 

Age  at  Entry,  6  Years. 

1 
2 
3 

4 

i 

1.5 
1 

1 
1 

1 

1.5 
1 

1 
1 

8 

5 

6 

0 

No.  OF  Entrants,  1. 

$1,000  Insured. 

6 

.5 

.5 

5 

1 

.5 

1 

.5 

7 

1 
2 
3 
4 

7 

2 

6.0 

2 

6.0 

8 

9 

JO 

Age  at  Entry,  3  Years. 

5 
B 

11 

0 
1 

No.  OF  Entrants,  8. 

$3,000  Insured. 

3 

5 

7 
8 
9 

1 

.5 

1 

.5 

13 

U 
15 

1.5 
3 

1.5 

3 

2.5 

2 
3 

1 

1 

2.5 

2 

1 

1 

1 

^    9.0 

1 

9.0 

2 

6 

4 
5 

1 

1 
.5 

1 

1 
.5 

7 

Age  at  Entry,  7  Years. 

8 

No.  OF  Entrants,  4. ' 

$4,000  Insured. 

i 

2 

10.5 

1 

2 

10.5 

0 

1 

7 

2 

2 

1 

1 

3.5 

1 

3.5 

8 

2 

3 

3 

9 

3 

1 

2.5 

1 

2.5 

10 

4 

2     i 

2 

11 

128 


TABLE     II. 


OBSERVATIONS  ON  FEMALE  LIFE. 


Age  at  Entry,  7  Years. 

Age  at  Entry,  9  Years. 

No.  OP  Entrants,  4. 

$4,000  Insured. 

•a 

be 
•«5 

>^5 

No.  op  Entrants,  7. 

$21,000  Insured. 

*a 

bio 

.2 
'53 

§1 

5= 

^M        j 

1  h  1 

1^ 
^2 

bi 

c 
'p. 

a  a) 
1.1 

5*" 

-a 

5 

1^ 

■la 

w2 

'x 
$ 

11 

1      'tf     • 

po     w2 

$ 

$ 

$ 

$ 

$         $ 

5 

1 

2 

1 

2 

i^ 

10 

2 

19 

6 

1 

1 

i5 

11 

\ 

2 

20 

7 

1 

.5 

1 

.5 

n 

12 

2 

21 

1 

3 

16.5 

1 

3 

16.5 

13 
14 

15 
16 

2 

2 

2 
2 

22 
23 

25 

Age  at  Entry,  8  Years. 

17 
18 

1 

2 
14 

2 
2 

26 

27 

0 

No.  OP  Entrants,  5. 

$5,000  Insured. 

8 

4 

3 

32.0 

7 

84.0 

2.5 

1 

2.5 

1 
2 
3 
4 

1 

2 

5 
4 
3 

2 

1 

2 

5 
4 
3 
3 

9 
10 
11 

Age  at  Entry,   10  Years. 

No.  OP  Entrants,  18- 

$22,000  Insurbd. 

5 
6 

1 

2 

1 

2 

IS 

U 
15 

0 

1 

1 

2 

1 

9 
17 

2 

3 

1 

11 
20.5 

10 
11 

7 

2 

1 

13.5 

1 

15.5 

12 

8 
9 

1 

1 

16 
17 

3 

4 

1 

1 

13 
12.5 

1 

1 

15 
14.5 

13 

10 
11 
12 
13 
14 

/ 

18 
19 
20 
21 

22 

5 
6 

7 
8 
9 

1 

2 
3 

11 
10 

7.5 

6 

6 

1 

3 

2 

13 
11.5 
9 

8 
8 

15 
16 
17 
18 
19 

15 
16 

1 

1 

23 

10 
11 
12 

1 

1 

5 

4.5 

3 

1 

1 

7 

6.5 
.  5 

20 
21 

9.9, 

3 

2 

29.5 

3 

2 

29.5 

13 
14 

3 
3 

5 
5 

23 
U 

. 

Age  at  Entry,  9  Years. 

15 
16 

17 

1 

2.5 

2 

2 

1 

4.5 

4 

4 

25 

26 
97 

0 

No.  OP  Entrants,  7. 

$21,000  Insured. 

9. 

18 

2 

2 

4 

4 

28 

1 

1 

3 

5 

1 

10 

6 

11 

1 

132.5 

9 

12 

1 

171.0 

1 
2 
3 
4 

5 

1 
1 

1 

1 

4.5 
3 
3 
3 

2.5 

5 
2 

1 
5 

14.5 
9 
9 
9 

6.5 

10 
11 
12 
IS 

U 

Age  at  Entry,   11  Years. 

0 

No.  OP  Entrants,  25. 

$40,000  Insured. 

11 

2 

1 

12 

6 

1 

19.5 

6 

1 

2 

15 

1 

1 

1 

21.5 

5 

1 

32.5 

12 

7 

1 

2 

16 

2 

1 

7 

16.5 

5 

5 

24.5 

13 

8 

1 

2 

17 

3 

2 

3 

1 

10.5 

2 

4 

2 

15 

U 

9 

1 

2 

18 

4 

1 

6 

1 

9 

15 

TABLE     II. 


139 


OBSERVATIONS  ON  FEMALE  LIFE. 


Age  at  Entry,   11  Years. 


Age  at  Entry,   12  Years. 


0 

1 
2 
3 

4 

5 
6 

7 
8 
9 

10 
11 
12 
13 
14 

15 
16 
17 
18 
19 


Years  of 
Insurance. 

No. 

OF  Entrants,  25. 

$40,000  Insured. 

be 

a 

to 

9.  ^ 

5'^ 

i 

1^- 

P 
h2 

.S     c« 

1  J  "S^- 

$ 

$ 

$ 

$ 

5 

5 

8 

6 

1 

5 

2 

8 

7 

4 

6 

8 

4 

6 

9 

4 

6 

10 

4 

6 

11 

2 

3 

4 

4 

12 

2 

2 

13 

2 

2 

14 

1 

1.5 

1 

1.5 

15 

1 

16 

1 

17 

1 

18 

1 

19 

1 

20 

1 

21 

1 

1 

1 

9 

15 

1 

108.0 

22 

16 

2 

157.0 

Age  at  Entry,   12  Years. 


16 
17 
18 
19 
20 

21 


H 

25 

26 
27 
28 
29 
30 

31 

32 


No. 

OF  Entrants,  27. 

$62,000  Insured. 

1 

13.5 

10 

31 

2 

4 

24 

10 

3 

50.5 

2 

3 

1 

18.5 

3 

10 

1 

34 

1 

2 

13 

1 

5 

22.5 

1 

11 

1 

19 

3 

10 

3 

18 

1 

1 

6.5 

1 

1 

14.5 

2 

4 
3 
3 

3 
3 
3 

6 

10 

7 
7 

7 
7 

7 

1 

3 
2 

2 
2 
2 
2 
2 

5 

7  • 
2 

2 
2 
2 
2 
2 

13 

U 
15 
16 

17 
18 
19 

20 
21 


2^ 

25 
26 

27 
28 
29 
30 
31 


><fl 


20 
21 
22 
23 


0 
1 
2 
3 

4 

5 
6 
7 
8 
9 

10 

11 
12 
13 
14 

15 
16 
17 
18 
19 

20 
21 
22 
23 
24 

25 
26 
27 
28 


No.  OF  Entrants,  27. 


14 


12 


K« 


136.5 


$62,000  Insured. 


36 


25 


^ 


259.5 


Age  at  Entry,   13  Years. 


No.  OF  Entrants,  27. 


17  10 


13.5 
24.5 
18.5 
14 

12 

10 
7 
6 
4 
2 

2 
2 
2 
2 
2 

2 

2 
2 
2 

2 

2 
2 
2 
2 
2 

2 
1 
1 
1 

146.5 


$42,000  Insured. 


28 


14 


21 

39 

21 

14.5 

13 

10.5 
7 
5 
3 

2 

'  2 

2 
2 
2 
2 

2 
2 
2 
2 
2 

2 
2 
2 
2 
2 

2 
1 
1 
1 

171.0 


bo 


3U 
35 


13 

U 
15 
16 
17 

18 
19 
20 
21 


25 
26 

27 

28 
29 
30 
31 
32 

33 
3J^ 
35 
36 
37 

38 
39 
¥> 


130 


TABLE     II. 


OBSERVATIONS  ON  FEMALE  LIFE. 


Age  at  Entry,  •14  Years. 


Age  at  Entry,   15  Years. 


0)5 


0 

4 

1 

7 

2 

2 

3 

4 

4 

2 

5 

2 

6 

3 

7 

3 

8 

1 

9 

2 

10 

11 

1 

12 

13 

1 

14 

1 

No.  OF  Entrants,  i 


33 


51 


lii 
^2 


41.5 
70.5 
51.5 
41.5 
31.5 

26 

20.5 

14.5 

9 

6.5 

4 

4 

2.5 

2 

1 


326.5 


$130,000  Insuebd. 

bb 

1 

■2a 

W2 

$ 

$ 

$ 

$ 

8 

3 

63.5 

13 

13 

112.5 

3 

17 

1 

84.5 

2 

9 

1 

67.5 

2 

5 

57.5 

2 

11 

47.5 

7 

2 

39 

4 

2 

30 

2 

2 

24 

15 

2 

20 
4 

1 

4 

1 

2.5 

1 

2 

1 

67 

1 

61 

2 

559.5 

Age  at  Entry,   15  Years. 


U 
15 
16 
17 
18 

19 

20 
21 
22 
2S 

25 
26 
27 
28 


No. 

OP  Entrants,  136. 

$308,000  Insured. 

0 

6 

5 

65.5 

13 

4 

102 

1 

6 

33 

108.5 

6 

33 

174.5 

2 

8 

11 

80.5 

16 

18 

143 

3 

1 

6 

2 

64 

1 

13 

c 
i 

111.5 

4 

5 

11 

52.5 

11 

19 

87.5 

5 

5 

4 

40 

6 

4 

65 

6 

7 

2 

2 

32 

12 

2 

2 

56 

7 

5 

5 

19.5 

5 

10 

36 

8 

5 

12 

6 

26 

9 

3 

7 

5 

20 

10 

1 

3.5 

1 

i 

1 

14.5 

11 

3 

1 

14 

12 

3 

14 

13 

3 

14 

14 

3 

14 

15 

1 

3 

5 

14 

16 

2 

9 

17 

2 

9 

18 

2 

9 

19 

2 

9 

20 

2 

9 

21 

2 

9 

22 

2 

9 

23 

2 

9 

24 

1 

2 

5 

9 

15 
16 
17 
18 
19 

20 
21 

22 
23 
2J^ 

25 
26 
27 
28 
29 

SO 
31 


3J, 

35 
36 
37 
38 
39 


No.  OF  Entrants,  136. 


54 


i».5 


78 


520.0 


$808,000  Insured. 


95    104     9 


■5B 


h2_ 

$ 

4 
4 


995.0 


Age  at  Entry,  16  Years. 


Age  at  Entry,   17  Years. 


No.  OF  Entrants,  209. 


16 
6 
•9 
4 


12 
51 
11 
13 
6 


98.5 
155.5 
116.5 

95.5 

81 


$.336,000  Insured. 


160 

273.5 
219.5 
175 
142.5 


bo 

< 


UO 


No. 

OF  Entrants,  164. 

$229,000  Insured. 

0 

9 

4 

80 

11 

6 

111.5 

1 

6 

41 

1 

130.5 

7 

50 

1 

187 

2 

11 

13 

1 

96.5 

13 

18 

1 

145 

3 

1 

6 

75 

1 

11 

116.5 

4 

6 

8 

67 

12 

19 

100.5 

5 

5 

4 

55 

4 

8 

75 

6 

13 

3 

46.5 

15 

7 

63.5; 

7 

5 

2 

31 

13 

2 

44     1 

8 

9 

1 

25 

7 

1 

30     1 

9 

'  5 

2 

14 

1 

2 

21     1 

1 

10 

2 

8 

8 

19     ' 

11 

1 

6 

5 

11 

12 

5 

6 

13 

5 

6 

14 

3 

5 

2 

6 

15 

2 

4 

16 

2 

4 

17 

2 

4 

18 

2 

4 

19 

1 

2 

1 

4 

20 

3 

21 

3 

22 

3 

23 

3 

24 

1 

3 

3 

77 

83 

4 

664.5 

102 

123 

4 

977.0 

16 
17 
18 
19 
20 

21 


2J, 
25 

26 
27 
28 
29 
30 

31 

32 
33 
34 
35 

36 

37 
38 
39 
40 


17 
18 
19 
20 
21 


TABLE    II. 


131 


OBSERVATIONS  ON  FEMALE  LIFE. 


Age  at  Entry,   17  Years. 


«a* 

No. 

OF  Entrants,  209. 

$.3-36,000 

a 

it 

5'^ 

13 
S 

Exposed 
to  Kisk. 

so 

c 

5" 

$ 

$ 

5 

8 

9 

64.5 

14 

18 

6 

17 

5 

49.5 

33 

7 

7 

9 

3 

1 

29 

15 

1 

8 

6 

2 

17 

9 

2 

9 

5 

10 

12 

10 

1 

4.5 

1 

11 

4 

12 

4 

13 

4 

14 

4 

15 

4 

16 

4 

17 

4 

18 

1 

4 

19 

3 

20 

3 

21 

3 

22 

1 

3 

1 

23 

1 

2 

1 

24 

1 
90 

1 

1 

112 

7 

768.5 

142 

178 

OS 


16 


113 
86.5 
49.5 
31 
21 

9 


3 
3 
3 

2 
1 

1,359.5 


Age  at  Entry,  18  Years. 


22 
23 
21 
25 
2G 

2  ( 
28 
29 
30 
31 

32 
33 
3J^ 
35 
.36 

37 
38 
39 
40 
41 


No. 

OP  Entrants,  372 

$651,000  Insured. 

0 

16 

31 

3 

170.5 

28 

32 

4 

309.5 

1 

11 

109 

1 

267.5 

11 

230 

1 

472 

2 

21 

40 

181 

27 

72 

309 

3 

12 

26 

3 

127 

18 

57 

7 

217.5 

4 

8 

12 

1 

93 

16 

16 

1 

156 

5 

11 

11 

1 

72.5 

12 

23 

2 

119.5 

6 

16 

5 

2 

52.5 

21 

6 

1 

91 

7 

8 

4 

30 

25 

4 

64 

8 

1 

2 

19 

1 

8 

33 

9 

4 

1 

16.5 

5 

1 

27.5 

10 

2 

12 

4 

22 

11 

2 

1 

10 

3 

5 

18 

12 

7 

10 

13 

7 

10 

14 

1 

7 

1 

10 

15 

1 

6 

1 

9 

16 

5 

8 

17 

5 

8  • 

18 

5 

8 

19 

5 

8 

18 
19 
20 
21 

22 

23 

25 
26 
?7 

28 
29 
30 
31 

32 

33 
34 
35 
36 
37 


Age  at  Entry,   18  Years. 


<M   ^ 

No. 

OF  Entrants,  372. 

1       $651,000  Ins 

°u 

n 
1 

S  § 

5" 

i 

w2 

fcb 

c 

"■§ 

'R 
w 

$ 

§■2 
8.1 

$ 

Oo 

20 

5 

21 

5 

22 

1 

5 

4 

23 

2 

4 

2 

24 

1 

2 

1 

25 

1 
118 

1 

1 

241 

13 

1,120.5 

180 

449 

22 

1 


bo 


38 
39 
40 

42 

43 


1,941.0 


Age  at  Entry,   19  Years. 


0 

No. 

OF  Entrants,  496. 

30 

35 

2 

230.5 

1 

20 

115 

3 

371.5 

2 

17 

61 

1 

260.5 

3 

18 

44 

1 

190 

4 

19 

13 

142.5 

5 

27 

8 

113 

6 

26 

7 

78.5 

7 

11 

6 

46 

8 

9 

3 

,30.5 

9 

i 

1 

19.5 

10 

1 

3 

10.5 

11 

8 

12 

8 

13 

1 

1 

7.5 

14 

6 

15 

1 

6 

16 

5 

17 

5 

18 

1 

5 

19 

4 

20 

1 

4 

21 

3 

22 

1 

2.5 

23 

1 

2 

24 

1 

1 

189 

298 

9 

1,560.0 

$831,000  Insured. 


47 
38 
23 
22 
30 


61 
176 
133 

87 


27  14 


266 


385 
631 
432.5 

296.5 
206.5 

146 

106.5 
64.5 
43.5 
30.5 

20 

17 

17 

16.5 

11 

11 


547  18  2,487.0 


19 
20 
21 

22 
23 

24 
25 
26 
27 
28 

29 
30 
31 

32 
33 

34 
35 
36 
37 
38 

39 
40 
41 

42 
43 


132 


TABLE     II. 


OBSERVATIONS  ON  FEMALE  LIFE. 


Age 

at  Entry,  20  Years. 

Age 

at  Entry,  21  Years. 

<M« 

No. 

OF  Entrants,  745. 

$1,287,000  Insured. 

<H^ 

No. 

OF  Entrants,  880. 

$1,548,000  Insured. 

4^ 

og 

u 

0§ 

bo 

< 

^^ 

si 
a 

'3 

S  'u 

O  3 

".5 

5" 

si 

0  3 
$ 

Si 
00 

•0  . 

9^ 

"S 
< 

M 

is" 

11 

5'^ 

1 
5 

i 

Si 

o  S 
o  S 

_  « 
58 

T 

$ 

$~ 

$ 

T 

$ 

0 

42 

68 

3 

338.5 

66 

103 

3 

592 

20 

0 

45 

56 

3 

412 

64 

78 

4 

735 

21 

1 

38 

167 

9 

548.5 

72 

265 

11 

982.5 

21 

1 

43 

225 

5 

663.5 

63 

400 

6 

1,202 

22 

2 

31 

71 

2 

382.5 

51 

159 

4 

687.5 

22 

2 

44 

72 

8 

467 

68 

159 

13 

853.5 

23 

3 

32 

37 

2 

295.0 

47 

87 

3 

509.5 

23 

3 

39 

60 

5 

349 

55 

110 

10 

638 

24 

4 

42 

37 

3 

224.5 

61 

72 

2 

380 

21, 

4 

30 

30 

1 

260 

49 

86 

1 

475 

25 

5 

23 

17 

4 

152.5 

45 

27 

3 

267.5 

25 

5 

36 

21 

1 

203.5 

53 

38 

1 

363 

26 

6 

23 

7 

1 

113.5 

38 

13 

1 

199.5 

26 

6 

32 

8 

1 

152 

65 

18 

3 

281 

27 

7 

20 

14 

2 

79 

42 

19 

3 

144.5 

27 

7 

35 

7 

2 

111.5 

48  117 

3 

195.5 

28 

8 

19 

3 

2 

48.5 

45 

6 

1 

87 

28 

8 

19 

5 

2 

68.5 

26 

8 

21 

132 

29 

9 

5 

2 

25 

8 

2 

37 

29 

9 

6 

2 

1 

44 

11 

6 

2 

78 

30 

10 

3 

2 

18 

7 

3 

26.5 

30 

10 

7 

1 

1 

35.5 

15 

2 

1 

61 

31 

11 

1 

14 

1 

18 

31 

11 

3 

3 

25.5 

4 

4 

42 

32 

12 

1 

13 

1 

17 

32 

12 

1 

21 

5 

36 

33 

13 

12 

16 

33 

13 

20 

31 

34 

14 

12 

16 

SJf 

14 

1 

20 

5 

31 

35 

15 

1 

12 

1 

16 

35 

15 

1 

19 

1 

26 

86 

16 

11 

15 

36 

16 

1 

18 

2 

25 

37 

17 

11 

15 

37 

17 

17 

23 

38 

18 

1 

11 

1 

15 

38 

18 

17 

23 

39 

19 

10 

14 

39 

19 

1 

16.5 

1 

22.5 

40 

20 

1 

10 

1 

14 

40 

20 

1 

16 

2 

- 

22 

41 

21 

1 

9 

3 

13 

41 

21 

1 

15 

1 

20 

42 

22 

8 

10 

42 

22 

2 

14 

3 

19 

^ 

23 

3 

8 

3 

10 

43 

23 

4 

12 

4 

16 

U 

24 

1 

1 

5 

1 

1 

7 

u 

24 

2 

8 

2 

12 

45 

25 

2 

3 

4 

5     ' 

45 

25 

4 

6 

8 

10 

46 

26 
27 
28 
29 

1 

1 
1 

1 

1 

1 
1 
1 

46 
47 
48 

49 

26 

2! 

2 

2 

2 

Jf7 

359 

49130 

3,013.5 

556 

927 

65 

5,374.5 

30 

1 

289 

1 

1 

1 

60 

425 

31 

2,380.0 

497 

756 

34 

4,119.5 

TABLE     II. 

OBSERVATIONS  ON   FEMALE   LIFE. 


133 


Age  at  Entry,  22  Years. 

9 

Ntjmber  of 

Ektrants,  1,141. 

$1,986,000  Insured 

Age 

ii 

at 

1  £S 

.     , 

Discon- 

Exposed to 
Risk. 

Amounts 

Amounts 

Death 

Exposed  to 

Exit. 

i  >*,g 

Existing. 

tinued. 

Died. 

Existing. 

Discontin'cd. 

Claims. 

Risk. 

$ 

$ 

$ 

$ 

0 

56 

75 

7 

533 

88 

116 

16 

935 

2Z 

1 

45 

278 

8 

864 

79 

482  . 

23 

1,525 

23 

2 

60 

121 

9 

611.5 

94 

262 

14 

1,051 

n 

3 

60 

61 

4 

451.5 

68 

145 

5 

739.5 

25 

4 

44 

39 

6 

337.5 

74 

60 

21 

564 

26 

5 

34 

25 

2 

255.5 

56 

57 

5 

410.5 

27 

6 

35 

11 

3 

201.5 

40 

14 

7 

314 

28 

7 

33 

16 

1 

150 

50 

44 

1 

238 

29 

8 

29 

19 

1 

98.5 

46 

29 

2 

150.5 

30 

9 

11 

2 

1 

58 

11 

6 

1 

85 

31 

10 

14 

2 

45 

21 

4 

70 

32 

11 

5 

1 

28.5 

10 

1 

44.5 

33 

12 

3 

23 

2 

34 

3J, 

13 

1 

19.5 

3 

30.5 

35 

14 

1 

19 

5 

2^9 

36 

15 

1 

17.5 

1 

23.5 

37 

16 

17 

23 

38 

17 

2 

2 

17 

2 

2 

23 

39 

18 

13 

19 

J,0 

19 

2 

13 

1 

. 

19 

Jfl 

20 

11 

18 

^ 

21 

11 

18 

JfS 

22 

2 

11 

3 

18 

U 

23 

■    .2 

9 

3 

15 

U5 

24 

4 

7 

8 

12 

46 

25 

2 

3 

2 

4 

47 

26 

1 

1 

2 

2 

Jf8 

445 

650 

46 

3,826.5 

665 

1,220 

101 

6,415.0 

Age  at  Entry,  23  1 

fears. 

0 

N 

[TUBER  OF  ] 

Bntrantb 

,  1,264. 

$2,268,000  Insured. 

23 

68 

81 

9 

591.5 

114 

130 

22 

1,069 

1 

59 

300 

7 

956 

92 

536 

11 

1,734 

2J, 

2 

82 

104 

8 

688 

114 

221 

.11 

1,252.5 

25 

3 

44 

73 

7 

509.5 

60 

176 

16 

929 

26 

4 

57- 

37 

5 

403.5 

84 

87 

15 

721.5 

27 

■  5 

51 

29 

5 

308.5 

66 

60 

9 

549 

28 

6 

52 

14 

3 

231 

80 

27 

5 

430.5 

29 

7 

55 

18 

160 

106 

18 

323 

SO 

8 

30 

2 

95 

67 

4 

206 

31 

9 

10 

2 

63 

26 

4 

135 

32 

10 

7 

52 

11 

107 

33 

11 

6 

1 

1 

44.5 

13 

2 

1 

95 

SA 

12 

3 

2 

36 

5 

1 

79.5 

35 

13 

32 

74 

36 

14 

9 

1 

31.5 

8 

2 

73 

87 

134 


TABLE    II. 


OBSERVATIONS  ON  FEMALE  LIFE. 


Age  at  Entry,  23  Years. 

zi 

. 

sfMBEB  OF  ] 

Bntbants 

,  1,264 

$2,268,000  Insueed. 

Age 

§i 

at 

£S 

.     . 

Difscon- 

Exposed  to 
Risk. 

Amounts 

Amounts 

Death 

Exposed  to 
Risk. 

Exit.  1 

^M 

Existing. 

tinned. 

Died. 

Existing. 

$ 

Discontin'ed. 

Claims. 

$ 

$ 

$ 

15 

2 

2 

29 

9 

6 

64 

38 

16 

25 

49 

39 

17 

1 

24.5 

1 

48.5 

JfO 

18 

2 

24 

16 

48 

U 

19 

2 

1 

22 

2 

3 

•    32 

^ 

20 

3 

19 

3 

27 

JfS 

21 

2 

16 

2 

24 

U 

22 

2 

1 

14 

3 

1 

22 

Jf5 

23 

3 

11 

7 

18 

Jf6 

24 

4 

8 

4 

11 

A7 

25 

3 

4 

3 

7 

It8 

26 

1 

4 

U9 

27 

1 
550 

1 

4 

4 

50 

665 

49 

4,400.5 

899 

1,269 

100 

8,136.5 

Age  at  Entry,  24  "5 

fears. 

0 

N 

(THBEB  OF 

Entbant 

5,  1,399. 

$2,603,000  Insttbkd. 

H 

64 

77 

6 

661 

102 

132 

5 

1,235.5 

1 

57 

328 

11 

1,088 

108 

567 

17 

2,080.5 

25 

2 

88 

130 

10 

791 

133 

240 

25 

1,552 

26 

3 

61 

84 

7 

586 

100 

191 

17 

1,178.5 

27 

4 

67 

51 

5 

450.5 

109 

156 

13 

888 

28 

5 

59 

34 

3 

336 

114 

96 

6 

640 

29 

6 

54 

11 

5 

251.5 

106 

25 

10 

459.5 

30 

7 

42 

14 

2 

180 

63 

26 

3 

318 

31 

8 

34 

8 

1 

125 

75 

15 

1 

231.5 

32 

9 

22 

7 

2 

82.5 

33 

14 

2 

141 

33 

10 

5 

1 

1 

54.5 

8 

1 

•2 

98.5 

Si 

11 

8 

1 

47.5 

11 

1 

87.5 

35 

12 

39 

76 

36 

13 

1 

39 

10 

76 

37 

14 

3 

1 

37.5 

8 

2 

65 

38 

15 

1 

34 

5 

56 

39 

16 

1 

33 

1 

51 

JfO 

17 

1 

32     . 

5 

50 

Jfl 

18 

1 

30.5 

1 

44.5 

J^ 

19 

30 

44 

43 

20 

30 

•   44 

U 

21 

2 

30 

5 

44 

45 

22 

1 

28 

1 

39 

46 

23 

4 

2 

27 

5 

2 

38 

Jf7 

24 

6 

21 

13 

31 

48 

TABLE     II. 


135 


OBSERVATIONS  ON  FEMALE  LIFE. 


Age  at  Entry,  24  Years. 

^1 

Number  of 

Entrant 

3,  1,399. 

$2,603,000  Insured. 

Age 

11 

at 
Exit 

Discon- 

Exposed to 

Amounts 

Amounts 

Death 

Exposed  to 
task. 

tHU 

tinued. 

Risk. 

Existing. 

Discontin'ed 

Claims. 

$ 

$ 

$ 

$ 

25 

8 

1 

15 

9 

1 

18 

49 

26 

5 

6 

7 

8 

50 

27 

1 

1 

1 

1 

51 

595 

748 

56 

5,086.5 

1,032 

1,467 

104 

9,596.0 

Age  at  Entry,  25  Years. 

0 

N 

CHBER  OF 

Entrants 

i,  1,547. 

. 

$3,119,000  Insubed. 

25 

66 

103 

3 

722 

134 

161 

3 

1,479 

1 

68 

347 

15 

1,201.5 

94 

697 

22 

-    2,472.5* 

26 

2 

79 

126 

9 

882 

107 

337 

24 

1,839.5 

27 

3 

49 

93 

6 

684.5 

71 

275 

12 

1,402.5 

28 

4 

73 

58 

4 

554 

93 

206 

10 

1,079 

29 

5 

81 

40 

3 

429 

136 

94 

3 

826 

30 

6 

62 

,      18 

4 

31G 

142 

45 

8 

617.5 

31 

7 

49 

19 

2 

231.5 

126 

37 

3 

426.5 

32 

8 

45 

8 

1 

167 

77 

19 

2 

269.5 

33 

9 

23 

4 

4 

115 

33 

4 

4 

179 

SJf 

10 

15 

1 

85.5 

23 

3 

138.5 

35 

11 

7 

2 

69 

15 

2 

113 

36 

12 

1 

2 

1 

60 

1 

1 

1 

96.5 

37 

13 

2 

2 

56 

3 

3 

92.5 

38 

14 

1 

1 

53 

2 

1 

88 

39 

15 

2 

1 

1 

50.5 

5 

4 

1 

83 

1,0 

16 

2 

2 

47 

2 

" 

4 

75 

41 

17 

3 

43 

3 

2 

69 

42 

18 

2 

1 

38.5 

2 

1 

63.5 

43 

19 

1 

36 

2 

61 

44 

20 

1 

35 

2 

59 

45 

21 

3 

34 

3 

57 

46 

22 

1 

31 

2 

54 

47 

23 

6 

2 

30 

9 

5 

52 

48 

24 

1 

10 

22 

16 

38 

49 

25 

7 

12 

15 

22 

50 

26 

i 
1 

5 

5 

7 

7 

51 

663 

825 

59 

6,010.0 

1,125 

1,889 

105 

11,760.0 

136 


TABLE    II. 


OBSERVATIONS  ON  FEMALE  LIFE. 


Age  at  Entry,  26 

Years. 

•si 

NUMBEB  OF 

Entrants,  1,664. 

$3,058,000  Insured. 

Age 

►2S 

at 

Discon- 

Exprtsed to 
Risk. 

Amounts 

Amounts 

Death 

Exposed  to 
Risk. 

T-rit 

>"& 

Existing. 

1 

tinued. 

1    Died. 

Existing. 

Discontin'ed 

Claims. 

ri  ft  1 1, 

1 

$ 

$ 

$ 

S 

0 

81 

119 

5 

772.5 

132 

231 

6 

1,410.5 

£6 

1 

77 

345 

17 

1,286.5 

129 

649 

35 

2,358.5 

27 

2 

82 

136 

8 

952 

128 

329 

16 

1,705.5 

S8 

3 

71 

,     94 

6 

747 

91 

244 

10 

1,275 

29 

4 

73 

66 

6 

590 

117 

165 

10 

969.5 

SO 

5 

73 

37 

3 

459.5 

92 

76 

2 

722 

SI 

6 

76 

18 

6 

356 

112 

40 

10 

570 

S2 

7 

60 

23 

3 

253.5 

113 

42 

4 

407 

S3 

8 

57 

4 

5 

177 

94 

6 

8 

266 

SU 

9 

30 

7 

1 

109.5 

42 

10 

2 

156 

S5 

10 

p     1^ 

4 

1 

73 

17 

5 

2 

104.5 

36 

11 

'       7 

1 

57.5 

11 

1 

82.5 

37 

12 

3 

48.5 

8 

67 

38 

13 

1 

47 

1 

63 

39 

14 

2 

46 

3 

62 

Jfi 

15 

2 

44 

6 

59 

Jfl 

16 

2 

42 

1 

53 

J^ 

17 

2 

40 

2 

52 

43 

18 

1 

37.5 

1 

1 

49.5 

U 

19 

36 

48 

45 

20 

3 

36 

5 

48 

46 

21 

4 

1 

33 

6 

1 

43 

47 

22 

3 

28 

3 

36 

48 

23 

•  3 

25 

8 

33      1 

49 

24 

9 

1 

22 

11 

1 

25 

60 

25 

8 

12 

8 

13 

51 

26 

4 

4 

5 

5 

52 

742 

858 

64 

6,335.0 

1,137 

1,807 

108 

10,083.5 

Age  at  Eu 

try,  27  ^ 

fears. 

0 

Ni 

7HBEB  OP  ] 

Sntbants 

,  1,624. 

13,233,000  Insured. 

27 

79 

75 

9 

774.5 

113 

118 

16 

1,557.5 

1 

69 

335 

12 

1,293.5 

138 

627 

20 

2,672.5 

28 

2 

105 

148 

9 

971 

176 

390 

18 

2,006 

29 

3 

74 

108 

6 

729 

123 

288 

10 

1,473 

SO 

4 

82 

60 

5 

565 

140 

173 

13 

1,109.5 

31 

5 

85 

28 

5 

434 

137 

99 

12 

820.5 

32 

6 

56 

18 

6 

321 

88 

41 

15 

601.5 

33 

7 

59 

17 

4 

241.5 

93 

42 

3 

457 

34 

8 

51 

8 

4 

166 

105 

18 

6 

331 

35 

9 

31 

4 

105 

51 

5 

208.5 

36 

TABLE    II. 


137 


OBSERVATIONS  ON  FEMALE  LIFE. 


Age  at  Entry,  27  Years. 

i 

Number  of 

Entrants,  1,624. 

$3,233,000  Insured. 

Age 

u 

at    1 

£S 

. 

Discon- 

, 

Exposed  to 

Amounts 

Amounts 

Death 

Exposed  to 
Risk. 

Exit. 

>"& 

Existing. 

tinued. 

Died. 

Risli. 

Existing. 

Discontin'ed. 

Claims 

$ 

$ 

$ 

$ 

10 

10 

3 

1 

70.5 

26 

8 

2 

151 

37 

11 

9 

1 

57.5 

17 

2 

118 

38 

12 

4 

1 

47.5 

10 

1 

99.5 

39 

13 

1 

1 

1 

42.5 

1 

1 

1 

88.5 

40 

14 

1 

40 

2 

86 

41 

15 

39 

84 

42 

16 

1 

1 

38.5 

1 

2 

83.5 

43 

17 

1 

37 

3 

81 

44 

18 

1 

1 

36 

1 

1 

78 

45 

19 

2 

1 

33.5 

3 

1 

75.5 

46 

20 

3 

2 

30 

8 

4 

70 

47 

21 

26 

60 

48 

22 

3 

26 

6 

60 

49 

23 

6 

23 

9 

54 

50 

24 

6 

17 

14 

45 

51 

25 

8 

11 

23 

31 

52 

26 

3 

3 

8 

8 
12,510.0 

63 

749 

811 

64 

6,178.5 

1,295 

1,819 

119 

Age  at  Entry,  28  1 

rears. 

0 

N 

CTMBEB  OF  ] 

Entrants 

,  1,852. 

$3,462,000  Insubbd. 

28 

70 

102 

4 

875 

Ill 

168 

7 

1,647 

1 

75 

382 

12 

1,485 

112 

678 

29 

2,837 

29 

2 

112 

158 

8 

1,128 

167 

422 

8 

2,146 

30 

3 

93 

91 

10 

883.5 

187 

158 

21 

1,681 

31 

4 

100 

67 

8 

701.5 

143 

180 

13 

1,304 

32 

5 

88 

36 

8 

542 

127 

77 

13 

1,019.5 

33 

6 

107 

15 

2 

420.5 

185 

36 

3 

823 

34 

7 

89 

15 

4 

296.5 

197 

42 

4 

596 

35 

8 

57 

6 

2 

193 

116 

24 

3 

362 

36 

9 

37 

6 

3 

128 

64 

18 

4 

222 

37 

10 

18 

4 

1 

83 

27 

8 

2 

141 

38 

11 

8 

1 

1 

61.5 

18 

2 

1 

107 

39 

12 

4 

1 

51.5 

14 

1 

86.5 

40 

13 

2 

47 

3 

72 

41 

14 

2 

45      1 

3 

69 

42 

15 

2 

1 

43 

3 

2 

66 

43 

16 

2 

1 

40 

6 

1 

61 

44 

17 

2 

37 

7 

54 

45 

18 

1 

1 

34.5 

1 

1 

46.5 

46 

19 

2 

1 

32.5 

2 

5 

43.5 

47 

138 


TABLE    II. 


OBSERVATIONS  ON  FEMALE  LIFE. 


!i 

Age  at  Entry,  28  Years. 

NXTMBBB  OF 

Entrants,  1,852. 

$3,462,000  Insured. 

Age 

at 

Discon- 

Exposed to 
Risk. 

Amounts 

Amounts 

Deatli 

Exposed  to 

Exit. 

>*S 

Existing. 

tinued. 

Died. 

Existing. 

Discontin'ed. 

Claims. 

Risli. 

$ 

$ 

$ 

$ 

20 

2 

1 

30 

2 

1 

38 

48 

21 

4 

27 

4 

35 

49 

22 

3 

23 

5 

31 

50 

23 

7 

20 

10 

26 

51 

24 

2 

1 

13 

2 

1 

16 

52 

25 

8 

10 

10 

13 

53 

26 

1 

2 

1 

3 

H 

27 

1 

2 

55 

28 

1 

1 

2 

2 

56 

897 

886 

69 

7,255.0 

1,526 

1,820 

116 

13,549.0 

Age  at  Ee 

itry,  29  1 

fears. 

0 

N 

[7MBEB  OF 

Entrants 

,  1,713. 

$3,520,000  Insured. 

29 

78 

89 

6 

812 

150 

139 

12 

1,690.5 

1 

63 

323 

18 

1,378.5 

107 

599 

54 

2,919.5 

30 

2 

79 

133 

16 

1,069.5 

130 

354 

31 

2,282 

31 

Q 

81 

104 

10 

856 

125 

309 

25 

1,789.5 

32 

4 

93 

57 

8 

684.5 

146 

208 

18 

1,381 

33 

5 

89 

47 

5 

531.5 

152 

124 

8 

1,051 

SI, 

6 

90 

23 

5 

402.5 

186 

60 

8 

799 

35 

7 

79 

27 

3 

282.5 

160 

60 

8 

545 

36 

8 

55 

8 

3 

183 

94 

21 

6 

336.5 

37 

9 

38 

3 

1 

119.5 

77 

9 

2 

221.5 

38 

10 

15 

6 

3 

76 

24 

10 

7 

133 

39 

11 

5 

3 

1 

53.5 

12 

5 

2 

94.5 

40 

12 

1 

46 

2 

78 

41 

13 

1 

1 

3 

44.5 

2 

1 

13 

75.5 

42 

14 

3 

40 

9 

60 

43 

15 

3 

1 

1 

36.5 

2 

1 

3 

50.5 

u 

16 

3 

32 

11 

45 

45 

17 

1 

1 

28.5 

1 

1 

33.5 

46 

18 

1 

1 

27 

1 

2 

32 

47 

19 

25 

29 

Jt8 

20 

2 

25 

3 

29 

49 

21 

1 

23 

1 

26 

50 

22 

2 

22 

3 

25 

51 

23 

5 

20 

6 

22 

52 

24 

8 

15 

9 

16 

53 

25 

4 

7 

4 

7 

54 

26 

3 

3 

3 

3 

55 

803 

826 

84 

6,843.5 

1,420 

1,901 

199 

13,774.5 

TABLE    II. 


139 


OBSERVATIONS  ON  FEMALE  LIFE. 


Age  at  Entry,  30  Years. 

;i 

Number  or 

Entrants,  1,944. 

13,837,000  iNsirBBD. 

Age 

II 

at 

Discon- 

Exposed to 

Amounts 

Amounts 

Deatli 

Exposed  to 
Rislv. 

Exit. 

Existing. 

tinued. 

Died. 

Risk. 

Existing. 

Discontin'ed. 

Claims. 

t 

$ 

$ 

$ 

0 

90 

79 

8 

932.5 

149 

150 

16 

1,843.5 

30 

1 

76 

356 

18 

1,589 

116 

659 

51 

3,192.5 

31 

2 

111 

146 

9 

1,244 

174 

354 

14 

2,519 

32 

3 

93 

102 

18 

1,000 

144 

299 

.    38 

2,004.5 

33 

4 

103 

82 

8 

797 

156 

232 

17 

1,557 

3^ 

5 

125 

50 

6 

620 

207 

174 

9 

1,181 

35 

6 

87 

23 

11 

452.5 

166 

61 

34 

847.5 

36 

7 

110 

21 

332.5 

176 

67 

583.5 

37 

8 

67 

15 

2 

204.5 

109 

31 

3 

358.5 

38 

9 

43 

2 

127 

76 

6 

228 

39 

10 

14 

.  1 

1 

82.5 

22 

1 

1 

148.5 

40 

11 

11 

3 

67 

31 

3 

125 

41 

12 

2 

2 

1 

52 

6 

6 

5 

88 

42 

13 

1 

1 

48 

1 

1 

74 

43 

14 

1 

1 

46 

5 

1 

72 

44 

15 

2 

44 

3 

36 

45 

16 

1 

1 

41.5 

1 

3 

61.5 

46 

17 

1 

40 

1 

59 

47 

18 

1 

n 

1 

38 

1 

3 

1 

56.5 

48 

19 

35 

2 

53 

49 

20 

1 

. 

33 

1 

51 

50 

21 

1 

32 

1 

50 

51 

22 

1 

2 

1 

30 

2 

4 

1 

47 

52 

23 

10 

1 

27 

13 

1 

42 

53 

24 

8 

16 

16 

28 

54 

25 

4 

• 

8 

3 

12 

55 

26 

4 

4 

9 

9 

56 

968 

884 

92 

7,943.0 

1,589 

2,050 

198 

15,357.5 

Age  at  Ed 

try,  31  1 

fears. 

0 

Ni 

JMBEB  OF  ] 

Entrants 

,  1,674. 

$3,563,000  Insdtred. 

31 

75 

64 

4 

805 

116 

108 

18 

1,727.5 

1 

93 

313 

13 

1,374.5 

158 

628 

15 

3,007 

32 

2 

107 

125 

10 

1,049.5 

135 

368 

17 

2,336 

33 

3 

85 

98 

6 

821 

141 

306 

25 

1,847 

34 

4 

91 

75 

5 

643.5 

148 

232 

8 

1,412 

35 

5 

79 

39 

6 

490.5 

.  134 

225 

11 

1,027.5 

36 

6 

85 

18 

3 

377 

215 

46 

4 

747 

37 

7 

80 

18 

5 

271 

144 

27 

12 

.  491.5 

38 

8 

53 

6 

4 

174 

77 

13 

10 

315.5 

39 

9 

29 

5 

1 

111.5 

54 

9 

1 

217.5 

40 

140 


TAHLE    II. 


OBSERVATIONS  ON   FEMALE  LIFE. 


Age  at  Entry,  31  Years. 


^1 

n  ei 

is 


10 

11 

12 
13 
14 

15 
16 

17 
18 
19 

20 
21 
22 
23 
24 

25 
26 


NuHBEB  OF  Entrants,  1,674. 


Existing. 


15 

11 

3 

1 

4 

2 

2. 
2 


3 
1 

2 
5 

4 

833 


Discon- 
tinued. 


Died. 


778 


63 


Exposed  to 
Risli. 


77 

55.5 

39.5 

35 

33.5 

28 
25 
23 
20 
20 

20 

18 

16.5 

15.5 

13 

6 
2 


6,565.0 


$3,563,000  INSCBED. 


Amounts 
Existing. 


24 

19 

7 

1 

14 

5 
4 


11 
2 

5 
13 

4 

2 


1,441 


A.mount8 
Discontin'ed. 


12 

7 
3 


1,992 


Death 
Claims. 


130 


Exposed  to 
Risk. 


$ 

152 
117.5 

88.5 
80 

78 

61.5 

55 

51 

42 

42 

42 
31 

28.5 

27 

21 

6 

2 


14,053.5 


Age 

at 

Exit. 


¥i 
U 

^6 

50 

51 
52 
53 

H 
55 

56 

57 


Age  at  Entry,  32  Years. 


Number  of  Entrants,  1,763. 


0 

81 

60 

8 

1 

65 

383 

14 

2 

87 

139 

10 

3 

78 

83 

10 

4 

101 

62 

5 

5 

84 

34 

8 

6 

103 

35 

4 

7 

87 

27 

2 

8 

53 

6 

1 

9 

30 

7 

1 

10 

19 

11 

14 

3 

12 

1 

1 

1- 

13 

1 

14 

2 

3 

1 

15 

4 

1 

16 

2 

1 

17 

1 

18 

1 

19 

2 

1 

851.5 
1,422.5 

1,082.5 

'  874.5 

714 


560 
433. 

295. 
190 
129. 


95 

74.5 

58.5 

56 

53.5 

48.5 

44 

40.5 

40 

39 


$3,671,000  Insured. 


139 
122 

193 
120 
158 

162 
183 
174 
106 
60 

22 

27 
2 


4 
16 

1 
5 


100 
755 
392 
256 
150 

145 

85 
50 
18 
15 

3 

2 

5 
1 


17 
23 
21 

19 

7 

22 
6 
6 
1 
5 


1,785.5 
3,037.5 
-2,319 
1,781 
1,439 

1,126.5 
827.5 
571 
357 
233.5 

161 
137.5 
108 
104 
98.5 


85 
65 
64 
63 


32 
33 
3Jf 
35 
36 

37 
38 
39 
Jfi 

Jf2 

U 
Jfi 

Jf7 
Jt8 

50 
51 


TABLE    II. 


141 


OBSERVATIONS  ON  FEMALE  LIFE. 


Age  at  Entry,  32  Years. 

!i 

NUMBEB  OF 

Entrants,  1,763. 

$3,671,000  Insubbd. 

Age 

at 

Exit. 

Discon- 

Exposed to 
Risk. 

Amounts 

Amounts 

Deatli 

Exposed  to 
Bisk. 

^'A 

Existing. 

tinued. 

Died. 

Existing. 

Discontin'ed 

Claims. 

$ 

$ 

$ 

$ 

20 

2 

1 

35.5 

3 

1 

56.5 

S2 

21 

2 

33 

3 

53 

53 

22 

7 

31 

8 

50 

5J, 

23 

6 

24 

11 

42 

55 

24 

8 

18 

15 

31 

56 

25 

6 

10 

10 

16 

57 

26 

4 

4 

6 

6 

58 

849 

846 

68 

7,258.5 

1,554 

1,980 

137 

14,707.5 

Age  at  Entry,  33  Years. 

0 

N 

UMBBR  OF 

Entrant 

5,  1,785. 

13,471,000  Insured. 

33 

101 

56 

9 

864.5 

180 

88 

24 

1,691.5 

1 

69 

324 

14 

1,457      ; 

112 

626 

26 

2,866 

SU 

2 

100 

129 

11 

1,147.5 

163 

310 

23 

2,260 

35 

3 

87 

100 

10 

922 

158 

268 

12 

1,785 

36 

4 

107 

65 

5 

742.5 

186 

179 

15 

1,391.5 

37 

5 

103 

41 

6 

577.5 

153 

145 

7 

1,028.5 

38 

6 

92 

24 

4 

436 

159 

62 

5 

765 

39 

7 

94 

22 

3 

317      f 

162 

50 

3 

545 

Jfi 

8 

71 

7 

205.5 

97 

10 

350 

U 

9 

28 

4 

2 

129 

53 

7 

1 

244.5 

J^ 

10 

15 

3 

1 

95.5 

30 

17 

1 

178.5 

^ 

11 

8 

3 

76.5 

16 

12 

133 

U 

12 

3 

4 

2 

65 

5 

11 

2 

105.5 

Ji5 

13 

1 

58 

1 

93 

U6 

14 

2 

3 

2 

55.5 

5 

3 

3 

90.5 

A7 

15 

6 

1 

49.5 

8 

2 

80 

1^8 

16 

5 

43 

10 

71 

Jfi 

17 

3 

1 

38 

6 

1 

61 

50 

18 

2 

2 

1 

33 

7 

2 

1- 

53 

51 

19 

3 

29 

3 

44 

52 

20 

26 

41 

53 

i   21 

1 

1 

25.5 

1 

1 

40.5 

H 

22 

1 

1 

23.5 

1 

3 

37.5 

55 

23 

4 

22 

6 

35 

56 

24 

7 

2 

18 

9 

2 

29 

57 

25 

6 

1 

9 

14 

1 

18 

58 

26 

2 

2 

3 

3 

59 

921 

790 

74 

7,467.5 

1,548 

1,796 

127 

14,040.5 
...  i.. 

142 


TABLE     II. 

OBSERViVTJOXS  ON  FEMALE   LIFE. 


Age  at  Entry,  34  Years. 

•si 

Number  of 

Ektrants,  1,688. 

$3,343,000  Insured. 

Age 

ii 

at 
Exit. 

Discon- 

Exposed to 
llisk. 

Amounts 

Amounts  ' 

Death 

Exposed  to 

>'A 

Existing. 

tinued. 

Died. 

Existing. 

Discontin'ed. 

Claims. 

Risk. 

$ 

i 

$ 

$ 

0 

102 

79 

7 

804.5 

181 

144 

22 

1,600.5 

3i 

1 

61 

308 

18 

1,346 

100 

605 

46 

2,695.5 

35 

2 

109 

124 

11 

1,051 

201 

313 

27 

2,090.5 

36 

3 

84 

96 

3 

821 

130 

282 

9 

1,565 

37 

4 

85 

62 

7 

655 

130 

179 

17 

1,195.5 

38 

5 

73 

48 

4 

508 

86 

102 

10 

908 

39 

6 

91 

24 

3 

395 

175 

98 

5 

712 

Jfi 

7 

76 

20 

3 

279 

94 

71 

10 

447.5 

U 

8 

62 

11 

1 

184.5 

84 

38 

2 

289 

J^ 

9 

32 

3 

4 

114.5 

44 

5 

10 

181.5 

43 

10 

14 

4 

75 

19 

4 

123 

u 

11 

6 

1 

1 

58.5 

9 

1 

1 

101.5 

43 

12 

4 

2 

50 

4 

4 

89 

46 

13 

3 

45 

3 

83 

47 

14 

1 

42 

2 

80 

48 

15 

3 

'       1 

40.5 

8 

4 

76 

49 

16 

1 

37 

1 

66 

50 

17 

36 

65 

51 

18 

36 

65 

52 

19 

2 

1 

36 

6 

1 

65 

53 

20 

3 

33 

4 

58 

54 

21 

3 

30 

4 

54 

55 

22 

2 

27 

6 

50 

56 

23 

9    ^ 

25 

14 

44 

57 

24 

7 

16 

15 

30 

58 

25 

5 

9 

6 

15 

59 

26 

2 

4 

2 

9 

60 

27 

2 

2 

7 

7 

61 

842 

783 

63 

6,760.5 

1,335 

1,850 

160 

12,765.5 

Age  at  Ee 

itry,  35  1 

fears. 

0 

N 

[JMBBB  OF  ] 

Entrants 

,  1,705. 

$3,622,000  Insured. 

35 

82 

77 

7 

814 

158 

123 

19 

1,749.5 

1 

69 

270 

16 

1,404 

124 

569 

45 

3,037.5 

36 

2 

94 

121 

11 

1,123.5 

188 

375 

20 

2,396.5 

37 

3 

102 

94 

9 

911 

156 

275 

13 

1,863.5 

38 

4 

100 

67 

4 

719.5 

125 

163 

4 

1,475.5 

39 

5 

91 

36 

3 

564 

142 

132 

5 

1,199 

40 

6 

117 

28 

7 

438 

188 

115 

14 

928.5 

41 

7 

94 

17 

3 

291.5 

182 

69 

10 

634.5 

4^ 

8 

53 

6 

1 

183 

108 

58 

1 

379 

43 

9 

34 

10 

1 

121 

41 

38 

2 

222 

44 

10 

18 

3 

1 

79.5 

35 

4 

1 

158 

45 

11 

•  7 

' 

1 

59 

12 

1 

120 

46 

12 

2 

51 

2 

107 

47 

13 

4 

1 

2 

48.5 

20 

3 

5 

103.5 

48 

14 

3 

1 

41.5 

2 

2 

76 

^j 

.    T^ABLE    II. 

OBSERVATIONS  ON  FEMALE  LIFE. 


143 


Age  at  Entry,  35  Years. 

Number  of 

ENTBiNTS,  1,705. 

$3,622,000  Insured. 

Age 

II 

at 

Existing. 

Discon- 
tinued. 

Died. 

Exposed  to 
Rislc. 

Amounts 
Existing. 

Amount? 
Discontin'ed. 

Deatli 
Claims. 

Exposed  to 
Risk. 

Exit. 

$ 

$ 

$ 

$ 

15 

2 

1 

38 

5 

1 

73 

50 

16 

1 

35 

5 

67 

51 

17 

1 

2 

1 

33 

1 

5 

2 

59.5 

52 

18. 

1 

1 

29.5 

5 

1 

53.5 

53 

19 

3 

1 

1 

27.5 

4 

2 

3 

47 

H 

20 

24 

3 

39 

55 

i   21 

23 

36 

56 

22 

2 

23 

4 

36 

57 

23 

8 

21 

9 

32 

58 

24 

6 

13 

7 

23 

59- 

25 

4 

7 

10 

16 

60 

26 

2 

3 

3 

6 

61 

27 

1. 

1 

3 

3 

62 

899 

735 

71 

7,137.0 

1,534 

1,934 

154 

14,941.0 

Age  at  En 

Ltry,  36  ^ 

fears. 

0 

N 

UMBER  OP 

Entrant! 

i,  1,551. 

$.3,002,000  Insured. 

36 

63 

63 

3 

744 

93 

127 

9 

1,437.5 

1 

70 

281 

13 

1,281.5 

133 

505 

29 

2,520.5 

37 

2 

80 

110 

8 

1,003 

121 

262 

31 

1,975 

38 

3 

88 

78 

7 

821 

186 

217 

11 

1,583.5 

39 

4 

111 

47 

8 

663.5 

181 

115 

8 

1,220.5 

AO 

5 

88 

38 

3 

502 

123 

86 

3 

931 

Jfl 

6 

78 

25 

5 

379.5 

110 

47 

8 

738.5 

J^ 

7 

77 

22 

1 

273 

166 

50 

2 

572 

AS 

8 

66 

8 

1 

180 

169 

19 

5 

369.5 

AA 

9 

26 

7 

1 

105.5 

44 

13 

1 

179.5 

A5 

10 

17 

3 

1 

73.5 

24 

5 

1 

125.5 

A6 

11 

6 

4 

52 

19 

9 

93.5 

A7 

12 

4 

44 

8 

70 

A8 

13 

2 

1 

39.5 

2 

1 

61.5 

AO 

14 

3 

1 

36.5 

7 

1 

58.5 

50 

15 

33 

51 

51 

16 

33 

51 

52 

17 

2 

33 

3 

51 

53 

18 

1 

31 

1 

48 

5A 

19 

1 

30 

1 

47 

55 

20 

1 

29 

1 

46 

56 

21 

6 

1 

28 

10 

1 

45 

57 

22 

5 

21 

5 

34 

58 

23 

5 

16 

9 

29 

59 

24 

4 

11 

9 

20 

60 

25 

6 

7 

10 

11 

61 

26 

1 

1 

1 

! 

1  • 

62 

810 

688 

53 

6,471.5  ! 

1,435 

1,457 

110    1 

12,370.5  1 

144 


TABLE    II. 


OBSERVATIONS  ON  FEMALE  LIFE. 


Age  at  Entry,  37  Years. 

•si 

1 

1                Number  op 

Entbants,  1,548. 

$3,045,000  Insured. 

Age 

at 
Exit. 

j  Existing. 

Discon- 
tinued. 

Died. 

Exposed  to 
Risk. 

Amounts 
Existing. 

1    Amounts 
Discontin'ed 

Deatli 
.     Claims. 

Exposed  to 
Rislc. 

$ 

1           $ 

$ 

$ 

0 

73 

64 

8 

742 

147 

'          86 

16 

1,479.5 

37 

1 

81 

270 

15 

1,268 

146 

500 

35 

2,546 

38 

2 

91 

103 

7 

985.5 

143 

223 

15 

2,003.5 

39 

3 

84 

92 

6 

790 

143 

280 

12 

1,594 

40 

4 

100 

51 

3 

628.5 

167 

123 

6 

1,237.5 

41 

5 

79 

32 

7 

484 

156 

94 

14 

956 

Jt2 

6 

91 

18 

1 

373 

134 

41 

2 

718.5 

4S 

7 

94 

12 

2 

266 

164 

39 

5 

542.5 

U 

8 

47 

7 

1 

160.5 

140 

24 

1 

342 

45 

9 

29 

1 

4 

108.5 

41 

10 

6 

184 

46 

10 

12 

3 

73.5 

19 

4 

130 

47 

11 

7 

2 

59 

8 

1 

108.5 

48 

12 

2 

1 

1 

50.5 

5 

1 

5 

99.5 

49 

13 

2 

1 

46.5 

4 

1 

88.5 

60 

14 

2 

44 

3 

84 

51 

15 

1 

2 

41 

1 

6 

78 

52 

16 

2 

1 

2 

38.5 

8 

1 

.    7 

73.5 

53 

17 

3 

1 

33.5 

4 

5 

55.5 

54 

18 

1 

30 

1 

49 

55 

19 

.   3 

27.5 

3 

46.5 

56 

20 

1 

26 

4 

45 

57 

21 

25 

41 

58 

22 

5 

25 

6 

41 

59 

23 

5 

20  ■ 

7 

35 

60 

24 

7 

1 

15 

12 

2 

28 

61 

25 

4 

7 

7 

14 

62 

26 

3 

3 

7 

.     7 

63 

826 

664 

58 

6,371.0 

1,477 

1,442 

126 

12,627.5 

Age  at  Eu 

try,  38  ^ 

["ears. 

0 

Ni 

TMBER  OF  I 

jNTBANTS 

1,508. 

$3,086,000  Insttbed. 

38 

69 

66 

5 

721 

148 

110 

13 

1,488 

1 

65 

240 

14 

1,248 

150 

464 

26 

2,583 

39 

2 

82 

119 

15 

989.5 

181 

316 

27 

2,017 

40 

3 

77 

76 

10 

795 

134 

237 

23 

1,532.5 

41 

4 

88 

67 

5 

636.5 

153 

155 

7 

1,179.5 

^ 

5 

107 

32 

6 

494 

159 

89 

14 

897.5 

43 

6 

97 

8 

5 

361 

159 

24 

7 

668 

4-^ 

7 

65 

17 

5 

246.5 

123 

45 

11 

467.5 

45 

8 

45 

6 

165 

82 

13 

304.5 

46    ■ 

9 

t._... 

43 

4 

115 

68 

8 

212 

47 

TABLE    II. 


145 


OBSEKVATIONS  ON   FEMALE   LIFE. 


" 

Age  at  Entry,  38  Years. 

NUHBEB  OF 

Entbants 

,  1,5()8. 

$3,086,000  Insured. 

Age 

II 

at 
Exit. 

Existing. 

Discon- 
tinued. 

Died. 

Exposed  to 
Rislt. 

Amounts 
Existing. 

Amounts 
Discontin'ed. 

Deatli 
Claims. 

Exposed  to 
Rislc. 

$ 

$ 

$ 

10 

10 

2 

1 

'69 

23 

12 

1 

134 

48 

11 

8 

2 

56 

16 

2 

103 

49 

12 

1 

47 

1 

86 

50 

13 

2 

46 

6 

85 

51 

14 

5 

1 

44 

14 

1 

79 

52 

15 

38 

64 

53 

16 

3 

1 

37.5 

5 

3 

62.5 

54 

17 

1 

34 

1 

56 

55 

18 

1 

5 

32.5 

1 

4 

54.5 

56 

19 

1 

27 

1 

50 

57 

20 

3 

5 

26 

4 

10 

49 

58 

21 

1 

1 

1 

17.5 

5 

5 

1 

32.5 

59 

22 

5 

15 

9 

24 

60 

23 

10 

15 

61 

24 

3 

10 

4 

15 

'62 

25 

5 

7 

7 

11 

*6S 

26 

2 

2 

4 

4 

64 

1 

787 

642 

79 

6,290.0 

1,456 

1,484 

146 

12,274.0 

Age  at  Entry,  39  Years. 

0 

Ni 

CTMBBR  OP  ] 

Entrants 

,  1,330. 

$2,782,000  Insured. 

39 

81 

45 

G 

642.5 

148 

80 

14 

1,351 

1 

51 

209 

10 

1,093.5 

102 

414 

14 

2,333 

40 

2 

101 

105 

4 

875.5 

209 

290 

5 

1,865 

41 

3 

72 

89 

8 

673.5 

130 

237 

12 

1,387.5 

42 

4 

65 

53 

10 

522.5 

73 

185 

25 

1,034.5 

4S 

5 

77 

29 

7 

406.5 

133 

78 

30 

805 

U 

6 

76 

20 

1 

298 

120 

48 

1 

579 

45 

7 

60 

10 

4 

206 

116 

29 

7 

419.5 

46 

8 

41 

5 

134.5 

99 

16 

274 

47 

9 

21 

3 

89.5 

37 

3 

165.5 

48 

10 

1<> 

67 

34 

127 

49 

11 

8 

1 

51 

10 

1 

93 

50 

12 

3 

2 

1 

41 

6 

6 

2 

79 

51 

13 

36 

68 

52 

14 

1 

1 

36 

1 

1 

68 

53 

15 

34 

66 

54 

16 

3 

34 

15 

66  , 

55 

17 

2 

30 

4 

49 

56 

18 

2 

3 

29 

2 

3 

47 

57 

19 

1 

2 

23 

5 

7 

38.5 

58 

146 


TABLE     II. 


OBSERVATIONS  ON  FEMALE  LIFE. 


Age  at  Entry,  39  Years. 

H 

Number  op 

Entrants,  1,330. 

$2,782,000  Insured. 

Age 

is 

at 

s£S 

. 

Discon- 

Died. 

Exposed  to 

Amounts 

Amounts 

Death 

Exposed  to 
lUsk. 

Exit. 

>'A 

Existing. 

tinued. 

Risk. 

Existing. 

Discontinued 

Claims. 

J 

$ 

$ 

$ 

20 

1 

21 

1 

30 

59 

21 

2 

1 

20 

3 

1 

29 

60 

22 

17 

25 

61 

23 

3 

2 

17 

!           4 

2 

25 

62 

24 

5 

12 

6 

19 

63 

25 

4 

7 

5 

13 

H 

26 

1 

3 

4 

8 

65 

27 

2 

2 

4 

4 

66 

697 

574 

59 

5,422.0 

1,267 

1,397 

118 

11,068.5 

Age  at  Entry,  40  ^ 

fears. 

tf 

N 

UMBER  OP 

Entrant 

i,  1,444. 

$2,888,000  Insured. 

Jfi 

73 

G3 

5 

690.5 

129 

108 

8 

1,390 

1 

67 

242 

17' 

1,182 

119 

527 

33 

2,379.5 

Al 

2 

94 

110 

5 

922 

174 

243 

19 

1,842.5 

J^ 

3 

62 

77 

10 

729.5 

88 

204 

20 

1,426 

43 

4 

•83 

65 

9 

586.5 

164 

184 

21 

1,124 

U 

5 

84 

22 

7 

451 

133 

64 

17 

815 

4S 

6 

87 

18 

5 

340 

160 

34 

10 

616 

46 

'7 

81 

16 

3 

231 

147 

33 

4 

412.5 

47 

8 

45 

4 

137 

87 

9 

240.5 

48 

9 

25 

2 

1 

89 

37 

6 

1 

146 

49 

10 

IG 

2 

01 

20 

3 

103.5 

50 

11 

7  ■ 

2 

43 

14 

3 

80.5 

51 

12 

1 

2 

34 

1 

7 

61.5 

52f 

13 

2 

1 

31.5 

3 

5 

54.5 

63 

14 

2 

1 

28.5 

10 

3 

47.5 

54 

15 

1 

26 

2 

36 

55 

16 

25 

34 

56 

17 

1 

1 

1 

24.5 

1 

2 

2 

33 

57 

18 

22 

29 

68 

19 

1 

22 

2 

^9 

59 

20 

21 

27 

60 

21 

2 

21 

1 

27 

61 

22 

1 

1 

1 

18.5 

1 

1 

1 

25.5 

62. 

23 

4 

16 

7 

23 

63 

24 

7 

1 

11.5 

9 

2 

15 

64 

25 

4 

4 

5 

5 

65 

747 

630 

67 

5,768.0 

1,311 

1,438 

139 

11,023.0 

TABLE    II. 


147 


OBSERVATIONS  ON  FEMALE  LIFE. 


Age  at  Entry,  41  Years. 

•Si 

Number  of 

Ektbants,  1,077. 

$2,277,000  Instjbed. 

Age 

ii 

at 

Discon- 

Exposed  to 
Bisk. 

Amounts 

Amount^ 

Death 

Exposed  to 
Risk. 

Exit. 

>"& 

Existing. 

tinaed. 

Died. 

Existing. 

Discontin'ed. 

Claims. 

$ 

$ 

$ 

$ 

0 

50 

35 

3 

521 

84 

67 

8 

1,105 

41 

1 

43 

182 

10 

898 

97 

374 

16 

1,931 

42 

2 

58 

.74 

10 

717 

122 

192 

20 

1,535 

43 

3 

53 

62 

5 

581 

107 

168 

14^ 

1,213 

U 

4 

74 

43 

4 

470.5 

139 

117 

8 

949.5 

45 

5 

68 

26 

5 

358 

111 

61 

12 

713.5 

46 

6 

63 

12 

4 

266 

116 

37 

9 

541.5 

47 

7 

64 

19 

2 

183.5 

,138 

60 

3 

368 

48 

8 

46 

3 

1 

106.5 

78 

12 

1 

191 

49 

9 

15 

2 

57 

21 

5 

103.5 

50 

10 

,    8 

6 

38 

11 

25 

67 

51 

11 

2 

27 

4 

44 

52 

12 

2 

1 

25 

2 

1 

40 

58 

13 

1 

22 

1 

37 

54. 

14 

3 

21 

8 

36 

55 

15 

18 

28 

56 

16 

1 

•18 

5 

28 

57 

17 

2 

1 

17 

3 

2 

23 

58 

18 

1 

1 

14 

1 

1 

18 

59 

19 

12 

16 

60 

20 

1 

12 

1 

16 

61 

21 

11 

15 

62 

22 

1 

11 

1 

15 

63 

23 

1 

1 

1 

9.5 

1 

1 

1 

13.5 

64 

24 

4 

7 

5 

11 

65 

25 

1 

3 

3 

6 

66 

26 

2 

2 

3 

3 

67 

564 

465 

48 

4,426.0 

1,062 

1,119 

96 

9,067.5 

Age  at  Entry,  42  Years. 

0 

Ni 

[TMBBE  OP  ] 

Entkakts 

,  1,101. 

$3,242,000  Insubed. 

42 

64 

42 

4 

529.5 

124 

71 

9 

1,085.5 

1 

39 

176 

10 

903 

56 

348 

27 

1,864 

43 

2 

65 

74 

10 

729 

119 

174 

.      23 

1,520 

^-^ 

3 

69 

55 

8 

589.5 

92 

162 

29 

1,210 

45 

4 

64 

35 

4 

467.5 

137 

81 

9 

967.5 

46 

5 

69 

22 

7 

371 

134 

67 

14 

747.5 

47 

6 

65 

25 

5 

271.5 

!         131 

58 

7 

537 

48 

7 

54 

11 

2 

183.5 

t        100 

23 

2 

358.5 

49 

8 

43 

5 

119.5    !:         86 

10 

240 

50 

9 

17 

2 

1 

73        1          42 

3 

1 

147.5 

51 

148 


TABLE     II. 


OBSERVATIONS   ON  FEMALE  LIFE. 


Age  at  Entry,  42  Years. 

it 

Number  op 

Entrants,  1,101. 

$2,342,000  Insured. 

Age 

gg 

, 

at 

k 

£S 

. 

Discon- 

Exposed to 
Risk. 

Amounts 

Amounts 

Death 

Exposed  to 
Risk. 

Exit. 

>"& 

Existing. 

tinued. 

Died. 

Existing. 

Discontin'ed. 

Claims. 

$ 

$ 

$ 

$ 

10 

11 

2 

53 

17 

4 

101 

52 

11 

9 

41 

26 

82 

53 

12 

2 

1 

32 

4 

1 

56 

5A 

13 

1 

29 

1 

51 

55 

14 

1 

1 

27.5 

2 

2 

49 

56 

15 

2 

26 

^      7 

46 

57 

16 

1 

2 

23 

2 

{> 

36 

58 

17 

2 

21 

2 

31 

59 

18 

19 

29 

60 

19 

1 

19 

2 

29 

61 

20 

18 

27 

62 

21 

1 

1 

18 

1 

2 

27 

63 

22 

16 

24 

eu 

23 

1 

16 

1 

24 

65 

24 

6 

15 

8 

23 

66 

25 

4 

.      9 

9 

15 

67 

26 

5 

5 

6 

6 

68 

596 

452 

53 

4,624.5 

1,109 

1,009 

124 

9,333.5 

Age  at  Entry,  43  1 

fears. 

0 

J 

Dumber  of 

Entbani 

s,  981. 

$2,065,000  Insured. 

43 

56 

37 

5 

472 

79 

49 

13 

1,008 

1 

38 

144 

8 

811 

92 

338 

17 

1,755 

U 

2 

65 

60 

7 

663 

114 

179 

19 

1,387.5 

45 

3 

52 

49 

6 

536.5 

82 

149 

12 

1,090.5 

46 

4 

69 

31 

5 

438.5 

140 

68 

14 

888 

47 

5 

62 

21 

3 

338.5 

153 

52 

2 

674 

48 

6 

64 

12 

3 

257 

106 

17 

19 

484.5 

49 

7 

66 

16 

3 

176 

123 

32 

4 

335 

50 

8 

40 

3 

97.5 

77 

4 

190 

51 

9 

12 

3 

54.5 

15 

9 

106.5 

52 

10 

12 

3 

3 

39.5 

25 

3 

9 

85.5 

53 

11 

2 

2 

1 

22 

4 

4 

1 

48 

54 

12 

2 

18 

6 

' 

41 

55 

13 

16 

35 

56 

14 

1 

1 

15.5 

5 

3 

33.5 

57- 

15 

14 

27 

58 

16 

1 

14 

1 

27 

69 

17 

1 

13 

3 

26      . 

60 

18 

12 

23 

61 

19 

1 

12 

2 

23 

62 

TABLE     II. 


149 


OBSERVATIONS  ON   FEMALE  LIFE 


Age  at  Entry,  43  Years. 

-4 

Number  op 

Entrants,  981. 

$2,065,000  Insured. 

Age 

ii 

at 

Discon- 

Exposed to 
Risk. 

Amounts 

Amounts 

Death 

Exposed  to 

Exit. 

>"& 

Existing. 

tinued. 

Died. 

Existing. 

Discontin'ed. 

Claims. 

Risk. 

$ 

$ 

$ 

20 

2 

11 

2 

21 

63 

21 

1 

1 

9 

,    1 

1 

19 

64 

22 

1 

7 

5 

17 

65 

23 

1 

6 

1 

12 

66 

24 

1 

5 

5 

11 

67 

25 

3 

4 

5 

6 

68 

26 

1 

1 

1 

1 

69 

552 

382 

47 

4,063.5 

1,041 

907 

117 

8,375.0 

Age  at  Entry,  44  Years. 

0 

J 

{UUBER  OF 

Entbani 

8,  926. 

$1,871,000  Insured. 

U 

67 

22 

5 

452 

125 

37 

14 

917 

1 

28 

136 

10 

764 

48 

296 

15 

1,547 

J-5 

2 

55 

54 

5 

631 

101 

125 

5 

1,273.5 

l6 

3 

45 

.47 

5 

520.5 

62 

139 

8 

1,035.5 

47 

4 

67 

32 

6 

431       1 

103 

78 

19 

857 

48 

5 

66 

13 

3 

335.5 

140 

50 

9 

671 

Jf9 

6 

63 

19 

5 

250.5    1 

155 

48 

13 

473 

50 

7 

49 

6 

2 

170 

73 

14 

2 

274 

51 

8 

42 

5 

2 

113.5 

64 

11 

3 

186.5 

52 

9 

23 

1 

2 

66.5 

43 

2 

3 

113 

53 

10 

9 

3 

1 

39.5 

18 

3 

2 

64.5' 

54 

11 

8 

1 

2 

27.5 

13 

1 

5 

42.5 

55 

12 

1 

1 

17 

1 

2 

24 

56 

13 

15 

21 

57 

14 

15 

21 

58 

15 

1 

15 

1 

21 

59 

16 

2 

14 

2 

20 

60 

17 

1 

12 

5 

18 

61 

18 

1 

10.5 

1 

12.5 

62 

19 

10 

12 

63 

20 

1 

1 

10 

1 

3 

12 

H  . 

21 

8 

8 

65    ' 

22 

1 

7.5 

1 

7.5 

66 

23 

1 

7 

1 

7 

67 

24 

3 

6 

3 

6 

68 

25 

1 

3 

1 

3 

69 

26 

1 

2        1 

1 

2 

70 

27 

1 

1        \ 

1 

1 

71 

532 

341 

53 

3,954.5 

959 

806 

106 

7,650.5 

150 


TABLE     II. 

OBSERVATIONS  ON  FEMALE  LIFE. 


Age 

at  Entry,  45  Years. 

Age 

at  Entry,  ' 

46  Years. 

<M  ^ 

No. 

OF  Ektrants,  931.  '  1      $1,804,000  Insttbed. 

*^ 

■"2 

No. 

OP  Entrants,  784. 

$1,608,000  Insubed. 

-t 

1 

be 

< 

®rl 

1 

1 
"3 

S  ® 

5*"  i  5 

ii 

^3 

c 
1  « 

U 

no 

il 

U 

5 

c 

T" 

$ 

si 

1   al 

i      WS 

$ 

i 

$ 

$ 

0 

44 

3l!6 

445 

93 

48 

8 

878 

45 

15 

10 

13 

61 

1 

41 

148;  4 

766 

62 

294 

3 

1,508 

46 

16 

10 

13 

62 

2 

58 

56 

4 

619 

153 

178 

'    4 

1,207 

47 

17 

10 

13 

63 

3 

45 

50 

5 

504 

70 

114 

ho 

904 

4B 

18 

1 

10 

3 

13 

64 

4 

67 

25 

5 

416.5 

105 

54 

19 

740 

49 

19 

1 

8.5 

1 

9.5 

65 

5 

65 

26 

5 

319 

120 

50 

'16 

564 

50 

20 

1 

8 

2 

9 

66 

6 

47 

8 

3 

232 

66 

16 

7 

395 

51 

21 

1 

7 

2 

7 

67 

7 

61 

8 

2 

174 

76 

14 

10 

307 

62 

22 

6 

0 

68 

8 

38 

5 

3 

104.5 

71 

10 

7 

209 

68 

23 

2 

1 

6 

1 

1 

'5 

69 

9 

19 

1 

3 

60.5 

35 

3 

5 

124.5 

54 

24 

2 

3 

2 

3 

70 

10 

11 
12 
13 
14 

15 
16 
17 
18 
19 

12 
2 

1 

4 

2 
2 

2 
1 

1 
1 

37 
23 
20 
17 
16 

15.5 

10 

10 

10 

10 

26 
2 
1 

6 

1 
11 

4 

1 

1 
10 

82.5 

50.5 

43 

39 

37 

36.5 

20 

20 

20 

20 

56 
66 
57 
58 
69 

60 
61 
62 
63 
64 

25 

1 
429 

1 

1 

1 

71 

321 

34 

3,155.5 

792 

75858 

'6,267.0 

Age 

at  Entry,  47  Years. 

0 

No. 

dpEktra 

jn-s,  653. 

$1,299,000  INSUEED. 

Jf7 

32 

21 

2 

316 

63 

32    9 

633.5 

li36 
2   43 

82 
52 

6 

2 

557 
448 

!61 

|81 

163 
102 

8 
3 

1,113.5 
912 

20 

1 

10 

2 

20 

65 

3   36 

34 

2 

360 

54 

92 

2 

731 

60 

21 

3 

9 

6 

18 

66 

4 

44 

28 

4 

291 

92 

89 

6 

584.5 

51 

22 
23 
24 

1 
3 

6 
6 
5 

2 
4 

12 
12 
10 

67 
68 
69 

5 

35 

12 

4 

223 

49 

45 

8 

419.5 

52 

6 

45 

4  .3 

176 

74 

11 

7 

334.5 

53 

7 

38 

2 

2 

125 

70 

7 

2 

244.5 

54 

25 

2 

2 

6 

6 

70 

8 
9 

10 

29 
21 

7 

4 
3 

1 

1 
•2 

82 
48.5 

23.5 

57 
45 

17 

10 
5 

6 

1 
2 

164 

98.5 

46 

55 
56 

57 

514 

365:42 

3,847.0 

906 

798 

100 

7,283.0 

Age 

at  Entry,  46  Years. 

11 
12 
13 
14 

5 
1 

1 

15.5 
'  10 
10 
10 

11 
1 

2 

25 
13 
13 
13 

58 
59 
60 
61 

No. 

OP  ENTEi 

LNTS,  784. 

$1,608,000  INSUBED. 

0 

53 

29 

4 

377.5 

93 

46  11 

781 

J^6 

15 

9 

12 

62 

1 

30 

1^8 

6 

634 

77 

273 

13 

1,321.5 

Jf7 

16 

9 

12 

63 

2 

48 

47 

3 

510.5  i    73  123 

6  1.033.5 

48 

17 

9 

12 

64 

3 

45 

40 

8 

416     1,  75107 

12  1    839.5 

49 

18 

9 

12 

65 

4 

50 

25 

2 

330.5 

100 

59 

3 

669.5 

50 

19 

1 

9 

1 

12 

66 

5 

45 

23 

2 

254.5  : 

93    55 

2 

509.5 

51 

20 

1 

8 

2 

11 

67 

6 

35 

9 

3 

191.5      721 

32 

1 

371 

52 

21 

7 

9 

68 

7 

46 

6 

1 

146 

79 

14 

1 

275 

53 

22 

1 

1 

7 

1 

1 

9 

69 

8 

43 

6 

93 

70 

30 

173 

54 

23 

3 

5 

3 

7 

70 

9 

15 

5 

44.5 

31 

7 

84.5 

55 

24 

1 

2 

2 

4 

71 

10 
11 
12 
13 

6 
4 
2 

2 

2 
1 

26 

9    11 

44.5 

56 

25 

1 

1 

2 

2 

72 

19 
13 
10 

8 
3 

5 

1 

30 
17 
13 

57 
58 
59 

380 

244 

29 

2,770.5 

686 

564 

i9 

5,447.5 

.14 

10 

13 

60 

TABLE     II. 


151 


OBSERVATIONS  ON  FEMALE  LIFE. 


Age  at  Entry,  48  Years. 


Age  at  Entry,  49  Years. 


0 
1 
2 
3 

4 

5 
6 
7 
8 
9 

10 
11 
12 
13 
14 

15 
16 
17 
18 
19 

20 
21 
22 
23 

24 

25 
26 


No.  OF  Entrants,  778. 


H 


30  !  30  3     374 


43     22  6     324 


51 
53 
36 
28 
14 

15 
1 

1 
1 
1 


1^ 
435 


103i4i  664.5 
50' 9    527 
53  7  I  406.5 


19  7 
1712 

5 

3 


304 


254.5 
178.5 
112.5 

71.5 

42 

28 
13 
11.5 

9.5 
8 

7 
7  . 

7 
7 

7 

6 
5 
4 
2 
1 

1 
1 


393,080.0! 


$1,622,000  Insuebd. 

a 

O  3 

si 

si 

11 

gig 

$  ■ 

$ 

1 

$ 

54 

59 

3 

781.5 

78 

213 

8 

1,399.5 

86 

131 

20 

1,141.5 

77 

136 

19 

902 

116 

75 

9 

700.5 

88 

44 

7 

516    1 

120 

62 

2 

368 

73 

20 

1 

205 

61 

8 

117 

17 

52 

11 

35 

2 

24 

2 

1 

21.5 

1 

3 

17.5 

1 

15 

14 
14 
14 
14 

5 

14 

1 

9 

2 

8 

4 

6 

1 

2 
1 

1 

1 

1 

799 

752 

71 

6,394.0 

Age  at  Entry,  49  Years. 


No. 

9F  Entrants,  555. 

$1,145,000  Insubkd. 

0 

37 

"l3 

3 

271 

125 

25 

7 

560 

1 

29 

74 

3 

465 

48 

133 

-9 

921.5 

2 

41 

29 

5 

381.5 

77 

72 

18 

762 

3 

37 

37 

6 

302.5 

51 

93 

14 

684.5 

4 

39 

15 

i 

233.5 

92 

55 

18 

445.5 

5 

40 

7 

4 

176.5 

60 

31 

11 

292.5 

6 

38 

9 

3 

124.5 

52 

15 

9 

198.5 

7 

27 

5 

3 

76.5 

40 

17 

6 

121.5 

8 

14 

2 

43 

24 

2 

66 

9 

6 

3 

26.5 

9 

5 

38.5 

10 

4 

2 

1 

18 

7 

3 

2 

25.5 

11 

4 

1 

11.5 

4 

1 

14.5 

12 

7 

10 

13 

7 

10 

14 

7 

10 

Jf8 
J,9 

50 
51 

52 

53 

H 
55 

56 

57 

58 
59 
60 
61 

62 

63 

H 
65 
66 

67 

68 
69 

70 
71 

72 

73 
U 


Jf9 
50 
51 

52 
53 

H 

55 
56 

57 
58 

59 
60 
61 
62 


to  d 


No. 

OP  Entrants,  555. 

$1,145,000  Insured. 

n-S 

■g^- 

« 

td 

% 
5 

^2 

$ 

u 

(5"" 

|j2 

$ 

$ 

$ 

7 

10 

7 

'  10 

7 

10 

1 

7 

1 

10 

1 

6 

1 

9 

1 

1 

4.5 

1 

3 

6.5 

1 

3 

2 

1 

4 
3 

2 

2 

3 

3 

321 

198 

36 

2,196.5 

595 

455 

95 

4,126.0 

Age  at  Entry,  50  Years. 


No. 

OF  Entrants,  588. 

$1,205,000  Insured. 

0 

36 

24  i  6 

282 

84 

50 

7 

577.5 

1 

26 

77   9 

483.5 

41 

196 

17 

966 

2 

41 

37   6 

391.5 

73 

93 

7 

763.5 

3 

31 

20   2 

316 

50 

64 

7 

605 

4 

51 

17  1  3 

264.5 

86 

45 

8 

493.5 

5 

39 

14   3 

195 

68 

42 

3 

356 

6 

39 

9 

3 

141.5 

62 

27 

5 

250.5 

7 

23 

6 

5 

92 

40 

10 

10 

165 

8 

25 

3 

1 

59.5 

39 

7 

2 

106.5 

9 

11 

1 

2 

31.5 

28 

1 

2 

61.5 

10 

4 

1 

17.5 

4 

1 

30.5 

11 

2 

1 

1 

12.5 

3 

2 

1 

25 

12 

2 

9 

3 

20 

13 

7 

17 

14 

7 

17 

15 

7 

17 

16 

7 

17 

17 

1 

7 

1 

17 

18 

1 

6 

1 

16 

19 

5 

15 

20 

1 

5 

5 

15 

21 

1 

3.5 

2 

9 

22 

1 

3 

5 

8 

23 

1 

^     i 

1 

3 

24 

1 

1 

2 

2 

334 

211 

43 

2,356.5 

590 

540 

75 

4,573.5 

be 


H 
65 
66 

67 
68 

69 
70 
71 

72 


50 
51 
52 
53 
5^ 

55 

56 
57 
58 
59 

60 
61 
62 
63 

65 
66 
67 
68 
69 

70 
71 

72 
73 

n 


152 


TABLE    II. 


OBSERVATIONS  ON  FEMALE  LIFE. 


Age 

at  Entry,  51  Years. 

Age  at  Entry, 

52  Years. 

Vl  "> 

No. 

OP  Entrants,  465. 

1       1905,000  Insured. 

1 

<«§■  No. 

OF  Entrants,  433. 

$902,000  Insured. 

•^ 

o2 

M 

°d 

w 

1       tl 

i        t» 

1       •< 

t-l 

tit 

c 

it 

•6 

5 

h2 

!    u 

a 

\    1 
i     $ 

1~ 

si 
Si 

14 

bo 

< 

'"I 

si 

kt 

Is 

1 

P 

ti 

c 

pa 
$ 

p 

$ 

p5 

T 

m2 

$ 

$ 

0 

30 

21 

1 

222 

37 

33 

1 

436 

51 

15 

1 

11 

1 

13 

57 

1 

27 

66 

3 

380 

38 

136 

9 

766 

52 

16 

2 

1 

10 

1 

1 

12 

68 

2 

34 

23 

7 

305.5 

52 

66 

11 

618 

53 

17 

1 

7 

2 

10 

69 

3 

25 

18 

2 

244 

43 

38 

5 

503 

5J, 

18 

6 

8 

70 

4 

42 

16 

1 

200 

68 

47 

1 

412.5 

55 

19 

1 

6 

1 

8 

71 

5 

33 

10 

4 

144 

65 

26 

12 

307 

56 

20 

5 

7 

72 

6 

26 

7 

1 

98.5 

60 

14 

1 

210 

57 

21 

1 

5 

1 

7 

73 

7 

19 

7 

3 

64.5 

35 

20 

4 

132 

58 

22 

2 

4 

3 

6 

u 

8 

15 

1 

39 

37 

1 

83 

59 

23 

1 

2 

1 

3 

75 

9 

10 

11 

6 

7' 

1 

22.5 

16 
8 

18 
10 

1 

44.5 

26 
13.5 

60 

61 

62 

24 

1 
273 

.    1 

2 

2 

76 

138 

22 

1,827.5 

531 

321 

50 

3,580.5 

2 

5 

12 
13 
14 

1 

7 
6 
6 

1 

11 
10 
10 

63 
6Jf 
65 

Age 

at  Entry,  53  Years. 

' 

1 

No. 

ar  Entrants,  3SJ0. 

$633,000  Insured. 

15 

6 

10 

66 

16 

6 

10 

67 

0 

15 

16 

2 

152 

14 

35 

2 

299 

53 

17 

6 

10 

68 

1 

26 

45 

3 

264.5 

61 

108 

18 

528 

H 

18 

1 

6 

1 

10 

69 

2 

17 

22 

2 

202 

41 

51 

6 

369.5 

55 

19 

5 

9 

70 

3 

21 

11 

2 

166.5 

27 

20 

3 

287 

56 

20 

5 

9 

71 

4 

21 

9 

1 

133.5 

34 

21 

1 

236.5 

57 

21 

1 

6 

2 

9 

72 

5 

15 

8 

3 

103 

24 

31 

6 

175.5 

58 

22 

4 

7 

73 

6 

25 

2 

2 

80 

33 

2 

2 

129 

59 

23 

1 

4 

1 

7 

7Jf 

7 

12 

2 

2 

51 

'28 

6 

2 

90 

60 

24 

1 

3 

3 

6 

75 

8 

16 

2 

35 

l23 

1 

56.5 

61 

25 

1 

2 

1 

3 

76 

9 

4 

1 

17.5 

14 

1 

32.5 

62 

26 

1 
268 

171 

1 

2 

470 

2 

77 

10 
11 
12 
13 
14 

15 

4 
1 
1 

1 

1 
1 

13 

8 
7 
6 
5 

5 

-  6 
2 
1 

1 

1 

1 

1 

18 

11 

9 

8 

7 

7 

63 

H 
65 
66 

67 

68 

261,816.0 

386 

49 

3,674.5 

Age 

at  Entry,  52  Yea 

rs. 

No. 

OF  Entb 

ANT8,  433. 

$902,000  iNi 

JURED. 

16 

4 

6 

69 

0  31 

6 

1 

213.5 

68 

8 

1 

447 

52 

17 

4 

*6 

70 

1   34 

53 

2 

368.5 

80 

101 

6 

774.5 

53 

18 

1 

3.5 

2 

5 

71 

2 

26 

22 

1 

295 

50 

60 

3 

608 

5J, 

19 

3 

4 

72 

3 

37 

16 

3 

249 

59    54 

6 

498 

55 

20 

3 

4 

73 

4 

34 

18 

7 

192 

641  53 

14 

379.5 

56 

21 

3 

4 

74 

5 

25 

8 

3 

138 

60  i  17 

8 

266.5 

57 

22 

1 

3 

1 

4 

75 

6 

26 

5 

2 

103.5 

41       9 

6 

185.5 

'58 

23 

1 

2 

1 

3 

76 

7 
8 

22 
11 

6 
3 

70 
43.5 

48       9 
13      9 

129.5 
72.5 

59 
60 

24 

1 

1 

2 

2 

77 

181 

119 

20 

1,275.5! 

312 

278 

43 

2,301.5 

9 
10 

13 
3 

1 

31 

17 

25 

3 

55 

61 

1 

7 

*J 

27 

62 

11 

2 

14 

6 

20 

63 

12 

12 

14 

6Jf 

13 

12 

14 

65 

14 

1 

11.5 

1 

13.5 

66 

' 

TABLE     II. 


153 


OBSERVATIONS  ON  FEMALE  LIFE. 


Age  at  Entry,  54  Years. 


Age  at  Entry,  55  Years. 


<mS 
On 


No.  OF  Entbants,  327. 


22 

24 

26 
14 
29 

19 
21 
16 
11 

7 

3 
4 


197 


18 
44 
15 
15 
5 

5 
5 
1 


111 


19 


B^ 


$675,000  Insubed. 


154.5 

263 

.207.5 

162.5 

136.5 

100.5 
76.5 
52.5 
34.5 
23 

16 
12 

7 
7 
6.5 

5 
5 
5 

5 
5 

4 

3.5 

3 

2 

2 


1,299.0 


fi     Po 

$ 

46 
38 
40 
22 

48 

$ 

31 
121 
42 
43 
12 

$ 

4 
11 

4 
2 
3 

43 
26 
32 
9 
12 

15 

15 

4 

1 

5 

8 
10 

5 
5 

1 

1 
5 

1 

5 

5 

335 

290 

50 

h2 


$ 
322 
533.5 
403 
316.5 
265 

200.5 
142.5 

107 
67.5 
58 

46 
33 

18 
18 
17.5 

16 
16 
16 
16 
16 

11 

8.5 
6 
5 
5 


2,663.5 


Age  at  Entry,  55  Years. 


55 
56 
57 
58 

59 
60 
6J 
62 
63 

6J, 
65 
66 
67 

68 

69 
70 
71 

72 
73 

74 

75 
76 
77 


No.  < 

>F  Entbants,  297. 

$638,000  Insubed.       ' 

j 

0 

14 

12 

2 

142.5 

38 

26 

3 

306 

1 

18 

46 

2 

246 

38 

81 

4 

530.5 

2 

17 

21 

4 

192.5 

22 

57  21 

419.5 

3 

20 

13 

3 

154.5 

46 

-2'Z  22 

337 

4 

14 

8 

3 

121 

30 

16     5 

250 

5 

12 

4 

2 

98 

26 

12  1  4 

201 

6 

26 

3 

80.5 

42 

10  10 

160 

7 

11 

1 

51.5 

25 

5 

2 

100.5 

8 

12 

1 

1 

38.5 

20 

1 

70.5 

9 

4 

2 

24 

5 

1 

48.5 

10 

4 

2 

17 

11 

8 

38 

11 

1 

10.5 

1 

21.5 

12 

1 

9 

1 

19 

13 

7 

17 

14 

6 

16 

55 

56 

57 
58 

50 

60 
61 
62 
63 
64 

65 
66 
67 
68 
69 


<o\  No.  OF  Entbants,  297. 


155114  28 


1,231.5 


$638,000  Insubed. 


i.s||l' 
(5""  (So 


307  240 


* 

16 
16 
16 
11 
11 

9 
1 


91  2,615.0 


Age  at  Entry,  56  Years. 


No. 

OF  Entbants,  226. 

$487,000  Insubed. 

0 

12 

6 

2 

110 

18 

16 

6 

235.5 

1 

11 

33 

4 

189.5 

20 

64 

10 

415 

2 

15 

16 

2 

150 

19 

35 

2 

335.5 

3 

10 

14 

1 

118 

19 

41 

1 

276.5 

4 

10 

7 

4 

96.5 

11 

14 

13 

229  ' 

5 

20 

4 

2 

77 

35 

9 

10 

193.5 

6 

13 

3 

51.5 

40 

12 

138 

7 

11 

2 

1 

36 

13 

6 

2 

89 

8 

9 

3 

23 

31 

6 

71 

9 

5 

2 

11 

18 

4 

34 

10 

4 

12 

11 

1 

4 

2 

12 

12 

3 

10 

13 

1 

1 

3 

2 

5 

10 

14 

1 

3 

15 

3 

16 

3 

17 

3 

18 

3 

19 

3 

20 

3 

21 

3 

22 

3 

23 

1 

3 

3 

119 

,85 

22 

886.5 

231 

197 

59 

2,091.0 

» 


bo 

< 


70 
71 

72 
78 
7A 

75 
76 


56 
57 
58 
59 
60 

61 
62 
63 
64 
65 

66 
67 
68 
69 
70 

71 

72 
73 
74 
75 

76 
77 
78 
79 


154 


TABLE     II. 

OBSERVATIONS  ON  FEMALE  LIFE. 


Age 

at  Entry,  57 

Years. 

Age 

1 
at  Entry,  58  Years. 

No.  OF  Entrants,  200. 

$455,000  Insured. 

w 
? 

bo 

^5 

No. 

OP  Entrants,  181. 

$402,000  Insured. 

ti 

a 

1 

§1 

■d 

W! 

4.T3 

11 

1^ 

1 

o  S 

-i 

1-^ 

feb 
s 

1^- 

■SE 

» 

«"" 

Q 

a2 

» 

5 

fio 

WS 

< 

(3 

o 

w2 

» 
$ 

P 
$ 

oo 

w2 

< 

1 

$ 

$ 

$ 

$ 

$ 

0 

11 

5 

3 

97.5 

23 

7 

12 

224 

57 

20 

4 

8 

78 

1 

17 

23 

5 

169.5 

27 

50 

14 

388 

58 

21 

2 

4 

0 

8 

79 

2 

5 

9 

3 

131.5 

13 

11 

5 

316.5 

59 

22 

1 

2 

2 

3 

80 

3 

4 

5 

12 
19 

9 
2 

1 
1 

114.5 
96 

23 

76 

19 

25 

7 

17 

2 

1 

17 

280.5 
239.5 

150.5 

60 
61 

62 

23 

1 

1 

1 

1 

81 

h 

65 

27 

841.0 

189 

147 

66 

1,793.5 

13 

5 

4 

72.5 

8 

14 

4 

1 

51 

22 

11 

5 

100.5 

6S 

7 

12 

1 

1 

33.5 

21 

5 

4 

65.5 

H 

Age 

at  Entry,  59   Years. 

8 

6 

20 

14 

38 

65 

1 

9 

10 
11 
12 
13 
14 

6 

1 
1 

2 

13 

6 
6 
5 
4 
4 

5 

1 

1 

8 

20 

11 
11 

10 
9 
9 

66 

67 
68 

69 
70 
71 

0 

1 

No. 

OF  Entrants,  134. 

$253,000  Insured. 

59 
60 

3 

6 

3 
14 

2 

65.5 
121 

4 
19 

7 
45 

2 

123 
219.5 

2 

11 

9 

1 

101.5 

8 

27 

1 

162.5 

61  \ 

3 

7 

3 

2 

83.5! 

20 

5 

3 

137.5 

62 

4 

8 

4 

3 

71 

7 

8 

4 

108 

63 

15 
16 
17 
18 
19 

1 

1 

4 

4 

2.5 

2 

2 

1 

5 

9 

9 

3.5 

3 

3 

72 
73 

U 
75 
76 

5 
6 

7 

12 

10 

9 

4 

2 
3 
3 

56 
40 

27 

10 
10 
24 

7 

2 
4 
2 

89.5 

74 
60 

65 
66 

8 
9 

1 
3 

2 

2 

14 
10 

2 
2 

11 

1 

28.5 
20 

67  ! 
68 

20 

21 

1 

1 

2 
2 

2 

;247 

142 

1 
66 

3 
3 

1,906.5 

77 
78 

10 
11 
12 
13 

1 
1 

1 

7 
6 
5 
4 

5 
1 
2 

18 
13 
12 
10 

69 
70 
71 

72 

118 

61 

21 

842.5 

.Age 

at  Entry,  58 

Yea 

rs. 

14 

4 

4 

10 
10 

73 
U 

15 

No.  OF  Entrj 

lnts,  181. 

$402,0( 

30  In 

JURED. 

16 

1 

4 

5 

10 

75 

17 

3 

5 

16 

0 

10 

3 

89 

24 

5 

198.5 

58 

18 

1 

1 

3 

1 

1 

5 

77 

1 

11 

25 

2 

155.5 

31 

42 

6 

352 

59 

19 

1 

3 

78 

2 

5 

12 

5 

124 

15 

18 

14 

285 

60 

AA          -< 

1 

3 

3 

79 

3 

4 

5 

9 

8 

14 

10 
4 

7 

1 
2 

3 

103 
86 

70.5 

13 
11 

39 

36 
18 

20 

2 
6 

8 

229 

187 

151 

61 

62 

63 

20 

1 

75 

39  20 

631.5 

118 

110 

25 

1,121.5 

6 

11 

2 

2 

49 

25 

5 

3 

91.5 

H 

Age 

at  Entry,  60  Years. 

7 
8 

6 
6 

2 

3 

34 
24 

7 
12 

3 

6 

59.5 
45 

65 
66 

No. 

OF  ENTRi 

lNTS,  122. 

$215,000  Insured. 

9 
10 

3 
2 

2 

18 
13 

4 
1 

6 

33 
23 

67 
68 

0 

60 

7 

2 

60 

22 

4 

105.5 

11 

1 

1 

11 

2 

2 

22 

69 

1 

6 

8 

3 

109 

7 

17 

3 

180.5 

61 

12 

9 

18 

70 

2 

8 

9 

4 

91.5 

11 

23 

4 

150.5 

62 

13 

2 

9 

6 

18 

71 

3 

4 

3 

1 

73.5 

8 

3 

3 

122.5 

63 

14 

7 

12 

72 

4 

8 

2 

2 

66 

8 

3 

6 

108.5 

64 

15 

1 

7 

2 

12 

73 

5 

6 

1 

3 

54.5 

12 

1 

4 

92.5 

65 

16 

1 

6 

1 

10 

U 

6 

8 

8 

3 

41 

14 

9 

5 

71.5 

66 

17 

5 

9 

75 

7 

6 

1 

25.5 

16 

1 

47.5 

67  \ 

18 

5 

9 

76 

8 

6 

1 

18.5 

.12 

1 

30.5 

68 

19 

1 

5 

1 

9 

77 

9 

4 

2 

11 

f    5 

2 

17 

69  \ 

TABLE    II. 

OBSERVATIONS   ON  FEMALE  LIFE. 


155 


Age  at  Entry,  60  Years. 


Age  at  Entry,  62  Years. 


10 
11 
12 
13 
14 

15 
16 
17 
18 
19 

20 
21 


0 
1 
2 
3 

4 

5 
6 

7 
8 
9 

10 
11 
12 
13 
14 

15 
16 
17 
18 
19 

20 
21 
22 
23 


No.  OF  Entrants,  122. 


a 
1 

".1 

i 

5 

Exposed 
to  Risk. 

6 
6 
6 

1 

1 

5.5 

1 

4 

1 

3 
2 
2 
2 

2 

2 

2 

2 

65 

38 

19 

593.0 

$215,000  Inscbed. 


$        $ 


118 


65 


32 


W2 


11 
11 
11 

10.5 

8 

7 
6 
6 
6 
6 

6 
6 


1,021.0 


70 
71 

72 
73 

u 

75 
76 
77 
78 
79 

80 
81 


Age  at  Entry,  61  Years. 


No.  OP  Entbants,  90 


1 


44.5 

80 
68 
54 
42 

33.5 
23 
15.5 
11 
5 

3 
3 
3 
3 
3 

2 
2 
2 
2 

2 

2 
1 
1 
1 


$195,000  Insubed. 


17    2 


1 


52  27  11  406.5    119 


57 


19 


96.5 
173 
151.5 
130.5 
109 

87.5 
51.5 
33.5 
18 
9 

3 
3 
3 
3 
3 

2 
2 
2 
2 
2 


6i 

63 
6J^ 
65 

66 
67 
68 
69 
70 

71 
72 
73 

U 

75 

76 

77 
78 
79 
80 

81 


2 

1  '  82 
1  83 
84 


890.0 


0 

1 

2 
3 

4 

5 
6 

7 
8 
9 

10 
11 
12 
13 
14 


No. 

OF  Entrants,  64. 

$111,000  Insched. 

1 
"S 

O  3 

11 

1.2 

5*" 

56 

OS'S 

<S5 

$ 

$ 

$ 

$ 

8 

27 

16 

55.5 

3 

5 

1 

43.5 

12 

9 

5 

90.5 

5 

2 

34.5 

8 

2 

65 

1 

2 

2 

29 

5 

4 

2 

57 

5 

3 

23.5 

13 

9 

43.5 

7 

1 

16.5 
9 

11 

2 

25 
13 

2 

2 

8 

3 

5 

10.5 

3 

5 

3 

5 

1 

1 

1.5 

1 

1 

1.5 

30 

19 

5 

197.5 

64 

38 

9 

366.5 

Age  at  Entry,  63  Years. 


Age  at  Entry,  64  Years. 


No.  OP  Entrants,  50, 


24.5 
46 
38.5 
32 

27 

20.5 
16 
14 
12 


$104,000  Insured. 


49.5 
96 

84.5 
76.5 

57 

42 
26 
25 
20 
15 


be 


62 
63 
64 
65 
66 

67 
68 
69 
70 
71 


I 

No. 

OF  Entrants,  61. 

$140,000  Insubed. 

3 

2 

29.5 

2 

3 

68.5 

2 

8 

52 

3 

14 

128 

1 

5 

3 

43.5 

1 

11 

15 

112.5 

4 

2 

1 

36 

9 

10 

7 

86 

8 

1 

3 

29.5 

21 

1 

10 

64.5 

4 

1 

1 

17.5 

3 

2 

7 

32 

6 

2 

11 
4 

8 

3 

19.5 
10 

"2 

4 

2 

2 

2 
2 

3 

10 

7 

7 
7 
7 

1 

2 

2 

7 

1 

1 

5 

5 

30 

21 

10 

238.0 

50 

44 

46 

571.0 

63 

64 
65 
66 
67 

68 
69 
70 
71 

72 

73 

74 
75 
76 
77 


64 
65 
66 
67 
68 

69 
70 

71  ^ 

72  \ 

73  \ 


156 


TABLE    II. 


,   OBSERVATIONS  ON  FEMALE  LIFE. 


1              Age 

1 

at  Entry,  64  Years. 

Age 

at 

Entry,  66  Years. 

•ss 

No.  OF  ENTBAirrs,  50. 

1104,000  Insubed. 

4.1 

•a 

«S| 

1 

No.  OP  Entrants,  38. 

1 

$54,000  Insured. 

t 

•«5 

bo 

°  s 

5 

« 

I§1 

T 

■as 

11 

as' 

^2 

i 

'  ^  1  '-d 

•a 

s 

"55 

.2--   §  «       M 

$ 

$ 

1 

$ 

$  1  $ 

$ 

10 

1 

2.5 

3 

7.5 

7^ 

0 

2 

13 

2 

26 

66 

11 

1 

2 

1 

6 

75 

1 

1 

3 

1 

24.5 

1 

6 

3 

49 

67 

12 

5 

76 

2 

6 

1 

18 

12 

3 

36 

68 

13 

5 

77 

3 

2 

14 

1 

27 

69 

14 

5 

78 

4 

2 

1 

12 

6 

1 

26 

70 

15 

1 

5 

79 

5 

9 

19 

71 

16 

1 

1 

o 

5 

80 

6 

7 
8 
9 

1 
2 
1 

1 

1 

1 

8.5 
6 
4 
3 

5 
4 
1 

3 

3 
1 

17.5 
8 
4 
3 

72 
73 
7Jf 
75 

32 

18 

10 

248.0 

41 

32 

31 

530.0 

Age 

at  Entry,  65  Years. 

10 
11 

1 

2 
2 

1 

2 

2 

76 

NTBiNTS,  42.'|       $86,000  IKSUKED. 

I| 

77 

0 
1 
2 
3 

No.  OF  E 

65 
66 

67 
68 

12 

1 

1 

1 

1 

78 

1 
2 

3 

6 

4 
5 

2 

1 

19 
34.5 

29 
24 

i  5 
2 
4 

16 

4 

13 

5 

1 

41 
70.5 
59.5 
52 

7 

12 

9 

117.0 

17 

23 

14 

220.5 

Age 

at 

Entry,  67  Years. 

4 
5 

6 

1 

1 

3 

17.5 

8 

9 

1 

2 

12 

35 
13 

69 
70 

0 

No.  OP  E 

NTBi 

lNts,  14. 

$19,000  Insured. 

67 

7 

9.5 

6 

2 

7 

6 

12 

71 

1 

1 

2 

14 

1 

2 

19 

68 

7 

1 

1 

4.5 

1 

1 

5.5 

72 

2 

1 

1 

10.5 

1 

1 

15.5 

69 

8 

1 

1 

2.5 

1 

2 

3 

73 

3 

2 

1 

8.5 

2 

1 

13.5 

70 

9 

1 

1 

7J, 

4 

6 

11 

71 

10 

75 

5 

6 

11 

72 

11 

76 

6 

6 

11 

73 

12 

77 

7 

6 

11 

71, 

13 

78 

8 

6 

11 

75 

14 

79 

9 

1 

5.5 

1 

10.5 

76 

15 

80 

10 

2 

5 

2 

10 

77 

16 

81 

11 

3 

8 

78 

17 

82 

12 

1 

1 

2.5 

1 

1 

7.5 

79 

18 

83 

13 

1 

6 

80 

19 

8J^ 

14 

1 

6 

81 

20 

85 

15 

1 

6 

82 

21 

86 

16 

1 

1 

6 

6 

83 

22 
23 

1 

-1- 

1     1 

1 

81 
88 

3 

4 

7 

90.0 

3 

4 

12 

172.5 

Age 

at 

Entry,  68  Years. 

22 

14 

6 

161.0 

40 

27 

19 

306.5 

0 

No.  OP  E 

NTRj 

LNTS,   5.! 

i 

$7,000  Insured. 

68 

2.5 

3.5 

1 

5 

7 

69 

2 

1 

5 

2 

7 

70 

3 

4 

5 

71 

4 

4 

5 

72 

TABLE    II. 

OBSERVATIONS  ON  FEMALE  LIFE. 


157 


1 

Age  at  Entry,  68  Years. 

Age  at  Entry,  70  Years. 

^8 

No.  OF  Entrants,  5 

$7,000  Insured. 

< 

"SS 

No.  OF  Entrants,  4. 

$7,000  Insured. 

4 

1 
1 

§1 

II 

i 

^B 

1 
$ 

a- 
$ 

5i 

5.2 
W2 

2^ 

11 

3 

So 

ti 
.S 

1-^ 

03 

$ 

$ 

% 

% 

$ 

5 

2 

4 

3 

5 

73 

5 

1 

1.5 

2 

4 

75 

6 

1 

3 

1 

3 

u 

6 

1 

3 

76 

7 

1 

1 

75 

7 

1 

3 

77 

8 

1 

1 

76 

8 

1 

3 

78 

9 
10 

1 

1 
1 

.  1 

1 
1 

77 
78 

9 

1 

1 

3 

3 

79 

2 

2 

16.0 

3 

4 

40.0 

3 

2 

30.5 

4 

3 

38.5 

Age  at  Entry,  71  Years. 

Age  at  Entry,  69  Years. 

No.  OF  Entrants,  0. 

$0,000  Insured. 

0 

$26,000  INSUBBD. 

69 

No. 

OF  Entbants,  8. 

•4 

13 

. 

1 
2 

8 
8 

36 

36 

70 
71 

Age  at  Entry,  72  Years. 

3 

4 

6 
6 

7 
8 
9 

1 
1 

2' 

•7.5 
6.5 

5 
3 
3 

- 

23.5 
20.5 

17 
2 
2 

73 
73 

U 

75 
76 
77 
78 

3 

1 

13 
1 

1 

6 

0 

1 
2 
3 

No.  OF  Entrants,  2. 

$3,000  Insured. 

72 
73 

u 

75 

1 

1 

1 
2 
1 
1 

1 
1 

2 

2 

1.5 
3 
2 
2 

1 

1 

5.0 

8.5 

1   10 

11 

79 
80 

12 

81 

Age  at  Entry,  73  Years. 

13 
14 

83 
83 

1 

15 

84 

No.  OF  Entrants,  0. 

$0,000  Insured. 

16 

85 

17 

86 

1        1 

18 

87 

19 
20 

88 
89 

Age  at  Entry,  74  Years. 

21 

1 

1 

90 

0 

No.  OF  Entrants,  1. 

'   $1,000  Insured. 

n 

3     4 

1 

57.0 

13 

12 

1 

144.0 

.5 

.5 

Age  at  Entry,  70  Years. 

1 

1 

.5 

1 

.5 

i5 

1 

1.0 

1 

1.0 

] 
0 

Ho.  OF  Entbants,  4. 

$7,000  iNSUBBD. 

70 

1 

3 

1 

3.5 

1 

1 

3.5 

1 

5.5 

71 

2 

3 

5 

72 

3 

3   • 

5 

73 

4 

3 

5 

n 

158 


TABLE     II. 

OBSERVATIONS  ON  FEMALE  LIFE. 


Age  at  Entry, 

75  Years. 

Age  at  Entry,  77  Years. 

n 

■si 

No.  OF  Entrants,  3. 

$4,000  Insured. 

is 

No.  OF  Entrants,  1. 

$2,000  Insured. 

•a' 

bo 

84 
85 
86 

M 

a 
1^ 

(5" 

S 

p 

W2 

si 

a 

pa 

5'i 

la 

m2    , 

.S      P  S 

s 

■a   . 
P 

«2 

si 

a 

ii'si 

^2 

0 

1 

2 

I 

5 
6 

1 

1 

1 

1.5 
2 

2 
2 
1.5 

1 
1 

$ 
1 

2 

1 

$ 
2 
3 
3 
3 
2 

1 
1 

75 
76 
77 
78 
79 

80 
81 

5 
6 
7 
8 
9 

1 

$ 

i 

$ 

$ 

2 

$ 
2 
2 

2 
2 
2 

1 

9.5 

2 

19.0 

Ages  at  Entry,  78  and  79  Years. 

1 

1 

1 

11.0 

1 

2 

1 

15.0 

Age  at  Entry, 

76  Years. 

No.  OP  Entrants,  0. 

$0,000  Insured. 

0 
1 
2 
3  . 

No.  OP  Enteants,  1. 

f  1,000  Insured. 

76 
77 
78 
79 

Age  at  Entry,  80  Years. 

" 

1 

.5 
1 
1 
1 

• 

1 

.5 
1 
1 

1 

0 

1 

No.  OF  Entrants,  1. 

$1,000  Insured. 

80 
81 

1 

.5 
1 

1 

.5 
1 

1 

3.5 

1 

3.5 

Age  at  Entry 

,  77  Years. 

1 

1.5 

1 

1.5 

Age  at  Entrj 

,81  Years. 

i     0 
1 

!    3 
1     4 

No.  OF  Entrants,  1. 

$2,000  Insured. 

77 
78 
79 
80 
81 

0 

1 

No.  OF  Entrants,  1. 

$1,000  IlAuRED. 

81 

82 

.5 
1 
1 
1 
1 

1 
2 
2 
2 

2 



1 

.5 

1 

1 

.5 

1 

1 

1.5 

1 

1.5 

TABLE    III. 


159 


MALE   LIFE   (A).     MORTALITY  AND    DEATH    CLALMS   PER   CENT.  OF  THE  LIVING  OR 

EXPOSED,   BY  EXPERIENCE  ENDING  (1874),  AND  BY  FINAL  SERIES  ; 

ALSO,  AVERAGE  SUM  INSURED  (1874.) 


Age  at 

Mortality, 

Death 

Death 

Claims. 

Average  Sum  Insured  (1874.) 

Age  at 

Begin- 

Per Cent. 

Claims, 

Per  Cent, 

Final  Se- 

Begin- 

ning of 
Year. 

(1874.) 

Per  Cent. 
(1874.) 

Final  Se- 
ries. 

ries. 

Existing. 

Discontin- 
ued. 

Died. 

Exposed. 

ning  of 
Year, 

$ 

$ 

$ 

$ 

$ 

10 

2,275 

1,575 

2,080 

10 

11 

1,923 

1,619 

2,063 

11 

12 

0.333 

0.244 

0.337 

1 

2,030 

1,679 

1,500 

2,052 

12 

13 

.457 

.268 

.266 

3 

1,898 

1,930 

1,200 

2,048 

13 

14 

.281 

.160 

.158 

4 

2,088 

1,900 

1,167 

2,041 

14 

15 

.370 

.280 

.277 

11 

1,991 

1,901 

1,500 

1,983 

15 

16 

.577 

.450 

.445 

27 

1,868 

1,879 

1,514 

1,939 

16 

17 

.594 

.501 

.503 

48 

1,870 

1,858 

1,625 

1,927 

17 

18 

.685 

.622 

.626 

92 

1,808 

1,844 

1,730 

1,906 

18 

19 

.813 

.741 

.740 

168 

1,797 

1,852 

1,728 

1,895 

19 

20 

.787 

.690 

.688 

247 

1,827 

1,886 

1,701 

1,939 

20 

21 

.693 

.575 

.579 

322 

1,896 

1,959 

1,673 

2,016 

21 

22 

.705 

.620 

.626 

511 

1,950 

2,038 

1,840 

2,093 

22 

23 

.662 

.631 

.646 

729 

1,979 

2,111 

2,063 

2,166 

23 

24 

\.651 

.627 

.648 

961 

2,010 

2,212 

2,152 

2,234 

24 

25 

.674 

.657 

.674 

1,258 

2,071 

2,292 

2,236 

2,292 

25 

26 

.674 

.662 

.680 

1,534 

2,124 

2,361 

2,294 

2,335 

26 

27 

.701 

.679 

.705 

1,869 

2,165 

2,413 

2,281 

2,353 

27 

28 

.684 

.688 

.712 

2,175 

2,216 

2,423 

2,373 

2,361 

28 

29 

.644 

.676 

.686 

2,376 

2,023 

2,465 

2,507 

2,389 

29 

30 

.669 

.690 

.706 

2,731 

2,052 

2,539 

2,530 

2,451 

30 

31 

.692 

.692 

.664 

3,093 

2,318 

2,598 

2,502 

2,502 

31 

32 

.690 

.704 

.687 

3,424 

2,352 

2,628 

2,570 

2,519 

32 

33 

.730 

.767 

.806 

3,926 

,  2,355 

2,651 

2,667 

2,538 

33 

34 

.749 

.790 

.849 

4,403 

2,418 

2,680 

2,699 

2,557 

34 

35 

.738 

.786 

.828 

4,525 

2,486 

2,687 

2,740 

2,575 

35 

36 

.759 

.862 

.861 

4,899 

2,503 

2,734 

2,943 

2,591 

36 

37 

.813 

.913 

.921 

5,432 

2,469 

2,786 

2,921 

2,600 

37 

38 

.847 

.901 

.918 

5,573 

2,458 

2,795 

2,783 

2,615 

38 

39 

.855 

.898 

.940 

5,827 

2,502 

2,828 

2,770 

2,639 

39 

40 

.881 

.924 

.975 

6,137 

2,514 

2,825 

2,796 

2,663 

40 

41 

.910 

.968 

.974 

6,145 

2,513 

2,881 

2,866 

2,694 

41 

42 

.957 

.978 

.984 

6,219 

2,561 

2,952 

2,787 

2,729 

42 

1     43 

1.015 

1.014 

1.085 

6,871 

2,597 

2,942 

2,755 

2,757 

43 

1    44 

.986 

.989 

1.080 

6,750 

2,610 

2,977 

2,791 

2,783 

44 

45 

.996 

1.024 

.1.066 

6,537 

2,641 

3,017 

2,890 

2,811 

45 

46 

1.092 

1.130 

1.184 

7,178 

2,675 

3,046 

2,943 

2,843 

46 

47 

1.146 

1.182 

1.260 

7,547 

2,712 

3,140 

2,968 

2,877 

47 

'  48 

1.151 

1.214 

1.232 

7,120 

2,740 

3,149 

3,065 

2,907 

48 

49 

1.192 

1.230 

1.270 

7,107 

2,764 

3,100 

3,031 

2,937 

49 

Note.  The  Percentages  by  Lives  and  by  Amounts  (1874")  were  found  from  the  sum  or  mean  of  data 
at  two  adjacent  Ages  in  Table  I  (A).  The  Final  Series  Percentages  depend  on  the  factor  of  Table 
III  (C)  discounted  at  4  per  cent,  per  annum,  and  applied  to  Death  Claims  and  Exposed  in  Table  I.  By 
(1874)  is  meant  the  experience  from  organization  to  the  year  1874  To  the  fifth  column  annex  ,000. 


160 


TABLE     III. 


MALE   LIFE  (A).     MORTALITY  AND  DEATH  CLAIMS  PER  CENT.   OF  THE  LIVING  OR 

EXPOSED,  BY  EXPERIEN(.^E  ENDING  (1874),  AND  BY  FINAL  SERIES ; 

ALSO,  AVERAGE  SUM  INSURED  (1874.) 


Age  at 
Begin- 

Mortality, 

Death 
Claims, 

Death 
Claims, 

Claims, 

Average  Sum  Insured  (1874.) 

Age  at 
Begin- 

Per Cent. 

Per  Cent. 

Final  Se- 

ning of 
Year. 

(1874.) 

Per  Cent. 

(1874.) 

Final  Se- 
ries. 

ries. 

Existing. 

Discontin- 
ued. 

Died. 

Exposed. 

ning  of 
Year. 

$ 

$ 

$ 

$ 

$ 

50 

1.305 

1.324 

1.440 

7,946 

2,796 

3,101 

3,010 

2,968 

50 

51 

1.377 

1.422 

1.554 

8,403 

2,835 

3,265 

3,091 

2,993 

51 

52 

1.416 

1.477 

1.564 

7,997 

2,840 

3,305  ' 

'  3,137 

3,008 

52 

53 

1.482 

1.508 

1.571 

7,577 

2,860 

3,407 

3,070 

3,018 

53 

54 

1.619 

1.672 

1.750 

8,018 

2,955 

3,524 

3,126 

3,027 

54 

55 

1.732 

1.826 

1.830 

7,685 

2,998 

3,449 

3,190 

3,026 

55 

56 

1.799 

1.922 

1.848 

7,222 

2,975 

3,423 

3,234 

3,026 

56 

57 

1.916 

2.028 

1.988 

7,301 

2,938 

3,510 

3,207 

3,030 

57 

58 

2.067 

2.129 

2.108 

6,950 

2,935 

3,535 

3,123 

3,033 

58 

59 

2.338 

2.332 

2.326 

7,073 

2,999 

3,563 

3,027 

3,036 

59 

60 

2.566 

2.596 

2.569 

7,327 

3,059 

3,603 

3,062 

3,027 

60 

61 

2.557 

2.705 

2.578 

6,654 

2,993 

3,606 

3,181 

3,008 

61 

62 

2.673 

2.840 

2.823 

6,413 

2,960 

3,699 

3,183 

2,995 

62 

63 

2.981 

3.132 

3.429 

6,899 

2,983 

3,788 

3,128 

2,978 

63 

Qi 

3.258 

3.610 

4.014 

7,362 

2,910 

3,493 

3,268 

2,950 

64 

65 

3.588 

4.061 

4.243 

6,908 

2,932 

3,429 

3,312 

2,927 

65 

66 

3.662 

3.766 

4.020 

5,399 

2,860 

3,594 

2,966 

2,884 

66 

67 

3.852 

4.092 

4.421 

5,096 

2,856 

3,533 

3,032 

2,854 

67 

68 

4.499 

4.607 

4.734 

4,974 

3,032 

3,686 

2,882 

2,814 

68 

69 

4.982 

4.980 

5.101 

4,491 

2,960 

3,400' 

2,731 

2,732 

69 

70 

5.063 

5.199 

5.753 

4,293 

2,740 

3,344 

2,728 

2,657 

70- 

71 

5.475 

5.435 

5.934 

3,832 

2,796 

2,875 

2,596 

2,615 

71 

72 

6.066 

6.016 

6.062 

3,275 

2,695 

2,542 

2,550  ■ 

2,572 

72 

73 

6.073 

5.694 

6.257 

2,849 

2,444 

2,727 

2,382 

2,540 

73 

74 

6.554 

5.814 

7.069 

2,640 

2,591 

2,500 

2,279 

2,569 

74 

75 

6.993 

6.504 

7.174 

2,185 

3,046 

1,778 

2,407 

2,588 

75 

76 

8.567 

7.136 

6.726 

1,671 

3,211 

1,824 

2,103 

2,524 

76 

77 

10.548 

8.420 

8.686 

1,712 

2,961 

2,000 

1,960 

2,456 

77 

78 

10.607 

10.758 

11.159 

1,633 

2,456 

2,000 

2,474 

2,439    . 

78 

79 

9.285 

10.362 

1L505 

1,137 

2,500 

2,077 

2,720 

2,437 

79 

80 

9.738 

8.968 

11.406 

688 

2,776 

2,222 

2,205 

2,394 

80 

81 

13.565 

11.070 

13.608 

•   526 

2,795 

2,200 

1,897 

2,325 

81 

82 

14.141 

12.747 

18.352 

502 

3,179 

2,143 

2,071 

2,298 

82 

83 

10.108 

10.982 

15.705 

230 

3,600 

1,000 

2,357 

2,170 

83 

84 

12.093 

11.401 

20.479 

182 

2,667 

1,667 

1,846 

1,958 

84 

85 

14.286. 

15.493 

36.489 

238 

.2,600 

2,000 

2,000 

1,844 

85 

86 

18.000 

20.253 

44.465 

173 

3,250 

1,778 

1,580 

86- 

87 

16.000 

13.861 

47.876 

83 

1,600 

1,167 

1,347 

87 

88 

18.182 

24.658 

31.326 

28 

1,200 

1,800 

1,327 

88 

89 

28.571 

41.860 

43.678 

8 

1,000 

1,000 

1,800 

1,229 

89 

All  Ages 

1.0280 

1.0959 

2,520 

2,711 

2,832 

2,656 

TABLE    III 


161 


MALE   LIFE  (B).     ANNUAL  MORTALITY  AND  DISCONTINUED  PER  CENT.   OF  THE  EX- 
POSED, ACCORDING  TO  YEARS  OF  INSURANCE.     ALSO,  AVERAGE  SUM  INSURED. 


•s  s 

Mortality 

Discontinued 

D.  and  Dis. 

Average  Sum  Insured. 

o   u 

**  PI 
0 

Per  Cent.  (1874.) 

Per  Cent.  (1874.) 

Per  Cent, 
(1874.) 

By  Am'ts. 

(1874.) 

0 

By  Lives. 

By  Am'ts. 

By  Lives. 

By  Am'ts. 

Existing. 

Discon- 
tinued. 

Died. 

Exposed. 

.629 

.631 

9.576 

7.764 

8.346 

$ 

2,558 

2,119 

$ 

2,646 

2,639 

1 

.810 

.856 

18.255 

16.470 

17.191 

2,595 

2,385 

2,821 

2,670 

1 

2 

.921 

.996 

10.383 

11.798 

12.680 

2,296 

3,077 

2,907 

2,689 

2 

3 

1.000 

1.061 

8.396 

9.833 

10.793 

!  2,354 

3,160 

2,841 

2,678 

3 

4 

1.091 

1.187 

G.969 

8.371 

9.462 

2,406 

3,224 

2,901 

2,666 

4 

5 

1.136 

1.226 

6.076 

7.405 

8.642 

2,614 

3,258 

2,867 

2,656 

6 

6 

1.168 

1.273 

5.019 

5.983 

7.181 

2,613 

3,143 

2,860 

2,625 

6 

7 

1.225 

1.338 

5.397 

5.483 

6.748 

2,601 

2,647 

2,846 

2,606 

7 

8 

1.196 

1.266 

3.446 

3.887 

5.104 

2,626 

2,934 

2,746 

2,596 

8 

9 

1.231 

1.255 

2.933 

3.150 

4.366 

2,494 

2,766 

2,623 

2,572 

9 

10 

1.273 

1.309 

2.760 

2.977 

4.247 

2,405 

2,799 

2,667 

2,593 

10 

11 

1.336 

1.447 

2.405 

2.466 

3.877 

2,432 

2,714 

2,867 

2,647 

11 

12 

1.491 

1.544 

1.909 

2.004 

3.517 

2,598 

2,830 

2,790 

2,695 

12 

13 

1.406 

1.475 

1.586 

1.732 

3.181 

2,820 

2,952 

2,836 

2,703 

13 

14 

1.464 

1.500 

1.789 

1.885 

3.358 

2,748 

2,829 

2,751 

2,684 

14 

16 

1.477 

1.497 

1.128 

1.171 

2.651 

2,735 

2,773 

2,707 

2,671 

15 

16 

1.727 

1.945 

1.128 

1.193 

3.115 

2,764 

2,812 

2,995 

2,660 

16 

17 

1.716 

1.838 

.889 

.988 

2.808  • 

2,456 

2,933 

2,828 

2,640 

17 

18 

1.664 

2.001 

.880 

.825 

2.809 

2,608 

2,484 

3,191 

2,655 

18 

19 

1.923 

1.814 

.791 

.782 

2.582 

2,842 

2,621 

2,502 

2,651 

19 

20 

1.934. 

2.061 

.792 

.922 

2.964 

2,713 

3,064 

2,807 

2,634 

20 

21 

2.162 

2.365 

.769 

.807 

3.153 

2,631 

2,747  !  2,866 

2,620 

21 

22 

2.460 

2.877 

.698 

.799 

3.654  . 

2,482 

2,987  1  3,055 

2,612 

22 

23 

2.670 

3.010 

.630 

.729 

3.718  i 

2,460 

3.016 

2,942 

2,610 

23 

24 

2.751 

2.905 

.447 

.399 

3.293  I 

2,326 

2,343 

■ 

2,775 

2,628 

24 

25 

2.799 

3.229 

.439 

.354 

3.572 

2,404 

2,208 

3,161 

2,740 

26 

26 

3.078 

3.311 

.830 

.866 

4.148  ' 

2,883 

3,036    3,133 

2,913 

26 

27 

2.892 

2.949 

.542 

•    .427 

3.363 

3,052 

2,300 

2,982 

2,925 

27 

28 

3.543 

3.394 

.696 

.374 

3.755 

2,979 

1,500 

2,677 

2,795 

28 

29 

2.692 

1.565 

1.355 

1.772 

3.309 

2,397 

3,400 

1,500 

2,580 

29 

30 

4.720 

6.452 

.602 

.643 

7.054 

2,805 

3,000 

3,875 

2,835 

30 

31 

.... 

.... 

.... 

.... 

.... 

2,286 

31 

32 

14.286 

6.250 

.... 

6.250 

.... 

1,000 

2,286 

32 

33 

16.667 

33.^333 

.  ■  •  • 

33.333 

.... 

.... 

5,000 

2,500 

33 

34 

25.000 

21.053 

44.444 

ii!iii 

30.000 

500 

2,000 

2,375 

34 

35 

3,500 

36 

36 

.... 

.... 

.... 

.... 

.... 

3,500 

36 

37 

.... 

.... 

3,500 

37 

38 

5o!66o 

28.571 

.... 

28.571 

.... 

2,666 

3,500 

38 

39 

Total 

100.000 

100.000 

.... 

100.000 

.... 

.... 

5,000 

5,000 

39 

1.028 

1.096 

9.114 

9.297 

10.293 

2,520 

2,711 

2,832 

2,656 

162 


TABLE     III. 


MALE    LIFE  (C).     LOGARITHM   OF   THE    MULTIPLIER  (w)   TO  CARRY    FORWARD    THE 

AMOUNTS  EXISTING  TO  THEIR  PROPORTIONAL  TERMINATIONS  INCLUSIVE 

IN  THE  FOLLOWING  COLUMNS  OF  TABLE  I,  THAT  IS,  TO 

FINAL  SERIES. 


Years  of 
Insurance. 

AGES  OF 

ENTRY 

• 

Years  of 
Insurance. 

16  to  19 

20,21 

22,  23 

24,  25  ' 

26,27 

28,29 

30,31 

32,33 

0 

0.00000 

0.00000 

0.00000 

0.00000 

0.00000 

0.00000 

0.00000 

0.00000 

0 

1 

.03167 

.03251 

.03076 

.03125  , 

.02975 

.02950 

.02880 

.02756 

1 

2 

.06848 

.07103 

.06595  i  .06651  > 

.06416 

.06304 

.06108 

.05870 

2 

3 

.11133 

.11282 

.10211  1  .10598  1 

.09944 

.09678 

.09379 

.09200 

3 

4 

.15424 

.15897 

.14333 

.14795 

.14100 

.13500 

.13075 

.12865 

4 

5 

0.21081 

0.22007 

0.20526 

0.20511 

0.19508 

0.18536 

0.17896 

0.17856 

5 

6 

.29008 

.30419 

.28311 

.27934 

.26141 

.24597 

.24303 

.24077 

6 

7 

.42017 

.41418 

.38348 

.37144 

.34663 

.32425 

.32288 

.31871 

7 

8 

.56518 

.56338 

.49498 

.48051 

.44877 

.42394 

.41637 

.41552 

8 

9 

.72039 

.72029 

.63628 

.00940 

.56752 

.53940 

.52961 

.53480 

9 

10 

0.90595 

0.88140 

0.76332 

0.73569 

0.08621 

•0.65580 

0.64871 

0.65832 

10 

11 

1.03608 

.98935 

.88288 

.85079 

.78971 

.76447 

.75669 

.76347 

11 

12 

.13428 

1.06705 

.06695 

.93098 

.87108 

.85081 

.84310 

.84680 

12 

13 

.18797 

.11745 

1.02247 

.98875 

.91419 

.90053 

.89185 

.89522 

13 

l'' 

.24499 

.17096 

.07471 

1.04638 

.90450 

.94898 

.94126 

.93814 

14 

15 

1.29687 

1.22848 

1.14839 

1.10994 

1.03495 

1.01171 

1.00502 

0.99013 

15 

16 

.34188 

.30143 

.20883 

.17915 

.09429 

.06871 

.06272 

1.04408 

16 

17 

.38040 

.39219 

.27400 

.24687 

.13776 

.11044 

.11365 

.08012 

17 

18 

.40808 

.45412 

.33330 

.30876  1 

.18436 

.15738 

.15951 

.11317 

18 

19 

.44173 

.49038 

.39645 

.35785 

.22871 

.20863 

.20061 

.10153 

19 

20 

1.44609 

1.42734 

1.28963 

1.26198 

1.23978 

1.20003 

20 

21 

■ 

.5x5848 

.47540 

.33599 

.29878 

.28672 

.25242 

21 

22 

.56209 

.52180 

.37204 

.33082 

.32485 

.28933 

22 

23 

.53941 

.57132 

.41461 

.37611 

.36530 

.32815 

23 

24 

.77465 

.68447 

.48049 

.44200 

.45187 

.38124 

24 

34,35 

36,37 

38,39 

40,41 

1 
42,  43 

44,45 

46,47 

48,49 

0 

0.00000 

0.00000 

0.00000 

0.00000 

0.00000 

0.00000 

0.00000 

0.00000 

0 

1 

.02736 

.02797 

.02612 

.02682 

.02637 

.02667 

.02592 

.02522 

1 

2 

.05863 

.05861 

.05685 

.05787 

.05685 

.05506 

.05485 

.05414 

2 

3 

.09011 

.09003 

.08992 

.08450 

.08871 

.08557 

.08437 

.18785 

3 

4 

.12711 

.12451 

.12542 

.11724 

.12499 

.12342 

.12055 

.12281 

4 

5 

0.17563 

0.17178 

0.17432 

0.16137 

0.17407 

0.17291 

0.16813 

0.16904 

5 

6 

.24009 

.23023 

.23728 

.23311 

.23927 

.23703 

.23415 

.24216 

6 

7 

.32266 

.31900 

.32222 

.32714 

.32248 

.33015 

.32644 

.34079 

7 

8 

.42283 

.42148 

.43019 

.43705 

.43852 

.44456 

.44387 

.46653 

8 

9 

.53758 

.54528 

.55948 

.57120 

.56882 

.57540 

.61384 

.63870 

9 

10 

0.65714 

0.66750 

0.68024 

0.69490 

0.70469 

0.70987 

0.76135 

0.77771 

10 

11 

.76034 

.77463 

.^9305 

.81533 

.81133 

.82799 

.89096 

.88884  1  11 

12 

.83(509 

.86817 

.87803 

.91130 

.91464 

.92110 

.98369 

.99857  12 

13 

.89591 

.92046 

.93184 

}  .96849 

.97285 

.98229 

1.05109 

1.05690 

13  1 

14 

.94054 

.96708 

.98309 

i  1.02026 

1 

i.02834 

1.03559 

.09971 

.10516 

14  ^ 

1 

TABLE    III. 


163 


MALE  LIFE  (C.)     LOGARITHM   OF   THE   MULTIPLIER  (tv)  TO    CARRY    FORWARD  THE 

AMOUNTS  EXISTING  TO  THEIR  PROPORTIONAL  TERMINATION  INCLUSIVE 

IN  THE  FOLLOWING  COLUMNS  OF  TABLE  I,  THAT  IS,  TO 

FINAL  SERIES. 


AGES    OP   ENTRY. 

15 

34,35 

36,37 

38,39 

40,41 

42,43 

44,46 

46,47 

48,49 

15 

0.99334 

1.02716 

1.05255 

1.09514 

1.08940 

1.09572 

1.15306 

1.17165 

16 

1.04190 

.08194 

.10557 

.15674 

.13412 

.14549 

.20908 

.24176 

16 

17 

.08799 

.13401 

.15389 

20898 

•    .17147 

.18669 

.24690 

.29332 

17 

18 

.12433 

.16757 

.19163 

.24450 

.21191 

.21942 

.28698 

.32466 

18 

19 

.16214 

.20506 

.23491 

.28703 

1    .25451 

.25687 

.33896 

.37522 

19 

20 

1.20632 

1.25361 

1.27022 

1.32455 

1.28544 

1.28311 

1.39109 

1.40787 

20 

21 

.23740 

.29230 

.30026 

.35877 

.31108 

.31230 

.41859 

.44997 

21 

22 

.27625 

.32312 

.33458 

.39109 

.34072 

.35177 

.46206 

.48151 

22 

23 

.30803 

.35808 

.38224 

.43614 

.37225 

.38598 

.52132 

.53881 

23 

24 

.37613 

.41130 

.42984 

.49325 

.46483 

.48744 

.59343 

.60108 

24 

25 

1.47904 

1.49640 

1.53001 

1.58489 

1.63230 

1.64291 

1.71368 

1.76675 

25 

26 

.62925 

.65588 

.67472 

.76986 

.81786 

.83406 

.87907 

.87790 

26 

27 

.94425 

.85502 

.91484 

.96749 

2.03817 

2.03844 

2.16395 

2.13867 

27 

28 

2.28653 

2.21526 

2.24928 

2.26639 

.47507 

.47829 

.50773 

.26995 

28 

0 

50,51 

52,53 

54,  55  1  56,  57 

58,59 

60,61 

62,63 

64,65 

0.00000 

0.00000 

0.00000 

O.OOOCO 

0.00000 

0.00000 

0.00000 

0.00000 

0 

1 

.02578 

.02589 

.03195 

.03235 

.02877 

.02832 

.03272 

.02596 

1 

2 

.05292 

.05435 

.06092 

.05647 

.05943 

.05577 

.06376 

.04455 

2 

3 

.08601 

.08721 

.09767 

.09116 

.09101 

.09351 

.10001 

.07247 

3 

4 

.12422 

.12676 

.13934 

.13230 

.   .13035 

.13840 

.12885 

.10867 

4 

5 

0.18118 

0.18340 

0.19199 

0.18767 

0.19541 

0.19452 

0.20007 

0.17234 

5 

6 

.26561 

.26048 

.27789 

.27283 

.29568 

.27301 

.28121 

.26813 

6 

7 

.36828 

.36581 

.38372 

.38968 

.40959 

.40603 

.42073 

.37843 

7 

8 

.51439 

.50572 

.52739 

.54590 

.56757 

.55388 

.65071 

.54104 

8 

9 

.66341 

.67694 

.68911 

.72297 

.74676 

.74438 

.83539 

.82438 

9 

10 

0.80739 

0.83452 

0.85481 

0.89414 

0.90593 

0.88890 

0.97509 

1.03826 

10 

11 

.92290 

.95311 

.98318 

1.01557 

1.07042 

1.00005 

1.07081 

.19434 

11 

12 

1.00623 

1.05377 

1.08678 

.10290 

.19273 

.12747 

.13848 

.19434 

12 

13 

.06246 

.09947 

.14336 

.17348 

.26270 

.17079 

.18068 

.20835 

13 

14 

.12941 

.15676 

.20055 

.25364 

.35345 

.20889 

.28163 

.23468 

14 

15 

1.20760 

1.20986 

1.26238- 

1.32928 

1. 51441 

1.25803 

1.29866 

1.25587 

15 

16 

.28547 

.27998 

.33082 

.37798 

.54211 

.29116 

.35042 

.25587 

16 

17 

.33760 

.35163 

.37702 

.45536 

.57575 

.32190 

.41536 

.27011 

17 

18 

.39651 

.40659 

.43473 

.50500 

.60526 

.35842 

.42304 

.27011 

18 

29 

.45631 

.44707 

.46092 

.53992 

.62313 

.35842 

.52626 

.27011 

19 

20 

1.48627 

1.50172 

1.50610 

1.55195 

1.66091 

1.35842 

1.55182 

1.27011 

20 

21 

.53167 

.52717 

.57961 

.61034  j 

.66091 

.38443 

.60981 

.47423 

21, 

22 

.55351 

.54756 

.60488 

.   .65609  1 

.72603 

.44570 

.65903 

.47423 

22' 

23 

.61165 

.58759 

.63576 

.69605  j 

.78501 

.45300 

.79733 

.47423 

23 

24 

.68100 

.66743 

.72109 

.75003 

i 

2.00995 

.61650 

.79733 

24 

164 


TABLE    IT. 


FEMALE  LIFE  (A).    MORTALITY  AND  DEATH  CLAIMS  PER  CENT.  OF  THE  LIVING  OR 

EXPOSED,  BY  EXPERIENCE  ENDING  (1874),  AND  BY  FINAL  SERIES. 

ALSO  AVERAGE  SUM  INSURED  (1874). 


1 

1  Mortality, 
Per  Cent. 

Death 

Claims. 

Per  Cent. 

Death 
Claims. 

Per  Cent. 

Final  Se- 

Average Sum  Insured  (1874) 

.S  o3 

bb  « 
^   to 

00  -^ 

(1874.) 

(1874.) 

ries. 

1    Existing. 

Discontin- 

Died. 

Exposed. 

SI 

<  fl 

$ 

ued. 

<  « 

$ 

$ 

9 

10 

1.639 

1.111 

2,800 

1,143 

1,000 

1,475 

10 

11 

1.047 

.671 

3,571 

1,143 

1,000 

1,560 

11 

12 

4,125 

769 

1,663 

12 

13 

1.072 

1.003 

2,500 

1,385 

1,500 

1,603 

13 

14 

.668 

.654 

1,933 

1,372 

1,500 

1,531 

14 

15 

.213 

.141 

1,444 

1,197 

1,000 

1,514 

15 

16 

.448 

.290 

1,207 

1,270 

1,000 

1,546 

16 

17 

1.071 

1.099 

.754 

1,333 

1,249 

1,700 

1,657 

17 

18 

.822 

.869 

(.671) 

1,485 

1,733 

1,818 

1,720 

18 

19 

.519 

.575 

[.757] 

1,552 

1,797 

1,900 

1,715 

19 

20 

1.007 

.906 

1,554 

1,679 

1,556 

1,729 

20 

21 

1.011 

.899 

1,522 

1,783 

1,556 

1,749 

21 

22 

.965 

1.136 

1.013 

1,608 

1,854 

2,068 

1,758 

22 

23 

1.109 

1.104 

(.999) 

1,55.5 

1,867 

1,758 

1,767 

23 

24 

.990 

.720 

[.850] 

1,545 

1,858 

1,323 

1,821 

24 

25 

1.007 

.929 

1,579 

1,920 

1,737 

1,883 

25 

26 

1.139 

1.291 

1,563 

2,016 

2,165 

1,910 

26 

27 

1.046 

1.134 

1.160 

1,582 

2,108 

2,081 

1,918 

27 

28 

.904 

1.026 

(1.065) 

1,581 

2,164 

2.181 

1,923 

28 

29 

.919 

1.069 

[1.182] 

1,633 

2,176 

2,252 

1,937 

29 

30 

1.009 

1.131 

sl,696 

2,126 

2,200 

1,964 

30 

31 

1.0^8 

1.059 

1^697 

2,186 

2,055 

1,996 

31 

32 

1.119 

1.046 

1.108 

1,643 

2,324 

1,882 

2.013 

32 

33 

1.126 

1.136 

(1.084) 

1,660 

2,352 

2,027 

2,009 

33 

34 

1.069 

1.102 

[1.133] 

1,749 

2,359 

2,070 

2,007 

34 

35 

1.0(i8 

1.160 

1,785 

2,425 

2,176 

2,003 

35 

36 

.958 

1.092 

1,840 

2,452 

2,252 

1,977 

36 

37 

.951 

1.079 

1.127 

1,793 

2,338. 

2,208 

1,945 

37 

38 

.977 

1.040 

(1.082) 

1,712 

2,213 

,  2,071 

1,946 

38 

39 

.944 

.815 

[1.207] 

1.773 

2,302 

1,697 

1,968 

39 

40 

.970 

.857 

1,748 

2,495 

1,740 

1,968 

40 

41 

1.012 

1.067 

1,723 

2,417 

2,076 

1,969 

41 

42 

1.095 

1.232 

1.163 

1,700 

2,366 

2,225 

1,978 

42 

43 

1.157 

1.383 

(1.104) 
[1.285] 

1,749 

2,482 

2,375 

1,987 

43 

44 

1.172 

1.300 

1,853 

2,507 

2,296 

1,978 

44 

45 

1.085 

1.088 

1,796 

2,358 

1,960 

1,955 

45 

46 

.981  . 

.946 

1,857 

2,335 

1,884 

1,953 

46 

47 

1.011 

.989     ' 

1.049 

1,935 

2,388 

1,904 

1,946 

47 

48 

.995 

1.094     i 

(1.103) 
[1.391] 

1,868 

2,261 

2,130- 

1,936 

48 

49 

1.040 

1.192 

1.837 

,  2,207 

2,227 

1,943 

49 

Note.  The  percentages  by  Mortality  and  by  Death  Claims  were  derived  from  the  sum  or  mean  of 
data  at  two  adjacent  Ages  in  Table  II  (A).  The  quinquennial  percentages  (Final  Series)  depend  on 
w .  t"  from  Table  IV  (C)  applied  to  Death  Claims  and  Exposed  to  Riijk  in  Table  II.     Under  these  and 


TABLE    TV. 


165 


FEMALE  LIFE  (A).  MORTALITY  AND  DEATH  CLAIMS  PER   CENT.  OF  THE  LIVING  OR 

EXPOSED,  BY  EXPERIENCE  ENDING  (1874j,  AND  BY  FINAL  SERIES. 

ALSO  AVERAGE  SUM  INSURED  (1874). 


Mortality. 

Death 
1     Cl&iins. 

Death 
Claims, 

Average  Sum  Insured  (1874). 

^  « 

"      hn 

Per  Cent. 

Per  Cent. 

Per  Cent. 
Final  Se- 

bo .5 

<  a 

(1874.) 

!      (1874.) 

ries. 

Existing. 

Discontin- 
ued. 

Died. 

Exposed. 

a>    bo 

<  a 

< 

$ 

$ 

f 

50 

1.171 

1.252 

1,825 

2,346 

2,078 

1,945 

50 

51 

1.251 

1.287 

1,759 

2,504 

.     1,987 

1,932 

51 

52 

1.500 

1.480 

1.310 

1,770 

2,483 

1,902 

1,928 

52 

63 

1.451 

1.633 

(1.432) 
[1.567] 

1,838 

2,556 

2,169 

1,927 

53 

54 

1.180 

1.443 

1,846 

2,654 

2,333 

1,908 

54 

55 

1.577 

1.610 

• 

1,802 

2,517 

1,933 

1,894 

55 

56 

2.081 

2.245 

1,800 

2,329 

2,058 

1,908 

56 

57 

2.169 

2.719 

1.959 

1,750 

2,282 

2,429 

1,938 

57 

58 

1.854 

2.002 

(2.015) 
[2.015] 

!      1,796 

2,172 

2,128 

1,971 

58 

59 

1.721 

1.757 

1,942 

2,194 

2,026 

1,985 

59 

60 

1.773 

2.306 

1,893 

2,581 

2,543 

1,955 

60 

61 

1.866 

2.277 

1,898 

2,741 

2,344 

1,921 

61 

62 

2.266 

2.569 

2.687 

1,792 

2,454 

2,151 

1,898 

62 

63 

2.880 

3.131 

(2.822) 

1,712 

2,032 

2,083 

1,916 

63 

64 

3.868 

4.023 

[2.863] 

1,914 

1,769 

2,049 

1,970 

64 

65 

3.348 

3.421 

2,130 

1,889 

2,033 

1,990 

65 

66 

3.237 

4.340 

2,078 

2,089 

2,625 

1,958 

66 

67 

4.024 

6.409 

4.357 

1,750 

2,039 

3,000 

1,884 

67 

68 

5.134 

6.496 

(4.937) 

1,529 

2,042 

^333 

1,844 

68 

69 

5.674 

5.961 

[4.370] 

1,607 

2,077 

2,000 

1,904 

69 

70 

3.697 

4.664 

1,515 

1,400 

2,500 

1,981 

70 

71 

3.563 

5.495 

1,750 

2,143 

3,125 

2,027 

71 

72 

4.167 

5.989 

5.250 

1,773 

2,167 

2,875 

2,000 

72 

73 

4.459 

4.831 

(5.617) 
[6.844] 

1,864 

2,000 

2,143 

1,978 

73 

74 

8.907 

8.696 

2,071 

2,571 

1,909 

1,956 

74 

75 

10.369 

11.475 

1,300 

2,250 

2,100 

1,887 

75 

76 

9.032 

8.108 

1,333 

1,000 

1,714 

1,910 

76 

77 

16.000 

13.492 

14.776 

1,600 

.... 

1,700 

2,016 

77 

78 

19.149 

16.915 

(12.232) 
[10.662] 

2,250 

1,500 

1,889 

3,138 

78 

79 

15.385 

3.889 

3,250 

1,500 

2,000 

2,215  , 

79 

80 

25.000 

20.408 

3,500 

1,667 

2,042 

80 

81 

40.000 

32.836 

.... 

1,571 

1,914 

81 

82 

18.182 

30.435 

.... 

3,500 

2,091 

82 

83 

11.111 

37.500 

(22.01) 
[12.51]  ! 

1,000 

6,000 

1,778 

83 

84 



1,000 



■1,286 

84 

85 

16.667 

25.000 

*  •  •  • 

2,000 

1,333 

85 

86 

20.000 

33.333 

.... 

2,000 

1,200 

86 

87 

.... 

1 

1,000 

.... 

1,000 

87 

88 

.... 

.... 

(21.43) 

[22.82] 

1,000 

.... 

1,000 

88 

89 

AU 
Ages. 

50.000 

50.000 

1,000 

1,000 

89 

1.1581 

1.2344 

1 

i 

1,744 

2,216 

2,070 

1,942 

enclosed  in  parentheses  are  the  quinquennial  values  from  the  preceding  column  or  from  Death 
Claims  (1874).  And  the  values  in  brackets  are  the  quinquennial  ratios  from  the  Female  Experience 
of  the  Twenty  British  Offices. 


166 


TABLE     lY 


FEMALE  LIFE  (B)      ANNUAL  MORTALITY  AND  DISCONTINUED  PER  CENT.  OF  THE  EX- 
POSED   ACCORDING  TO  YEARS  OF  INSURANCE.     ALSO,  AVERAGE  SUM  INSURED. 


«>-  2 

Mortality 

Discontinued 

D.  and  Dis. 

Average  Sum  Insured.              <»  «  1 

0 

Per  Cent 

.  (1874.) 

Per  Cent 

.   (1874.) 

Per  Cent. 
(1874.) 

(1874.) 

•0    oS 

B7  Lives. 

By  Am'ts. 

By  Lives. 

By  Am'ts. 

By  Am'ts. 

Existing. 

Discon- 
tinued. 

Died. 

■ 

Exposed. 

jS  s 

.861 

.934 

9.146 

7.716 

8.579 

1,790 

$ 

1,665 

2,158 

1,989 

0 

1 

1.081 

1.120 

20.576 

19.700 

20.610 

1,782 

1,914 

2.082 

2,010 

1 

2 

1.062 

1.088 

11.549 

14.037 

14.978 

1,708 

2,476 

2,061 

2,010 

2 

3 

1.139 

1.274 

10.633 

14.148 

15.248 

1,622 

2,672 

2,206    1,973 

3 

4 

1.156   • 

1.321 

8.781 

12.083 

13.250 

1,688 

2,701 

2,206 

1,930 

4 

5 

1.280 

1.434 

7.210 

10.566 

11.853 

1,685 

2,821 

2,121 

1,893 

5 

6 

1.401 

1.541 

5.561 

7.282 

8.713 

'  1,776 

2,476 

2,063 

1,875 

6 

7 

1.331 

1.353 

6.955 

8.636 

9.875 

1  1,830 

2,335-  1,895 

1,864 

7 

B 

1.064 

1.159 

4.504 

6.270 

7.358 

1,854   ,  2,578  ,  2,000  !  1,836 

8 

U 

1.726 

1.541 

4.226 

4.923 

6.390 

j  1,718 

2,097  i  1,600 

1,792 

9 

10 

1.382 

1.359 

3.892 

4.896 

6.190  1 

1,685 

2,286 

1,778 

1,808 

10 

11 

1.494 

1.598 

3.365 

3.316 

'    4.861 

1,952 

1,800 

1,955 

1,828 

11 

12 

1.329 

1.197 

2.397 

2.516 

3.684 j 

1,869     1,897 

1,625 

1,804 

12 

13 

1.538 

2.110 

1.269 

1.362 

3.443  i 

2,419     1,928 

2,471 

1,801 

13 

14 

1.056 

.921 

1.628 

1.512 

2.419 

2,463     1,647 

1,545 

1,772 

14 

15 

1.143 

1.796 

1.247 

1.440 

3.210 

1,978   '  2,000 

2,727 

1,736 

15 

16 

1.672 

2.742 

.672 

.922 

3.639 

2,649     2,333 

2,800 

1,708 

16 

17 

1.314 

1.455 

1.195 

1.527 

2.960 

1,906     2,100 

1,818 

1,642 

17 

18 

2.171 

1.646 

1.538 

1.100 

2.728 

2,077     1,167 

1,235 

1,630 

18 

19 

1.509 

1.605 

1.373 

1.689 

3.266 

1,815     2,000 

1,727 

1,624 

19 

20 

1.901 

2.813 

.589 

.734  1 

3.526 

1,756     2,000 

2,385 

1,611     20  1 

21 

2.875 

2.833 

.646 

1.325  1 

4.121 

1,511     3,250 

1,556 

1,579 

21 

22 

.897 

.568 

1.253 

1.358 

1.919 

1,633     1,714 

1,000 

1,578 

22 

23 

2.459 

1.949 

.414 

.393 

1      2.335 

1,434     1,500 

1,250 

1,577 

23 

24 

3.121 

3.293 

.288 

.352 

3.633 

1,633   ,  2,000 

1,727 

1,637 

24 

25 

1.031 

.631 

.631 

1,615 

1,000 

1,634 

25 

26 

1,593 

1,686 

26 

27 

2,500 

2,182 

27 

28 

1,500 

1,333 

28 

29 

1,000 

29 

30 

1,000 

1,000 
1,942 

30 

1.158 

1.234 

10.954 

12.412 

\  13.499 

1,744     2,216 

2,070 

TABLE    lY. 

FEMALE   LIFE   (C.)     LOGARITHM    OF   THE   AVERAGE   FACTORS  (tcl  (WV^),  TO  CARRY 
FORWARD  THE  AMOUNTS  EXISTING  IN  TABLE  II  TO  THEIR  PROPORTIONAL  TER- 
MINATIONS INCLUSIVE  IN  THE  FOLLOWING  CJOLUMNS,  i.  e.  TO  FINAL  SERIES. 


Years  of 

• 

Insurance. 
n. 

Log  w. 

hog(w.V^) 

Years. 
n. 

10 

Log  w. 

hog{tV.V"') 

Years. 
n. 

Log  w. 

Log(w.'y") 

0 

0.00000 

0.00000 

0.86339 

0.69306 

20 

1.21692 

0.87625  1 

1 

.02133 

.00430 

11 

.95711 

.76974 

21 

.24727 

.88957 

z 

.04603 

.01196 

12 

1.03036 

.82596 

22 

.27938 

.90465 

3 

.08533 

.03423 

13 

.05439 

.83296 

23 

.33135 

.93958 

4 

.12601 

.05788 

14 

.07156 

.83309 

24 

.44621 

1.03741 

5 

0.18963 

0.10446 

15 

1.10460 

0.84910 

25 

1.69101 

1.26518 

6 

.27044 

.16824 

16 

.12902 

.85649 

7 

.38586 

.26663 

17 

.15871 

.86914 

1 

V — 
1.04 

8 

.54308 

.40681 

18 

.17888 

.87228 

9 

.72467 

.57137 

19 

.19810 

.87447 

TABLE  Y. 

PROBABLE  LOSS  AND  ACTUAL  LOSS  BY  STATES  AND  TERRITORIES. 


167 


states,  &c. 


Alabama . . 
Arizona . . 
Arkansas . 
California. 
Colorado. . 


Connecticut 

Dakota 

Delaware 

District  of  Columbia. 
Florida 


Georgia 

Idaho 

Illinois 

Indiana 

Indian  Territory. 

Iowa  

Kansas.   

Kentucky  ...... 

Louisiana 

Maine 


Maryland 

Massachusetts. 
Michigan. ..  . 
Minnesota. . . . 
Mississippi 


Missouri , 

Montana 

Nebraska 

Nevada 

New  Hampshire. 

New  Jersey 

New  Mexico 

New  York. 

North  Carolina . 
Ohio 


Oregon 

Pennsylvania .  . 
Rhode  Island . . 
South  Carolina. 
Tennessee 

Texas 

Utah 

Vermont 

Virginia 

Washington . . . 

West  Virginia. . 

Wisconsin 

Wyoming 

Unknown , 


British  America . 
Other  Foreign . . 


Total $104,531,520 


Probable  Loss. 


$1,204,521 

2,230 

295,413 

2,489,469 

150,821 

3,604,783 

5,412 

253,963 

580,298 

181,635 

950,653 

23,532 

7,320,753 

2,465,769 

10,007 

1,659,034 

454,910 

2,169,340 

1,363,520 

1,826,915 

2,573,670 
11,977,364 

2,371,856 
735,380 
795,476 

4,336,484 

21,824 

223,736 

157,256 

1,264,848 

2,666,988 

17,778 

22,271,323 

843,815 

5,689,260 

164,380 
10,393,537 

1,058,688 

753,060 

1,383,648 

778,713 

14,328 

723,750 

646,188 

23,270 

314,438 

3,009,760 

4,022 

37,337 

1,425,150 
841,215 


Actual  Loss. 


$1,618,048 

5,000 

508,119 

3,414,340 

131,000 

3,369,951 

5,000 

224,526 

660,006 

303,852 

911,536 

15,743 

6,365,344 

2,590,728 

5,000 

1,255,512 
.  391,470 
2,237,220 
2,400,915 
1,511,492 

3,311,815 

10,309,004 

2,119,010 

785,907 

1,308,632 

4,810,720 

5,000 

136,300 

177,905 

1,123,093 

2,515,832 

29,500 

21,059,726 

1,069,409 

5,292,302 

141,000 

9,578,003 

945,152 

864,635 

2,262,121 

1,358,972 

39,500 

578,092 

673,350 

6,000 

255,755 

2,316,213 

1,000 

67,818 

1,033,812 
948,616 


$102,048,996 


Satio. 


100:134 

224 

172 

97 

87 

94 

92 

88 

114 

167 

96 
67 
87 
105 
50 

76 

86 

103 

176 

83 

129 

86 

89 

107 

164 

111 
23 
61 

113 

89 

94 
166 

95 
127 

93 

86 
92 

•89 
115 
163 

175 

276 

80 

104 

81 

77 

182 

73 
113 


98 


Note.  Tables  V,  VI  and  VII  refer  to  the  common  American  Table  of  1858.  To  change  to  the 
Thirty  Offices  Table,  subtract  J^tt  part  from  the  Probable  Loss.  Or  add  ^ih  to  the  last  term  of  the 
Ratio. 


168 


TABLE    YI. 


ORDER  AND  VARIABILITY  OF  RATIOS  OF  PROBABLE  TO  ACTUAL  LOSS  IN 

THIRTY-FIVE  STATES. 


States  and  District. 


Iowa 

Wisconsin 

Vermont 

West  Virginia. 
Maine 


EatioB. 


Number  of  Companies. 


27      12     6      9 


Oregon . 

Kansas 

Massachusetts. 

Illinois 

Delaware 


Rhode  Island 

Michigan 

New  Hampshire. 
Pennsylvania . .  . 
Ohio 


Connecticut. 
New  Jersey. . 
New  York. . 
Georgia .... 
California  . 


Kentucky . 
Virginia . . 
Indiana . . . 
Minnesota . 
Missouri. . 


District  of  Columbia. 
South  Carolina...... 

North  Carolina 

Maryland 

Alabama 


100 :  76 

77 
80 
81 
83 

86 
86 
86 

87 
.88 

89 
89 
89 
92 
93 

94 
94 
95 
96 
97 

103 
104 
105 
107 
111 

114 
115 
127 
129 
134 


Tennessee . 
Mississippi. 

Florida 

Arkansas.  . 

Texas 

Louisiana. 


Average . 


62 

74 
78 
58 


93     78 


102 

68 
80 
81 


77 
96 
81 
82 
83 

73 

78 
90 
89 
96 

106 

86 

104 

114 

96 

95 
123 
103 
137 
108 


163  156 

164  121 
1671120 


94 

88 

81 

100 


172 
175 
176 

98 


230 
170 


103 

112 
88 
86 

109 

98 
84 
92 
95 

97 

104 
111 

98 
118 
105 

81 

100 

99 

94 

121 

124 
71 

105 
131 
148 

123 

43 

357 

180 
192 


119  218 


90 


96 


80 
81 
82 
93 
83 

50 
92 
95 
98 
104 

84 
93 
91 
97 
102 

104 

105 

98 

96 


123 

130 

116 

92 

122 

141 
113 
163 
119 
156 

179 
203 
219 
117 
177 
211 

111 


Thousand  Dollars  Loss. 


12 


Frob.  L.  Act.  L, 


870 
2,122 
305 
108 
512 

72 

218 

3,654 

2,776 

43 


538 

1,559 

236 

63 

475 

74 

149 

2,934 

2,259 

1 


316   242 

686   657 

377   307 

3,030  1 2,472 

2,107  1,746 


1,234 

1,185 

9,071 

353 

959 

701 
309 

1,045 
469 

1,835 

280 
499 
306 
847 
531 

498 
310 
120 
141 
256 
525 


1,074 


905 
921 
8,126 
314 
920 

743 
.  265 
1,088 

537 
1,768 

266 
615 
315 
1,161 
571 

777 
376 
145 
324 
434 
625 


970 


Frob.  L.  Act.  L 


611 

530 

288 

23 

1,113 

40 

124 

7,244 

2,823 

80 

687 
1,203 

742 
3,018 
2,229 

1,683 
598 

7,690 
117 
880 

736 
97 
855 
144 
906 

173 

91 
214 
746 

70 

176 
33 
18  i 
6  ! 
35  I 
43 


999 


575 
468 
234 
23 
870 

42 

139 

6,346 

2,427 

87 

572 
1,012 

683 
2,872 
2,169 


9 


Frob.  L.  Act.  L 


177 
358 
131 
184 
202 

52 

113 

1,080 

1,722 

132 


143 

289 
107 
170 
167 

26 

103 

1,029 

1,680 

137 


156   131 

484   450 

146  i  134 

4,346  14,234 

1,354   377 


1,751   687 

.663   885 

7,515,  5,510 

137   481 
923   651 


595 

97 

846 

136 

1,101 

214 
65 
225 
979 
104 

218 
14 
63 
10 

67 
93 

954 


733 
241 
565 
122 

1,595 


714 
932 
5,419 
460 
571 

900 
312 
657 
113 
1,942 


127  179 
163  '  185 
324  529 
981  , 1,171 
603   943 

710  1,268 
453   918 


44 
149 

488 
796 

749 


97 
174 

857 
1,683 

838 


TABLE    YII.  169 

PROBABLE  LOSS  AND  ACTUAL  LOSS  BY  COUNTIES  IN  TWELVE  STATES. 
STATE   OP  ALABAMA. 


Counties. 

Frob.  Loss. 

Actual  Loss. 

Counties. 

Prob.  Loss. 

Actual  Loss. 

Autauga  . . 

$3,403 

•    5,220 

Lowndes  . . 

18,785 

17,720 

Baker  . . 

219 

.... 

Macon  . . 

18,814 

25,820 

Baldwin  . 

1,952 



Madison 

26,163 

44,600 

Barbour  . .  . 

22,093 

10,220 

Marengo . . 

25,991 

21,000 

Bibb  .. 

1,882 

5,220 

Marion 

535 

Blount 

198 

.  •  •  • 

Mobile . 

394,284 

544,453 

Bullock  . . 

11,868 

18,440 

Monroe  .  . . 

3,782 

5,220 

Butler  . . . 

12,833 

20,880 

Montgomery  . . 

94,225 

171,574 

Calhoun 

7,739 

15,420 

Morgan 

2,763 

1,000 

Chambers 

16,168 

20,880 

Perry  . . 

63,414 

63,260 

Cherokee 

528 



Pickens  . . 

19,328 

39,000 

Choctaw  . . . 

4,220 

.... 

Pike  . . . 

2,091 



Clarke  ... 

985 

.... 

Kaudolph 

1,236 

! 

Clay 

1,169 

.... 

Russell  . . 

6,529 

30,440 

Coffee  . . . 

552 

Shelby 

4,831 

6,500 

Colbert 

3,029 

10,440 

St.  Clair 

2,685 

5,220 

Conecuh  . . . 

1,831 

5,000 

Sumpter  . . 

14,185 

10,000 

Coosa 

1,291 

>  •  •  • 

Talladega 

18,576 

19,100 

Covington  . .  . 

19 

.... 

Tallapoosa 

'      3,169 

.... 

Crenshaw  .  . . 

2,049 

*  *  .  • 

Tuscaloosa 

18,138 

5,000 

Dale  ... 

1,389 

-  •  . 

Walker 

411 

5,000 

Dallas  . . 

114,320 

151,700 

Washington  . .  . 

1,581 

10,220 

Elmore 

7,586 

2,500 

Wilcox  . . 

28,311 

33,000 

Escambia  . . . 

227 

Unknown 

6,085 

15,000 

Etowah 
Fayette 

2,596 

597 



Additional 
Total 

103,216 

134,941 

1,204,521 

1,618,048 

Franklin 

3,575 

.... 

Ratio 

100 

:134 

Greene  . . 
Hale  .. 

37,285 
7,901 

79,140 
6,000 

Henry  . . . 

2,895 

! 

Alluvial. 

396,236 

544,453 

Jackson 

1,065 

.... 

Ratio 

100 

:137 

Jefferson 

6,371 

10,440 

Middle  . . 

175,977 

194,580 

Lauderdale 

4,616 

10,440 

Ratio 

100 

:111 

Lawrence 

11,310 

5,220 

Upland 

523,007 

729,074 

Lee 

22,109 

27,600 

Ratio 

100 

:139 

Limestone 

7,523 

5,220 

STATE  OP  ARKANSAS. 

Arkansas  . 

$3,270 

15,660 

Crittenden  . 

5,901 

16,630 

Ashley  . 

995 

5,000 

Cross  . 

837 

.... 

Benton 

411 

Dallas  .  . . 

3,457 

10,000 

Bradley  . . . 

1,656 

Desha  . 

3,625 

13,220 

Calhoun  . . . 

1,169 

.... 

Drew  . 

5,876 

15,660 

Carroll 

95 

Franklin 

197 

5,000 

Chicot  . 

4,588 

5,220 

Fulton 

334 

2,500 

Clarke 

2,390 

Grant' ... 

496 

.... 

Columbia  . .  . 

2,071 

5,220 

Greene  . .  . 

1,890 

5,220 

Conway 

2,178 

5,000 

Hempstead . . 

4,046 

10,220 

Craighead  . .  . 

199 

5,220 

Hot  Springs  . . . 

1,439 

.... 

Crawford 

6,868 

10,440 

Independence 

4,718 

5,000 

170  TABLE    YII. 

PROBABLE  LOSS  AND  ACTUAL  LOSS  BY  COUNTIES  IN  TWELVE  STATES. 


STATE    OP    ARKANSAS.— Continued. 


Counties. 

Frob.  Loss. 

Actual  Loss, 

Counties, 

Prob  Loss, 

Actual  Loss. : 

Izard 

131 

Scott 

322 

Jackson  . . . 

9,044 

19,440 

Sebastian 

7,581 

15,220 

Jefferson  . 

25,782 

42,050 

Sevier  . . 

104 

.... 

Johnson 

1,556 

1,000 

Sharpe 

142 

.... 

Lafayette  .  . . 

1,148 

St.  Francis. 

2,677 

10,220 

Lawrence 

599 

.... 

Union  . . . 

9,463 

Little  River  . . . 

1,484 

10,000 

Washington 

1,071 

.... 

Madison 

103 

.... 

White 

3,322 

5,220 

Marion 

65 

.... 

Woodruff  . . . 

9,075 

8,000 

Mississippi  . 

2,849 

Yell 

1,361 

6,000 

Monroe  . . . 

3,041 

5,424 

Unknown 

15,615 

4,000 

Montgomery 
Ouachita 
Perry  , 
Phillips  . 
Pike 

19 
8,744 

15,660 

Additional 
Total 

9,909 

6,000 

295,413 

508,119 

42,049 
570 

98,335 
3,000 

Ratio 

100 

:  172 

Poinsett  . . . 

149 

Alluvial  . 

98,449 

221,995 

Polk 

7 

Ratio 

100 

:226 

Pope 

482 

i,'66o 

Middle  ... 

125,202 

196,084 

Prairie  . . . 

3,829 

7,220 

Ratio 

100 

:157 

Pulaski  . .  . 

71,442 

110,120 

Upland 

46,238 

80,040 

Randolph 

2,724 

5,000 

Ratio 

100 

-.173 

Saline 

248 

... 

S 

.TATE   OP 

PLORIDA. 

Alachua  . 

6,419 

42,500 

Orange . 

350 

Baker  . 

404 

' ' '  * 

Polk  . 

12 

.... 

Bradford  . 

282 

Putnam  . 

3,385 

1,000 

Clay  . 

566 

5,'66o 

Santa  Rosa  . 

4,455 

.... 

Columbia  . 

86 

3,000 

St.  Johns  . 

2,527 

.... 

Dade. 

369 

.... 

Sumpter  . 

62 

.... 

Duval. 

31,126 

66,111 

Suwannee  . 

1,201 

Escambia  . 

23,796 

29,000 

Volusia  . 

17 

1,000 

Franklin  . 

7,689 

7,000 

Wakulla  . 

57 

Gadsden  . 

5,465 

15,000 

Walton  . 

164 

Hamilton  . 

753 

Unknown 

380 

11,000 

Hernando  . 

380 

.  •  .  . 

Additional 

18,781 

35,706 

Hillsborough  . 

564 

Jackson  . .  . 

5,960 

25,000 

Total 

181,635 

303,852 

Jefferson  . 

9,911 

10,000 

Ratio 

100 

:  167 

Leon  (Tallahassee). 
Levy  . 

23,461 
90 

33,435 

Madison  . . . 

22,798 

7,550 

Alluvial . 

133,347 

224,596 

Marion  . 

1,942 

Ratio 

100 

:  169 

Monroe(KeyWest). 

4,971 

2,000 

Middle  . . . 

28,758 

32,550 

Nassau. 

3,212 

9,550 

Ratio 

100 

:113- 

TABLE    YII.  171 

PROBABLE  LOSS  AND  ACTUAL  LOSS  BY  COUNTIES  IN  TWELVE  STATES. 
STATE    OF    GEORGIA. 


Counties. 

Prob.  Loss. 

Actual  Loss. 

Counties. 

Prob.  Loss. 

Actual  Loss. 

Appling  .  .  . 

1263 

Jackson 

1,058 

.... 

Baker  . .  . 

1.028 

Jasper 

916 

.... 

Baldwin 

9,221 

Jefferson  . . . 

9,169 

Bartow 

3,524 

14,500 

Johnson  . . , 

4,477 

11,250 

Berrien  . . . 

99 

.   •>   r    . 

Jones 

404 

.... 

Bibb 

63,130 

78,380 

Laurens  . . . 

945 

•  •  •  • 

Brooks  . . . 

2,003 

.... 

Lee  . .  . 

4,811 

10,220 

Brvan  . .  . 

52 

.... 

Liberty  . . . 

1,045 

.... 

Bullock   ... 

95 

Lincoln 

2,185 

.... 

Burke  . .  . 

5,033 

7,666 

Lowndes  . .  . 

5,637 

2,500 

Butts 

13 

Lumpkin 

297 

.... 

Calhoun  . .  . 

99 

Macon  . . . 

4,294 

5,220 

Camden . 

1,876 

2^566 

Marion  . . 

2,005 

10,220 

Campbell 

2,913 

.... 

Mcintosh  . . . 

429 

•  •  .  • 

Carroll 

1,174 

•  •  •  • 

Merriweather 

343 

.  .  -  . 

Case 

285 

Miller  . . . 

180 

•  •  .  • 

Catoosa 

47 

.... 

Mitchel  . . . 

1,718 

Charlton . 

241 

5,000 

Monroe 

7,202 

5,220 

Chatham  . .  . 

200,436 

259,895 

Montgomery  . .  . 

544 

.... 

Chattahoochee  . ; 

185 

.... 

Morgan 

7,512 

10,440 

Chattooga 

496 

.... 

Murray 

808 

.... 

Cherokee 

231 

.... 

Muscogee  . . 

47,445 

59,597 

Clarke 

26,408 

15,220 

Newton 

3,407 

.... 

Clay  . . . 

1,449 

Oglethorpe 

4,318 

.... 

Clinch  ... 

279 

Pierce  . . . 

883 

7,500 

Cobb 

17,259 

10^666 

Pike 

1,757 

5,000 

Coffee  . . . 

73 

.... 

Polk 

492 

6,000 

Columbia 

7,171 

2,000 

Pulaski  .  . . 

7,502 

11,440 

Coweta 

9,870 

10,440 

Putnam 

9,462 

Crawford 

142 

Quitman  . .  . 

633 

•  •  •  . 

Dade 

269 

.... 

Eandolph  .  . . 

6,901 

Decatur  . . . 

4,064 

17,220 

Eichmond  . . . 

107,140 

83,160 

De  Kalb 

1,868 

Schley  . . 

959 

.... 

Dooly  . .  . 

492 

Scriven  . . . 

483 

.... 

Dougherty  . . . 

16,371 

28,308 

Spalding 

16,084 

.  ■ . . 

Early  . .  . 

3,137 

Stewart  . . 

4,885 

Effingham  . .  . 

427 

Sumpter  . . . 

20,040 

21,240 

Elbert 

1,305 

Talbot  . . 

5,004 

5,000 

Floyd 

13,686 

Tatnall  . .  . 

•   475 

.... 

Forsyth 

703 

Taylor  . . 

1,815 

.... 

Fulton 

101,439 

59',  666 

Telfair  . . . 

1,273 

.... 

Glynn  . . . 

3,361 

5,000 

Terrell  . . . 

10,814 

5,000 

Gordon 

664 

Thomas  . . . 

10,459 

5,330 

Greene 

1,963 

3^666 

Troup 

9,145 

5,220 

Gwinnett 

198 

.... 

Twiggs  . . . 

2,882 

10,000 

Hall 

98 

Union 

76 

•  •  •  . 

Hancock 

4,262 

13,666 

Upson  . . 

578 

•  •  •  . 

Harris  . . 

558 

.... 

Walker 

82 

•  •  •  • 

Hart 

18 

Walton 

3,753 

•  •  •". 

Heard 

793 

Ware  .  . . 

707 

•  •  •  • 

Henry 

15 

.... 

Warren 

3,506 

.  •  .  . 

Houston  . . . 

12,837 

17,940 

Washington  . . . 

3,451 

15,000 

Irwin  . . . 

424 

Wayne.  . . . 

347 



173 


TABLE     YII. 


PROBABLE  LOSS  AND  ACTUAL  LOSS  BY  COUNTIES   IN  TWELVE  STATES. 
STATE  OF  GEORGIA.— Continued. 


Counties. 

Prob.  Loss. 

Actual  Loss. 

Counties. 

Froh.  Loss. 

Aotual  Loss, 

Webster  ...   * 

$394 

Alluvial  . 

2,117 

7,500 

White 

760 

.... 

Ratio 

100 

:354 

Whitfield 

5,686 

10,440 

-Middle  . . . 

524,221 

603,540 

Wilcox  . .  . 

83 

1,000 

Ratio 

100 

:  115 

Wilkes 

7,320 

10,000 

Upland 

355,738 

257,860 

Wilkinson  . .  . 

983 

Ratio 

100 

:  72 

Worth  . . . 

66 

i  Unknown 

6,691 

8,500 

Additional 

61,886 

38,636 

Total 

950,653 

911,536 

Ratio 

100 

:  96 

STATE  OP  LOUISIANA. 

r 

Parishes. 

Parishes. 

Ascension  . 

$937 

•  •  ■  • 

Plaquemines  . 

2,577 

7,000 

Assumption  . 

2,088 

.... 

Point  Coupee  . 

19,361 

27,380 

Avoyelles  . 

19,799 

20,880 

Rapides  . 

9,458 

7,000 

Bienville  . . . 

2,968 

5,220 

Richland  . 

2,320 

5,220 

Bossier  . 

4,734 

5,220 

St.  Charles  . 

472 

.... 

Caddo  , 

50,677 

134,090 

St.  Helena  . . . 

2,070 

.... 

Calcasieu  . 

505 

St.  James  . 

1,040 

10,000 

Caldwell  . 

1,297 

3,000 

St.  Landry  . 

10,677 

10,440 

Carroll  . 

12,683 

15,440 

St.  Martin  . 

13,457 

^  5,220 

Catahoula  .  . . 

3,347 

10,220 

St.  Mary  . 

6,668 

11,440 

Claiborne  . .  . 

5,832 

St.  Tammany  . 

502 

Concordia  . 

4,094 

Tangipahoa  . 

848 

i,6oo 

De  Soto- .  .  . 

4,138 

15,220 

Tensas  . 

14,095 

20,880 

E.  Baton  Eouge  . 

14,447 

18,440 

Terrebonne  . 

3,703 

30,000 

E.  Feliciana  . 

21,616 

61,100 

Union    . .  . 

2,413 

.... 

Franklin  . 

4,861 

14,220 

Vermilion  .    . 

468 

5,220 

Grant  . 

■  2,747 

.... 

Washington  .  . . 

2,631 

. . .  .• 

Iberia  . 

1,091 

... 

W.  Baton  Rouge . 

3,181 

10,220 

Iberville  . 

5,275 

15,660 

W.  Feliciana  . 

10,751 

32,440 

Jackson  . . . 

•   487 

Winn  . . . 

15 

Jefferson  . 

16,427 

li,300 

Unknown 

20,208 

23,000 

Lafayette  . 

6,290 

.... 

Additional 

67,231 

153,000 

Lafourche  . 
Livingston  . 
Madison  . 

7,505 

583 

3,618 

26,262 
26,'220 

Total 
Ratio 

1,363,520 
•100 

2,400,915 
:  176 

Morehouse  .  • 

8,024 

8,350 

Alluvial  . 

1,252,180 

2,194,255 

Natchitoches  . 

4,096 

10,000 

Ratio 

100 

:  175 

Orleans  . 

949,144 

1,593,793 

Middle  . .  . 

23,901 

30,660 

Ouachita  . 

10,064 

52,820 

Ratio 

100 

:128 

TABLE     YII. 


173 


PROBABLE  LOSS  AND  ACTUAL  LOSS  BY  COUNTIES  IN  TWELVE  STATES. 


STATE  OF  MISSISSIPPI. 


Counties. 

Frob.  Loss. 

Actual  Loss, 

Counties.                Pr 

ob,  Loss. 

Actual  Loss. 

Adams . 

33,747 

43,220 

Montgomery  . .  . 

49 

5,220 

Alcorn  . . 

3,239 

Neshoba  . . 

105 

.... 

Amite  . . . 

21,673 

5,000 

Newton  . . 

.      910 

.... 

Attala  . . . 

1,546 

10,000 

1  Noxubee  . . 

23,170 

15,255 

Bolivar  . 

16,677 

93,520 

Oktibbeha  . . 

12,837 

5,179 

Calhoun  . . . 

1,933 

Panola  . 

17,765 

26,100 

Carroll  . . . 

14,214 

15,440 

Perrv  . . . 

99 

5,220 

Chickasaw  . . 

5,995 

10,440 

Pike" . .  . 

10,667 

51,440 

Choctaw  . . . 

5,584 

12,720 

Pontotoc  . . 

2,006 

.  •  •  . 

Claiborne  . 

7,535 

5,000 

Prentiss   . . 

29 

•  •  •  • 

Clark  . . . 

12,427 

17,220 

Eankin  . .  . 

3,947 

11,500 

Coahoma  . 

12,571 

27,440  !'  Scott  ...                | 

942 

\       

Copiah  .  . . 

18,284 

19,930 

Simpson  . . . 

132 

.... 

Covington  . .  . 

2,500 

:  Smith  ... 

2,075 

.... 

De  Soto  . 

22,695 

43,760 

Sunflower. 

3,488 

10,220 

Franklin  . .  . 

3,183 

]  Tallahatchie 

13,442 

10,440 

Grenada  . . . 

22,809 

39,540 

1  Tippah  . . 

2,151 

.... 

Hancock  . 

794 

3,000 

Tishemingo  . . 

1,927 

Harrison  . 

5,734 

12,440 

Tunica  . 

7,191 

10,220 

Hinds  . .  . 

41,040 

90,660 

Union  . . 

1,141 

5,220 

Holmes  .    . 

8,614 

23,440 

Warren(Vicksb'g). 

95,136 

151,200 

Issaquena  . 

5,243 

5,000 

Washington  - 

19,770 

51,760 

Itawamba  . . 

1,438 

.... 

Wayne  .  . . 

194 

.... 

Jackson  . 

4,850 

.... 

Wilkinson  . 

8,559 

20,000 

Jasper  . .  . 

2,305 

Winston  . . 

2,545 

2,000 

Jefferson  . 

9,951 

30,660 

Yalabusha  . .  . 

22,858 

26,100 

Kemper  . . 

3,034 

7,000 

Yazoo  . 

29,381 

18,720 

Lafayette  . . . 

14,357 

15,660 

Unknown 

21,650 

51,000 

Lauderdale  . . 

12,515 

18,000 

Additional 

42,622 

104,368 

LaWrence  .  . . 
Leake  . . . 
Lee  . . 

6,739 

877 

3,151 

6,564 

10,000 

5,000 
5,220 

Total                       ^ 
Eatio 

95,476 
100 

1,308,632 
:  164 

Lincoln  . . . 

Alluvial .                     a 

01,087 

552,260 

Lowndes  . . . 

50,669 

82,670 

Ratio 

100 

:  184 

Madison  . . . 

25,873 

41,220 

Middle  ...                  4 

-16,626 

585,344 

Marion  . . , 

Eatio 

100 

:  140 

Marshall  . . . 

34,520 

16,*550 

Upland 

13,491 

15,660 

Monroe  . . 

6,308 

15,220 

Eatio 

100 

:  116 

STATi 

3  OP  NORTH   CAROLINA. 

' 

Alamance 

4,556 

5,000 

Camden  . 

878 

Alexander 

8 

.  •   •    • 

Carteret . 

7,652 

18,500 

Anson 

5,714 

1,000 

Caswell 

1,488 

15,000 

Beaufort  . 

7,920 

2,000 

Catawba 

1,841 

Bertie  . 

15,815 

24,000 

Chatham 

6,455 

8,000 

Bladen  . . , 

10,342 

12,000 

Cherokee 

57 

... 

Brunswick  . 

66 

.... 

Chowan  . 

4,866 

16,000 

Buncombe 

653 

.... 

Cleaveland 

3,450 

7,500 

Burke 

458 

7,'o6o 

Columbus  . .  . 

2,068 

2,000 

Cabarrus 

3,494 

2,000  ' 

Craven  . 

41,103 

82,620 

Caldwell 

2,299 

1,000  1 

Cumberland  . . . 

23,112 

17,000 

174  TABLE     YII. 

PROBABLE  LOSS  AND  ACTUAL  LOSS  BY  COUNTIES  IN  TWELVE  STATES. 
STATE  OP  NORTH  CAROLINA.— Continued. 


Counties. 

Prob.  Loss.  ■ 

Actual  Loss. 

Counties. 

Prob.  Loss. 

Actual  Loss. 

Currituck  . 

$286 

Pasquotank  . 

8,794 

15,000 

Davidson 

3,280 

Perquimans  . 

4,307 

4,000 

Davie 

1,215 

Person 

110 

.... 

Duplin  . . . 

6,115 

.... 

Pitt  . .  . 

13,556 

22,000 

Edgecombe  . . . 

48,389 

11,000 

Polk 

123 

.... 

Forsyth 

1,508 

2,000 

Randolph 

1,653 

.... 

Franklin  . . . 

8,369 

6,000  i    Richmond  ...        | 

4,481 

... 

Gaston 

3,246 

20,000 

Robeson  . . . 

6,924 

6,500 

Gates  . 

4,909 

16,500 

Rockingham 

2,100 

.... 

Granville 

14,830 

.  •  • 

Rowan 

18,079 

15,000 

Greene  . .  . 

13,266 

13,000 

Rutherford 

1,719 

.... 

Guilford 

7,260 

7,000 

Sampson  ... 

7,421 

2,000 

Halifax  . .  . 

28,183 

55,000 

Stanley 

123 

.... 

Harnett  . . . 

3,368 

...  * 

Stokes 

180 

Haywood 

114 

.... 

Surry 

285 

.... 

Henderson 

178 

.... 

Tyrrell . 

1,526 

2,000 

Hertford  . . . 

3,576 

5,000 

Union 

761 

.... 

Hyde  . 

726 

.... 

Wake  . . . 

128,886 

131,633 

Iredell 

5,252 

5,000 

Warren 

11,350 

13,000 

Jackson 

1,045 

.... 

Washington  . 

5,868 

1,085 

Johnston  . . . 

12,848 

20,000 

Watauga 

38 

.... 

Jones . 

1,593 

7,000 

Wayne  . . . 

22,752 

33,000 

Lenoir  . . . 

22,149 

62,000 

Wilkes 

354 

.... 

Lincoln 

4,430 

.  .  .  .  ' 

Wilson  . . . 

21,075 

36,500 

Macon 

285 

Yadkin 

855 

5,000 

Madison 

237 

Unknown 

16,053 

33,500 

Martin  . 
McDowell 
Mecklenburg 
Mitchell 

13,783 

3,872 

47,667 

45 

20,'o6o 

2,000 

66,720 

Additional 

Total 
Ratio 

32,981 

38,000  ] 

843,815 
100 

1,069,409 
:127 

Montgomery 

101 

More 

2,104 

.... 

Alluvial . 

225,053 

353,555 

Nash  . .  . 

2,740 

5,000 

Ratio 

100 

:157 

New  Hanover  . 

103,265 

144,850 

Middle  . . . 

390,924 

442,633 

Northampton  . .  . 

1,304 

3,000 

Ratio 

100 

:113 

Onslow  . 

1,696 

Upland 

178,804 

201,721 

Orange 

13,932 

19,501 

Ratio 

100 

:113 

STATE  OP  SOUTH  CAROLINA. 

Abbeville 

26,231 

23,940 

Edgefield 

7,285 

Anderson 

14,784 

33,820 

Fairfield 

13,682 

28,390 

Barnwell  . . . 

9,449 

2,000 

Georgetown  . 

7,177 

.... 

Beaufort . 

8,462 

15,000 

Greenville 

15,789 

17,914 

Charleston  . 

347,589 

417,440 

Horry  . 
Kersnaw  . . . 

5,360 

10,340 

Chester 

21,728 

31,000 

9,373 

•  •  •  • 

Chesterfield  . . . 

4,883 

5,000 

Lancaster 

4,257 

2,500 

Clarendon  . . . 

4,263 

1,500 

Laurens 

17,988 

38,720 

Colleton  . 

5,899 

3,658 

Lexington  . . . 

1,190 

. . . 

Darlington  . . . 

5,804 

7,000 

Marion  .  .• 

16,865 

10,000 

TABLE   YII.  175 

PBOBABLE  LOSS  AND  ACTUAL  LOSS  BY  COUNTIES  IN  TWELVE  STATES. 
STATE  OF  SOUTH  CAROLINA— Continued. 


Counties. 

Prob.  Loss. 

Actual  Loss. 

Counties. 

Prob.  Loss. 

Actual  Loss. 

Marlborough  . . . 

$5,412 

Unknown 

5,542 

9,000 

Newberry 

26,516 

10,720 

Additional 

1,715 

1  Oconee 
Orangeburgh  .  . . 
Pickens 

7 

20,718 

628 

16,253 

Total 
Eatio 

753,060 
100 

864,635 
:115 

Eichland  (Cohim- 
bia)  . . . 

90,086 

120,440 

Alluvial . 

374,487 

446,438 

Spartanburg 

7,446 

15,000 

Ratio 

100 

:119 

Sumter  . . . 

16,034 

15,000 

Middle  . . . 

192,307 

182,193 

Union 

6,707 

15,000 

Ratio  - 

100 

:95 

Williamsburg  . . . 

8,230 

5,000 

Upland 

179,009 

227,004 

York 

15,961 

10,000 

Ratio 

100 

:127 

- 

STATE  OF  TENNESSEE. 

Anderson 

1,365 

Henderson  . . 

1,683 

Bedford 

16,423 

31,660 

Henry  .  . . 

4,250 

10,220 

Benton  . . 

614 

Hickman 

2,329 

•  •  •  • 

Bledsoe 

545 

Humphreys 

710 

5,000 

Blount 

1,263 

•  •  .  ■ 

Jefferson 

1,337 

•  •  •  • 

Bradley 

8,422 

2,000 

Johnson 

99 

•  .  .  • 

Campbell 

1,585 

Knox 

27,321 

28,440 

Cannon 

99 

Lake  . 

616 

.... 

Carroll 

2,692 

.... 

Lauderdale  . 

16,212 

15,660 

Carter 

1,022 

.... 

Lawrence 

314 

.... 

Cheatham 

130 

Lincoln 

18 



Claiborne 

397 

.... 

Macon 

160 

Cocke 

149 

5,000 

Madison  . . . 

44,568 

38,320 

Coffee 

552 

2,000 

Marion 

2,555 

2,000 

Crocket 

99 

■  •  •  • 

Marshall 

4,325 

Cumberland 

802 

Maury 

59,708 

68,441 

Davidson     (Nash- 

McMinn 

3,602 

1,000 

ville) 

147,911 

208,386 

McNairy 

1,632 

.... 

Decatur  . . 

560 

Meigs 

992 

.... 

De  Kalb 

397 

2,000 

Monroe 

4,599 

3,0*68 

Dickson 

665 

.... 

Montgomery 

54,768 

48,640 

Dyer  . 

9,871 

10,440 

Obion  . . . 

9,517 

20,880 

Fayette  . . . 

40,039 

60,600 

Perry 

1,041 

•  •  •  • 

Franklin 

7,482 

2,500 

Polk 

3,238 

.... 

Gibson  . . . 

12,263 

20,880 

Rhea 

518 

.  •  .  • 

Giles 

22,868 

15,660 

Roane 

1,953 

.... 

Grainger 

2,629 

.... 

Robertson 

3,454 

10,440 

Greene 

2,675 

2,000 

Rutherford 

26,064 

73,880 

Grundy 

294 

.... 

Scott 

4,215 

.... 

Hamilton 

13,934 

5,000 

Sequatchie 

49 

.... 

Hancock 

496 

•  *  •  • 

Sevier 

397 

.... 

Hardeman  . . . 

8,174 

5,320 

Shelbv(Memphis  . 

652,127 

1,439,536 

Hardin  . . 

3,369 

.... 

Smith 

1,187 

•  •  .  • 

Hawkins 

496 

Stewart 

2,534 

•  •  •  • 

Haywood  . . . 

49,859 

47,040 

Sullivan 

1,381 



176  TABLE    Yll. 

PROBABLE  LOSS  AND  ACTUAL  LOSS  BY  COUNTIES  IN  TWELVE  STATES. 
STATE    OP   TENNESSEE. -Continued. 


Counties. 

Prob.  Loss. 

Actual  Loss. 

Counties. 

Prol).  Loss. 

Actual  Loss. 

Sumner 
Tipton  . 
Union 

$5,652 

29  610 

1,190 

11,220 
23,000 

Additional 

Total 
Eatio 

14,405 

5,000 

1,383,648 
100 

2,262,121 
:163 

Warren 

146 



Washington 

458 

.... 

Wayne 

843 

5,220 

x\lluvial . 

708,436 

1,488,636 

Weakley  . . . 

6,564 

6,220 

Ratio 

100 

:210 

Wiiite 

99 

.... 

Middle  . . . 

181,460 

209,380 

Williamson 

3,683 

5,000 

Ratio 

100 

:115 

Wilson 

9,317 

5,550 

Upland 

467,280 

544,055 

Unknown 

12,067 

15,000 

Ratio 

100 

:116 

STATE   OF  TEXAS. 

Anderson 

3,419 

2,500 

Freestone 

5,956 

20,880 

Angelina  . . . 

642 

Frio  . . . 

846 

.... 

Atascosa  . . . 

1,522 

Galveston  . 

158,697 

389,487 

Austin   ... 

11,964 

26,880 

Gillespie 

595 

.... 

Bastrop  . . . 

3,163 

Goliad  . . . 

3,523 

.... 

Bee  ... 

351 

Gonzales  . . . 

12,321 

20,677 

Bell 

1,720 

10,000 

Grayson 

9,657 

22,440 

Bexar 

35,418 

32,220 

Grimes  . . . 

10,750 

5,220 

Blanco 

528 

.... 

Gaudalupe  . . .' 

•     5,869 

5,220 

Bosque  . . . 

2,625 

Hardeman 

95 

.... 

Bowie 

5,458 

10,440 

Hardin  . 

290 

5,000 

Brazoria  . 

14,540 

41,220 

Harris  . . . 

69,767 

177,280 

Brazos  . .  . 

24,633 

25,660 

Harrison  . . . 

17,623 

26,100 

Burleson  . . . 

2,321 

10,000 

Hays 

2,712 

.... 

Burnet 

2,412 

-  >  •  • 

Henderson 

347 

.... 

Caldwell  . . 

4,412 

10,000 

Hill  . . . 

2,650 

.... 

Calhoun  . 

8,331 

.     15,000 

Hood 

5 

.... 

Cameron  . 

2,210 

5,000 

Hopkins 

644 

.... 

Chambers  . 

458 

•  •  .  . 

Houston  . . . 

4,699 

8,000 

Cherokee  . . . 

690 

Jack 

563 

•  •  •  • 

Coleman 

76 

>  •  «  • 

Jackson  . 

49 

•  •  •  • 

Collin  . .  . 

1,864 

.... 

Jasper  . 

1,552 

2,000 

Colorado  . . . 

8,446 

13,720 

Jefferson  . 

3,331 

16,660 

Comal 

3,514 

1,000 

Johnson 

1,700 

.... 

Comanche 

480 

Karnes  .  . . 

4,726 

Cook 

758 

.  .  •  . 

Kaufman 

1,227 

5,660 

Coryell 

899 

... 

Kendall 

517 

.... 

Dallas  . . . 

5,105 

10,220 

Kerr 

47 

.... 

Davis 

1,007 

5,000 

Kinney 

960 

Denton 

1,719 

Lamar 

4,201 

10,440 

De  Witt  . . . 

4,042 

16,060 

Lampasas 

248 

.... 

Ellis  . . . 

6,164 

5,220 

Lavacca  , . , 

14,609 

5,220 

El  Paso 

190 

.... 

Leon  . .  . 

1,991 

.... 

Falls 

3,912 

20,440 

Liberty  . 

2,987 

6,220 

Fannin  . . . 

5,821 

10,440 

Limestone 

13,644 

10,220 

Fayette  . .  . 

10,816 

21,390 

Live  Oak  . . 

972 

5,220 

Fort  Bend  . 

3,696 

20,660 

Llano 

1,266 

TABLE    YII 


177 


PROBABLE  LOSS  AND  ACTUAL  LOSS  BY  COUNTIES  IN  TWELVE  STATES. 
STATE  OP  TEXAS.— Continued. 


Counties. 

Prob.  Loss. 

Actual  Loss. 

Counties. 

Prol).  Loss. 

Actual  Loss. 

Madison  . . . 

1396 

Titus 

2,789 

Marion 

28,156 

85,498 

Ti'avis 

13,656 

7,500 

Matagorda  .  ' 

6,716 

5,000 

Trinity  . . . 

397 

McLennan  ... 

34,387 

46,880 

Tyler... 

47 

Medina 

532 

3,000 

Upshur 

1,898 

Milam  . .  . 

4,625 

6,330 

Uvalde 

1,759 

.... 

Montgomery  . . . 

3,417 

5,000 

Van  Zandt 

190 

.... 

Nacogdoches  . . . 

902 

.... 

Victoria  . 

5,609 

5,220 

Navarro 

14,073 

5,220 

Walker  .  . . 

3,203 

7,500 

Newton  . 

7 

Washington  .  . . 

•  30,767 

47,100 

Nueces  . 

1,986 

*  .  •  * 

Wharton  . 

144 

Orange  . 

1,661 

Williamson 

1,113 

3,66o 

Palo  Pinto 

787 

Wilson  . . . 

930 

Panola  . . . 

1,633 

Wise 

8 

i,66o 

Parker 

3,316 

5,230 

Wood 

418- 

.... 

Polk  . .  . 

168 

.... 

Unknown 

36,794 

5,000 

Red  River 
Refugio  . 
Robertson  . . . 

5,887 

1,779 

33,096 

66,100 

Additional 

Total 
Ratio 

31,065 

6,000 

778,713 
100 

1,358,973 
:175 

Rusk  . . . 

3,239 

3,000 

Sabine  . . . 

967 

Alluvial  .    ■ 

314,043 

511,467 

San  Saba 

376 

Ratio 

100 

:339 

Shelby  . . . 

3,013 

.... 

Middle  . . . 

333,901 

573,267 

Smith 

1,301 

Ratio 

100 

:172 

Starr 

396 

Upland 

184,655 

264,238 

Tarrant 

3,661 

5,330 

Ratio 

100 

:143 

S-] 

[•ATE    OP 

VIRGINIA. 

Accomack  . 

3,163 

13,000 

Elizabeth  City 

3,087 

Albemarle 

8,819 

15,000 

Essex  . .  . 

3,388 

i6,'66o 

Alexandria 

37,319 

35,500 

Fairfax 

7,147 

9,000 

Amelia  . . . 

100 

5,000 

Fauquier 

2,647 

Amherst 

1,350 

Fluvanna 

123 

5,660 

Appomattox 

47 



Franklin 

411 

.  *  •  > 

Augusta 

10,080 

18,500 

Frederick 

897 

15,750 

Bedford 

541 

Giles 

228 

-  •  «  • 

Botetourt 

385 

.  •  •  ■ 

Gloucester  . .  . 

2,356 

2,500 

Brunswick  . . . 

1,397 

13,000 

i  Goochland  . . . 

139 

.... 

Buckingham 

449 

■  Greenville  . . . 

1,436 

.... 

Campbell 

38,090 

10,000 

Halifax 

1,181 

.... 

Caroline  . .  . 

1,276 

1  Hanover  . .  . 

3,342 

.... 

Charles  Citj  . . . 

884 

.... 

Henrico  . . . 

149,712 

127,500 

Charlotte 

3,117 

31,500 

Henry 

7 

.... 

Chesterfield  . . . 

8,259 

13,500 

Highland 

48 

'     

Clark 

1,036 

.... 

Isle  of  Wight  . . . 

260 

.... 

Craig 

6 

.... 

James  City  . . . 

617 

.... 

Culpepper 

2,026 

10,000 

King  and  Queen... 

48 

.... 

Cumberland 

115 

King  George  . . . 

665 

.... 

Dinwiddle  . .  . 

134,043 

84,'50'0 

j  King  William  . . . 

847 



178  TABLE    YII. 

PROBABLE  LOSS  AND  ACTUAL  LOSS  BY  COUNTIES  IN  TWELVE  STATES. 
STATE  OP  VIRGINIA.— Continued. 


Counties. 

Prob.  Loss. 

Actaal  Loss. 

Counties. 

Prob.  Loss. 

Actual  Loss. 

Lancaster  . . . 

■    $279 

2,000 

Roanoke 

3,972 

5,000 

Lee 

11 

.... 

Rockbridge 

1,662 

5,000 

Loudon 

12,313 

3o,*o6o 

Rockingham 

636 

Louisa 

48 

.... 

Shenandoah 

271 

.... 

Lunenburg  . . . 

230 

.... 

Smyth 

815 

1,000 

Madison 

584 

Southampton  . . . 

1,285 

Matthews  . . . 

595 

•  •  •  . 

Spottsylvania  . . . 

25,838 

18,100 

Mecklenburg  . . . 

1,171 

2,000 

Stafford 

693 

. . .  - 

Middlesex  . . . 

1,075 

.... 

Surry  . .  . 

33 

.... 

Montgomery 

503 

.... 

Sussex  . . . 

798 

5,000 

Nansemoiid. . . 

2,932 

.... 

Warren 

261 

5,000 

Nelson 

296 

Warwick  .  . . 

30 

New  Kent  . . . 

749 

2,'o'6o 

Washington 

1,347 

9,000 

Norfolk  . .  . 

42,309 

59,000 

AVestmoreland  . .  . 

551 

.... 

Northampton  . 

38 

.... 

:  Wythe 

363 

j  Northumberland- 

813 

.... 

i  York  ... 

1,950 

i,'66o 

Nottoway  . . . 

47 

Unknown 

11,378 

27,000 

Orange 
1  Page 
Pittsylvania 
Powhatan  ... 
Prince  Edward 

1,359 
190 

5,075 

1« 

564 

3,000 

Additional 

Total 
Ratio 

Alluvial . 

104,312 

81,500 

673,350  1 
:104 

646,188 
100 

3,567 

13,000 

Prince  George  . .  . 

922 

5,000 

Ratio 

100 

:364 

Princess  Anne 

1,095 

2,500 

Middle  . . . 

385,727 

349,100 

Prince  William  . 

366 

1,000 

Ratio 

100 

:90 

Rappahannock 

91 

2,000 

Upland 

141,204 

202,750 

Richmond  . .  . 

7,543 



Ratio 

100 

:144 

STATE  OF  INDIANA. 

Adams 

$2,636 

2,500 

Floyd 

68,366 

60,713 

Allen 

83,143 

84,500 

Fountain 

6,716 

7,000 

Bartholomew 

24,058 

29,500 

Franklin 

4,579 

7,000 

Benton 

293 

.... 

Fulton 

5,691 

8,100 

Blackford 

310 

750 

Gibson 

17,638 

21,000 

Boone 

9,993 

14,500 

Grant 

6,392 

3,000 

Brown 

1,078 

5,000 

Green 

3,805 

2,000 

Carroll 

9,535 

9,000 

Hamilton 

17,261 

21,249 

Cass 

21,080 

20,000 

:  Hancock 

8,126 

2,500 

Clarke 

35,387 

40,000 

Harrison 

3,741 

.... 

Clay 

12,967 

9,000 

Hendricks 

14,113 

11,000 

Chnton 

1,217 

.... 

Henry 

13,671 

19,390 

Crawford 

6,709 

16,900 

Howard 

5,267 

5,000 

Daviess 

11,227 

16,000 

Huntington 

10,303 

6,343 

Dearborn 

35,840 

24,500 

Jackson 

14,297 

13,000 

Decatur 

18,782 

14,000 

Jasper 

679 

.... 

DeKalb 

6,249 

2,000 

Jay 

668 

.... 

Delaware 

21,134 

45,220 

Jefferson 

69,401 

68,000 

Du  Bois 

3,402 

11,000 

Jennings 

2,003 

.... 

Elkhart 

8,649 

1,100 

Johnson 

21,018 

7,300 

Fayette 

17,726 

4,200 

Knox 

7,807 

3,000 

TABLE    YII,  179 

PROBABLE  LOSS  AND  ACTUAL  LOSS  BY  COUNTIES  IN  TWELVE  STATES. 
STATE    OF   INDIANA.— Continued. 


Counties. 

Prob.  Loss. 

Actual  Loss. 

Counties. 

Prob.  Loss. 

■ 

Actual  Loss. 

Kosciusko 

$10,464 

4,500 

Scott 

124 

1,000 

La  Grange 

1,879 

4,000 

Shelby 

20,163 

37,000 

Lake 

1,392 

Spencer 

31,383 

43,894 

La  Porte 

54,045 

45,760 

Starke 

360 

.... 

Lawrence 

7,266 

348 

Steuben 

1,757 

.... 

Madison 

48,863 

65,088 

St.  Joseph 

50,975 

60,350 

Marion 

220,246 

214,050 

Sullivan 

5,157 

4,000 

Marshall 

15,564 

18,200 

Switzerland 

10,845 

9,200 

Martin 

425 

2,000 

Tippecanoe 

40,246 

42,080 

Miami 

16,601 

10,500 

Tipton 

6,181 

2,800 

Monroe 

10,969 

4,000 

Union 

2,481 

.... 

Montgomery 

20,974 

26,100 

Vanderburgh 

54,739 

75,642 

Morgan 

14,592 

8,500 

Vermillion 

2,107 

.... 

Newton 

2,064 

.... 

Vigo 

57,339 

72,500 

Noble 

6,564 

5,000 

Wabash 

18,655 

12,325 

Ohio 

1,662 

.  •  .  • 

Warren 

2,758 

2,000 

Orange 

7,355 

4,165 

Warrick 

8,856 

1,000 

Owen 

5,134 

2,000 

Washington 

5,378 

9,500 

Parke 

5,799 

12,400 

Wayne 
Wells 

69,563 

56,500 

Perry 

7,791 

5,500 

1,632 

.... 

Pike 

302 

White 

745 

.... 

Porter 

27,004 

21,800 

Whitley 

1,888 

5,000 

Posey 

33,638 

50,100 

Unknown 

7,077 

8,900 

Pulaski 
Putnam 
Randolph 

27 
49,785 
15,568 

34,*ldo 
13,900 

Additional 

Total 
Ratio 

836,541 

975,321 

2,465,769 
100 

2,590,728 
:105 

Ripley 

957 

2,000 

Rush 

8,932 

2,500 

180 


TABLE    YIII. 


THIRTY  OFFICES'  EXPERIENCE.     COMMUTATION  TABLE  FOR  THE  SPECIAL  CLIMATIC 

RATIOS  1.405  AND  1.805. 


4  PER  CENT. 


Arvp. 

1.405 

1.805 

.400 

1.405 

1.805 

.400 

1.405 

1.805 

.400 

A  ftp. 

AvTCi* 

Da,. 

Dx. 

Diff. 

N.. 

1,089,675 

Diff. 

TTa.. 

TTfl). 

Diff. 

iLVJXii 

lo- 

10 

64,393 

61,391 

3,002 

1,232,048 

142,373 

13.803 

17.878 

4.075 

11 

61,221 

58,089 

3,132 

1,167,655 

1,028,284 

139,371 

13.969 

18.030 

4.061 

ll 

12 

58,204 

54,963 

3,241 

1,106,434 

970,195 

136,239 

14.143 

18.190 

4.047 

12 

13 

55,334 

52,005 

3,329 

1,048,231 

915,231 

133,000 

14.327 

18.360 

4<033 

13 

14 

52,605 

49,205 

3,400 

992,897 

863,226 

129,671 

14.520 

18.539 

4.019 

14 

15 

50,009 

46,554 

3,455 

940,291 

814,022 

126,269 

14.723 

18.728  4.005 

15 

16 

47,540 

44,045 

3,495 

890,282 

767,468 

122,814 

14.937 

18.928  3.991 

16 

17 

45,192 

41,670 

3,522 

842,742 

723,423 

119.319 

15.164 

19.139 

3.975 

17 

18 

42,959 

39,422 

3,537 

797,550 

681,753 

115,797 

15.402 

19.362 

3.960 

18 

19 

40,834 

37,294 

3,540 

754,591 

642,332 

112,259 

15.652 

19.598 

3.94^ 

19 

20 

38,813 

35,279 

3,534  i 

713,757 

605,038 

108,719 

15.917 

19.847 

3.930 

20 

21 

36,891 

33,372 

3,519 

674,944 

569,759 

105,185 

16.196 

20.111 

3.915 

21 

22 

35,061 

31,566 

3,495 

638,054 

536,387 

101,667 

16.489 

20.389 

3.900 

22  1 

23 

33,322 

29,857 

3,465 

602,992 

504,820 

98,172 

16.799 

20.683 

3.884 

23 

24 

31,666 

28,239 

3,427 

569,670 

474,963 

94,707 

17.126 

20.993 

3.867 

24 

25 

30,092 

26,707 

3,385 

538,004 

446,724 

91,280 

17.470 

21.322 

3.852 

25 

26 

28,593 

25,256 

3,337 

507,912 

420,018 

87,894 

17.834 

21.669 

3.835 

26 

27 

27,167 

23,882 

3,285 

479,319 

394,762 

84,557 

18.217 

22.036 

3.819 

27 

28 

25,810 

22,581 

3,229  ! 

452,152 

370,880 

81,272 

18.622 

22.425 

3.803 

28 

29 

24,519 

21,350 

3,169 

426,342 

348,298 

78,044 

19.049 

22.835 

3.786 

29 

30 

23,290 

20,183 

3,107 

401,822 

326,949 

74,873 

19.500 

23.269 

3.769 

30 

31 

22,120 

19,078 

3,042 

378,532 

306,766 

71,766 

19.976 

23.729 

3.753 

31 

32 

21,007 

18,031 

2,976 

356,412 

287,688 

68,724 

20.479 

24.215 

3.736 

32 

33 

19,947 

17,040 

2,907 

335,405 

269,657 

65,748 

21.010 

24.730  3.720 

33 

34 

18,938 

16,101 

2,837 

315,458 

252,617 

62,841 

21.571 

25.274 

3.703 

34 

35 

17,977 

15,211 

2,766 

296,520 

236,516 

60,004 

22.164 

25.851 

3.687 

35 

36 

17,062 

14,368 

2,694 

278,543 

221,305 

57,238 

22.791 

26.461 

3.670 

36 

37 

16,190 

13,569 

2,621 

261,482 

206,937 

54,545 

23.454 

27.108 

3.654 

37 

38 

15,359 

12,812 

2,547 

245,292 

193,369 

51,923 

24.155 

27.793 

3.638 

38 

39 

14,568 

12,094 

2,474 

229,933 

180,557 

49,376 

24.898 

28.519 

3.621 

39 

40 

13,815 

11,413 

2,402 

215,364 

168,463 

46,901 

25.683 

29.288 

3.605 

40 

41 

13,096 

10,768 

2,328 

201,550 

157,050 

44,500 

26.514 

30.104 

3.590 

41 

42 

12,411 

10,156 

2,255 

188,454 

146,282 

42,172 

27.396 

30.969 

3.573 

42 

43 

11,758 

9,576.12,182  | 

176,043 

136,125 

39,918 

28.328 

31.886 

3.. 558 

43 

44 

11,135 

9,025.7|2,109 

164,285 

126,549 

37,736 

29.317 

32.860 

3.543 

44 

45 

10,541 

8,503. 4'2,038 

153,150 

117,523 

35,627 

30.366 

33.893 

3.527 

45 

46 

9,974.0 

8,007.71,966.2 

142,609 

109,020 

33,589 

31.478 

34.991 

3.513 

46 

47 

9,432.9 

7,537.3  1,895.0 

132,635 

101,012 

31,623 

32.658 

36.156 

.3.498 

47 

48 

8,916.3 

7,090.6  1,825.7 

123,202 

93,474.9 

29,727 

33.910 

37.394 

3.484 

48 

49 

8,423.0 

6,660.41,756.0 

114,286 

86,384.3 

27,902 

35.240 

38.710 

3.470 

49 

50 

7,951.9 

6,263.5  1,688.4 

105.863 

79,717.9 

26,145 

36.653 

40.109 

3.456 

50 

51 

7,501.6 

5,880.71,620.9 

97,910.9 

73,454.4 

24,457 

38.154 

41.597 

3.443 

51 

52 

7,071.2 

5,516.9  1,554.3 

90,409.3 

67,573.8 

22,836 ; 

39.751 

43.181 

3.430 

52 

53 

6,659.7 

5,171.11,488.6 

83,338.1 

62,056.7 

21,281 

41.450 

44.867 

3.417 

53 

54 

1 

6,266.1 

4,842.3  1,423.8 

76,678.5 

56,885.8 

19,793 

43.258 

46.663 

3.405 

54 

D,4^p.c. 

D,5p.c.; 

N,  4^  p.c. 

N,  5  p.  c. 

Insurance  1000 

TABLE    YTII. 


181 


THIRTY  OFFICES'  EXPERIENCE.    COMMUTATION  TABLE  FOR  THE  SPECIAL  CLIMATIC 

RATIOS  1.405  AND  1.805. 


4  PER  CENT. 


1.405 

1.805 

.400 

1.405 

1.805 

.400 

1.405 

1.805 

.400 

AQE. 

55 

D^. 

Da:. 

Diff. 

N«. 

N.. 

DiflF. 

TTfl).' 

T^x' 

DifE. 

AGE. 

55 

5,889.8 

4,529.8 

1,360.0 

70,412.4 

52,043.4 

18,369.0 

45.184 

48.577 

3.393 

56 

5,529.4 

4,232.4 

1,297.0 

64,522.7 

47,513.7 

17,009.0 

47.235 

50.616 

3.381 

56 

57 

5,184.5 

3,949.6 

1,234.9 

58,993.3 

43,281.3 

15,712.0 

i  49.422 

52.791 

3.369 

57 

58 

4,854.8 

3,680.4 

1,173.9 

53,808.8 

39,331.7 

14,477.1 

51.752 

55.111 

3.359 

58 

59 

4,538.1 

3,424.3 

1,113.8 

48,954.5 

35,651.4 

13,303.1 

54.239 

57.588 

3.349 

59 

60 

4,235.4 

3,180.7 

1,054.7 

44,416.4 

32,227.1 

12,189.3 

56.896 

60.233 

3.337 

60 

61 

3,945.5 

2,948.8 

996.7 

40,181.0 

29,046.4 

11,134.6 

159.732 

63.060 

3.328 

61 

62 

3,667.9 

2,728.3 

939.6 

36,235.5 

26,097.6 

10,137.9 

i  62.763 

66.081 

3.318 

62 

63 

3,402.2 

2,518.6 

883.6 

32,567.6 

23,369.3 

9,198.3 

66.004 

69.313 

3.309 

63 

64 

3,147.9 

2,319.3 

828.6 

29,165.4 

20,850.1 

8,315.3 

69.472 

72.770 

3.298 

64 

65 

2,904.7 

2,129.9 

774.8 

26,017.5 

18,531.4 

7,486.1 

73.182 

76.472 

3.290 

65 

66 

2,672.2 

1,950.1 

722.1 

23,112.8 

16,401.5 

6,711.3 

77.154 

80.434 

3.280 

66 

67 

2,450.3 

1,779.6 

670.7 

20,440.6 

14,451.5 

5,989.1 

81.411 

84.682 

3.271 

67 

68 

2,238.6 

1,618.1 

620.5 

17,990.3 

12,671.9 

5,318.4 

85.971 

89.232 

3.261 

68 

69 

2,037.1 

1,465.5 

571.6 

15,751.7 

11,053.8 

4,697.9 

90.866 

94.116 

3.250 

69 

70 

1,845.6 

1,321.4 

524.2 

13,714.6 

9,588.3 

4,126.3 

96.111 

99.351 

3.240 

70 

71 

1,664.1 

1,185.8 

478.3 

11,869.0 

8,266.9 

3,602.1 

101.74 

104.97 

3.23 

71 

72 

1,492.5 

1,058.4 

434.1 

10,204.9 

7,081.1 

3,123.8 

107.79 

111.00 

3.21 

72 

73 

1,330.8 

939.23 

391.6 

8,712.4 

6,022.8 

2,689.6 

114.28 

117.49 

3.21 

73 

74 

1,179.0 

828.18 

350.8 

7,381.7 

5,083.5 

2,298.2 

121.26 

124.45 

3.19 

74 

75 

1,037.2 

725.09 

312.1 

6,202.62 
5,160.42 

4,255.34 

1,947.3 

128.76 

131.93 

3.17 

75 

76 

905.40 

629.93 

275.5 

3,530.25 

1,635.2 

136.82 

139.97 

3.15 

76 

77 

783.67 

542.64 

241.0 

4,260.02 

2,900.32 

1,359.7 

145.50 

148.63 

3.13  , 

77 

78 

671.93 

463.05 

208.9 

3,476.35 

2,357.68 

1,118.7 

154.82 

157.94 

3.12 

78 

79 

570.22 

391.09 

179.2 

2,804.41 

1,894.63 

909.8 

164.87 

167.96 

3.09 

79 

80 

478.45 

326.59 

151.9 

2,234.19 

1,503.54 

730.65 

175.69 

178.75 

3.06 

80 

81 

396.47 

269.33 

127.1 

1,755.74 

1,176.95 

578.79 

187.35 

190.38 

3.03 

81 

82 

324.06 

219.10 

105.0 

1,359.27 

907.62 

451.65 

199.95 

202.94 

2.99 

82 

83 

260.89 

175.55 

85.34 

1,035.21 

688.52 

346.69 

213.55 

216.51 

2.96 

83 

84 

206.60 

138.36 

68.24 

774.32 

512.97 

261.35 

228.36 

231.26 

2.90 

84 

85 

160.63 

107.06 

53.57 

567.713 

374.607 

193.11 

244.48 

247.33 

2.85 

85 

86 

122.41 

81.199 

41.21 

407.081 

267.547 

139.53 

262.25 

265.03 

2.78 

86 

87 

91.272 

60.254 

31.02 

284.668 

186.348 

98.320 

282.16 

284.88 

2.72 

87 

88 

66.390 

43.619 

22.77 

193.395 

126.094 

67.301 

304.82 

307.46 

2.64 

88 

89 

47.042 

30.760 

16.28 

127.006 

82.475 

44.531 

331.93 

334.50 

2.57 

89 

90 

31.844 

20.723 

11.12 

79.9643 

51.715 

28.249 

359.77 

362.26 

2.49 

90 

91 

20.473 

13.260 

7.213 

48.1201 

30.992 

17.128 

387.00 

389.39 

2.39 

91 

92 

12.567 

8.1007 

4.466 

27.6470 

17.732 

9.9150 

416.10 

418.37 

2.27 

92 

93 

7.3390 

4.7081 

2.631 

15.0799 

9.6315 

5.4484 

448.21 

450.36 

2.15 

93 

94 

4.0382 

2.5783 

1.460 

7.7408 

4.9234 

2.8174 

483.21 

485.21 

2.00 

94 

95 

2.0773 

1.3199 

.7574 

3.70262 

2.3451 

1.3575 

522.56 

524.38 

1.82 

95 

96 

.99391 

.62854 

.3654 

1.62536 

1.0252 

.6002 

573.04 

574.65 

1.61 

96 

97 

.41960 

.26409 

.1555 

.63145 

.39664 

.2348 

626.04 

627.37 

1.33 

97 

98 

.16062 

.10061 

.0600 

.21185 

.13255 

.0793 

719.70 

720.58 

0.88 

98 

99 

.05123 

,  .03194 

.0193 

.05123 

.03194 

.0193 

961.54 

961.54 

0.00 

99 

D,4|p.c. 

D,5  p.c. 

1 

N,4|p.c. 

N,  5  p.  c. 

Insurance  1000 

182 


TABLE    IX. 


GENERAL  TABLE  OP  DISEASES  AND  DEATHS  IN   TWENTY-SEVEN   LIFE  INSURANCE 
COMPANIES  FROM  THEIR  ORGANIZATION  TO  THE  YEAR  1874. 


The  columns  headed  (2),  (5,)  (30)  record  the  Deaths  in  so  many  Companies. 


Number  of  Deaths. 

Variability.    M  and  F. 

Per  Cent. 

DISEASES. 

of  Total. 

1 

Hales. 

Females. 

Total. 

1      (2) 

(5) 

(20) 

All  Causes. 

35,442 

2,182 

37,624 

12,*845 

12,456 

12,323 

100.00 

Zymotic  Diseases 

6,356 

303 

6,659 

!  2,285 

2,172 

2,202 

17.70 

;  >* 

Constitutional  Diseases 

8,175 

548 

8,723 

i  2,898 

2,868 

2,957 

23.19 

!  P 

1  < 

Nervous  Diseases 

5,106 

193 

5,299 

1  1,977 

1,715 

1,607 

14.08 

1  ^ 

Circulatory  Diseases 

1,986 

106 

2,092 

1      785 

668 

639 

5.56 

P 

■Respiratory  Diseases 

4,771 

291 

5,062 

1,682 

1,641 

1,739 

13.45 

CQ 

Digestive  Diseases 

3,344 

273 

3,617 

1   1,251 

1,229 

1,137 

9.61 

Miscellaneous  Diseases' 

5,704 

468 

6,172 

j  1,967 

2,163 

2,042 

16.42 

Typhoid  Fever 

2,147 

107 

2,254 

i      744 

775 

735 

5.99 

Typhus  Fever 

159 

11 

170 

i        82 

48 

40 

.45 

1 

Cerebro-spinal  P'ever 

23 

1 

24 

'        23 

1 

0 

.06 

1 

Yellow  Fever 

252 

6 

258 

!        57 

88 

113 

.69 

Remittent  Fever 

412 

25 

437 

i      156 

122 

159 

1.16 

Intermittent  Fever 

159 

7 

166 

,        38 

56 

72 

.44 

Congestive  Fever 

213 

13 

226 

94 

66 

66 

.60 

Typlio-malarial  Fever 

46 

4 

50 

17 

21 

12 

.13 

Fever 

255 

12 

267 

66 

132 

69 

•    .71  ' 

Small  Pox 

298 

7 

305 

74 

101 

130 

.81 

Measles 

13 

2 

15 

4 

5 

6 

.04 

1    Scarlet  Fever 

38 

2 

40 

19 

15 

6 

.11 

i    Diphtheria  and             ) 
p    Malignant  sore  throat ) 

127 

6 

133 

36 

44 

53 

.35 

.o    Erysipelas 

374 

10 

384 

161 

128 

95 

1.02 

1  ,  Pyaemia 
P»|  Carbuncle 

70 

4 

74 

21 

27 

26 

.20 

62 

1 

63 

28 

16 

19 

.17 

Influenza 

12 

2 

14 

4 

7 

3 

.04 

Dysentery 

587 

35 

622 

254 

167 

201 

1.65 

Diarrhoea 

328 

22 

350 

129 

96 

125 

.93 

Cholera 

431 

15 

446 

155 

136 

155 

1.19 

Cholera-morbus 

195 

8 

203 

63 

79 

61 

.54 

Goitre 

4 

0 

4 

2 

2 

0 

01 

Malignant  pustule 

11 

0 

11 

2 

,  4 

5 

.03 

Glanders 

1 

0 

1 

1 

0 

^ ; 

.00 

Purpura  haemorrhagica 

21 

0 

21 

3 

5 

13  I 

.06 

Alcoholism 

117 

1 

118 

50 

31 

37  1 

.31 

Other  Zymotic  Diseases 

1 

2 

3 

2 
20 

0 

1 

.00 

Anaemia 

59 

12 

71 

33 

18 

.19 

'^    Cancer 

621 

44 

665 

241 

216 

208 

1.77 

g    Dropsy 

622 

56 

678 

205 

237 

236 

1.80 

■|    Gout 

23 

0 

23 

13 

4 

6 

.06 

•2    Rheumatism 

169 

11 

180 

52 

75 

53 

.48 

1 

Gangrene 

51 

0 

51 

18 

13 

20 

.14 

V 

Tubercular  meningitis 

10 

1 

11 

3 

3 

5 

.03 

Lumbar  abscess 

11 

0 

11 

6 

3 

2 

.03 

TABLE     IX. 


183 


GENERAL  TABLE  OF  DISEASES   AND  DEATHS   IN   TWENTY-SEVEN   LIFE  INSURANCE 
COMPANIES  FROM  THEIR  ORGANIZATION  TO  THE  YEAR  1874. 


The  columns  beaded  (3),  (5),  (20)  record  the  Deaths  in  so  many  Companies. 


1 

Number  of  Deaths. 

Variability.    M 

and  F. 

Per  Cent. 

DISEASES. 

of  Total.  1 

1 

Hales. 

Females 

Total. 

(2) 

(5) 

(20) 

All  Causes. 

35,442 

2,182 

37,624 
31 

12,845 

12,456 

12,323 

100.00  i 

1 

Scrofula 

25 

6 

15 

10 

6 

1      .08 

•1 

Tabes  Mesenterica 

88 

5 

93 

31 

36 

26 

.25 

5 

Morbus  Coxje 

12 

0 

12 

5 

3 

4 

.03    ' 

3 

Consumption 

6,474 

412 

6,886 

2,283 

2,231 

2,372 

18.31 

,S 

Other  Constitutional 

10 

1 

11 

6 

4 

1 

.03 

Apoplexy 

1,705 

61 

1,766 

653 

599 

514 

4.70 

Congestion  of  brain 

655 

14 

669 

234 

239 

196 

1.78 

Softening  of  brain 

399 

9 

408 

i      177 

93 

138 

1.09 

Paralysis 

841 

32 

873 

360 

250 

263 

2.32 

Disease  of  l)rain 

721 

37 

758 

239 

251 

268 

2.02 

Convuls'ns  and  epilepsy 

130 

8 

138 

52 

50 

36 

.37 

Insanity 

140 

6 

146 

63 

41 

42 

.39 

Anxiety 

2 

0 

2 

2 

0 

0 

.01 

Fright- 

1 

0 

1 

1 

0 

0 

.00 

. 

En  cephalitis 

277 

10 

287 

109 

101 

77 

.76 

1 

Cerebro-spinal  sclerosis 

1 

0 

1 

!                1 

0 

0 

.00 

1 

Cerebral  embolism 

1 

0 

1 

1 

0 

0 

.00 

^ 

Anffimia  of  brain 

8 

0 

8 

4 

2 

2 

.02 

Effusion  on  brain 

48 

3 

51 

10 

23 

18 

.14 

Neuralgia 

17 

1 

18 

5 

8 

5 

.05 

Progressive  muscular ) 
atrophy                     j 

3 

0 

3 

2 

1 

0 

.01 

Tetanus 

47 

4 

51 

10 

24 

17 

.14 

Inflam't'n  of  spinal  cord 

18 

0 

18 

10 

5 

3 

.05 

Disease  of  spinal  cord 

41 

2 

43 

.21 

10 

12 

.11 

Congest'n  of  spinal  cord 

3 

0 

3 

2 

0 

1 

.01 

— • 

Other  Nervous  Diseases 

48 

6 

54 

21 

18 

15 

.14 

Disease  of  heart 

1,297 

62 

1,359 

534 

418 

407 

3.61 

Peri-  and  endo-carditis  ^ 

104 

9 

113 

29 

38 

46 

.30 

Hypertrophy  of  heart 

100 

4 

104 

28 

47 

29 

.28 

Valvular  disease  of  heart 

98 

6 

104 

14 

55 

35  X 

.28 

Fatty  degen't'n  of  heart 

42 

3 

45 

21 

15 

9 

.12 

Dropsy  of  heart 

56 

6 

62 

27 

13 

22 

.16 

Rheumatism  of  heart 

66 

6 

72 

30 

17 

25 

.19 

i" 

Atrophy  of  heart 

4 

0 

4 

4 

0 

0 

.01 

1 

Paralysis  of  heart 

27 

1 

28 

3 

12 

13 

.07 

1 

Abscess  of  heart 

5 

0 

5 

1 

0 

4 

.01 

-^ 

Angina  pectoris 

79 

4 

83 

46 

17 

20 

.22 

Aneurism  of  aorta 

51 

1 

52 

25 

14 

13 

.14 

Rupture  of  aorta 

16 

1 

17 

6 

7 

4 

.05 

Embolus    of    pulmo- ) 
nary  artery               | 

5 

1 

6 

1 

3 

2 

.02 

Phlebitis 

18 

0 

18 

4 

9 

5 

.05 

Other  Circulatory 

18 

2 

20 

12 

3 

5 

.05 

184 


TABLE     IX. 


GENERAL  TABLE  OP   DISEASES   AND  DEATHS. 


Number  of  Deaths. 

Variability.    M. 

andF. 

1  Per  Cent. 

DISEASES. 

Males. 

Females. 

Total. 

(2) 

(5) 

(20) 

j  of  Total. 

1 

All  Causes. 

35,442 

2,182 

37,624 

12,845 

12,456 

12,323 

1  100.00 

Epistaxis 

8 

0 

8 

2 

3 

3 

.02 

Disease  of  Larynx 

112 

3 

115 

j        30 

44 

41 

.31 

Bronchitis 

437 

21 

458 

1      144 

144 

170 

1.21 

Pleurisy 

172 

7 

179 

75 

64 

40 

.48 

Congestion  of  Lungs 

568 

29 

597 

187 

198 

212 

1.59 

i 

Pneumonia 

2,713 

176 

2,889 

990 

899 

1,000 

7.68 

1 

Abscess  of  Lungs 

78 

6 

84 

25 

36 

23 

.22 

Hemorrhage  of  Lungs 

283 

7 

290 

93 

90 

107 

.77 

OS 

Disease  of  Lungs 

264 

31 

295 

92 

111 

92 

.78 

Emphysema,  Asthma 

63 

8 

71 

21 

25 

25 

.19 

Pulmonary  Apoplexy 

34 

1 

35 

10 

16 

9 

.09 

Gangrene  of  Lungs 

'  13 

0 

13 

4 

3 

6 

.03 

CEdema  of  Lungs 

16 

0 

16 

1 

7 

8 

.04 

Other  Kespiratory 

10 

2 

12 

8 

1 

3 

.03 

Inflammat'n  of  Stomach 

319 

39 

358 

121 

116 

121 

.95 

Ulceration  of  Stomach 

75 

6 

81 

34 

29 

18 

.22 

Disease  of  Stomach 

150 

5 

155 

58 

57 

40 

.41 

Hemorrhage  of  Stomach 

57 

1 

58 

18 

20 

20 

.15 

Congestion  of  Stomach 

23 

2 

25 

7 

9 

9 

.07 

Tumor  of  Stomach 

4 

0 

4 

3 

1 

0 

.01 

Inflammation  of  Bowels 

425 

45 

470 

189 

130 

151 

1.25 

Ulceration  of  Bowels 

67 

6 

73 

39 

15 

19 

.19 

Hemorrhage  of  Bowels 

84 

2 

86 

33 

24 

29 

.23 

Congestion  of  Bowels 

22 

5 

27- 

8 

14 

5 

.07 

Disease  of  Bowels 

100 

10 

110 

47 

32 

31 

.29 

Obstruction  of  Bowels 

36 

1 

37 

9 

12 

16 

.10 

Perforation  of  Bowels 

6 

1 

7 

3 

2 

2 

.02 

Peritonitis 

246 

41 

287 

101 

102 

84 

.76 

Gastro-euteritis 

165 

17 

182 

41 

74 

67 

.48 

> 

Disease  of  Stomach     \ 
and  Bowels                ) 

127 

7 

134 

31 

41 

62 

.36 

♦3 

s 

Hemorrhage 

9 

0 

9 

4 

3 

2 

.02 

to 

Strangulated  Hernia 

43 

12 

55 

f8 

17 

20 

.15 

p 

Colic,  Tympanites  and  ) 
Constipation              f 

69 

3 

72 

22 

28 

22 

.19 

Dyspepsia 

43 

3 

46 

13 

24 

9 

.12 

Gangrene  of  Tongue 

3 

0 

3 

1 

2 

0 

.01 

Stricture  of  (Esophagus 

11 

0 

11 

1 

8 

2 

.03 

Fistula  in  Ano 

12 

0 

12 

3 

5 

4 

.03 

Disease  of  Spleen 

22 

0 

22 

14 

4 

4 

.06 

Leucoeythaemia 

7 

1 

8 

3 

0 

5 

.02 

Ascites 

41 

8 

49 

15 

20 

14 

.13 

Abdominal  Tumor 

35 

3 

38 

11 

20 

7 

.10 

Undefined  Diseases,     ) 
Abdominal  Organs   ) 

11 

0 

11 ' 

7 

0 

4 

,03 

Jaundice 

75 

2 

77 

37 

21 

19 

.20 

Inflammation  of  Liver 

268 

15 

283 

80 

93 

110 

.75 

Cirrhosis  of  Liver 

104 

4 

108 

38 

33 

37 

.29 

Abscess  of  Liver 

79 

7 

86 

28 

32 

26 

.23 

TABLE    IX. 


185 


GENERAL  TABLE  OF  DISEASES  AND  DEATHS. 


Number  of  Deaths. 

Variability.    M. 

and  F.     | 

1 

Per  Cent.  | 
of  Total.  1 

DISEASES. 

Males. 

Females. 

Totol. 

(2) 

(5) 

(20) 

All  Causes. 

35,442 

2,182 

37,624 

12,845 

12,456 

12,323 

100.00  ! 

Diseases  of  Liver 

448 

19 

467 

153 

180 

134 

1.24 

Congestion  of  Liver 

63 

3 

66 

29 

22 

15 

.18 

Hypertrophy  of  Liver 

36 

2 

38 

11 

14 

13 

.10 

o 

Acute  Yellow  Atrophy  [ 
of  Liver                     ) 

9 

0 

9 

3 

3 

3 

.02 

s 

60 

Fatty  Degeneration  of  ) 
Liver                          J 

15 

1 

16 

4 

6 

6 

.04 

S 

Biliary  Calculus 

15 

0 

15 

6 

6 

3 

.04 

Obstruction  of  Hepa-) 
tic  Duct                     ) 

4 

0 

4 

1 

3 

.01 

Kupture  of  Gall  Bladder 

2 

0 

2 

1 

1 

.01 

Other  Digestive 

14 

2 

16 

6 
181 

9 

i 

.04 

Bright's  Disease 

550 

17 

567 

184 

202 

L51 

Inflammation  of  Kidneys 

60 

1 

61 

17 

24 

20 

.16 

Abscess  of  Kidneys 

12 

0 

12 

3 

5 

4 

.03 

Tumor  of  Kidney 

1 

0 

1 

1 

.  , 

. . 

Disease  of  Kidneys 

255 

9 

264 

116 

81 

67 

.70 

Diabetes 

158 

3 

161 

78 

•    44 

39 

.43 

Addison's  Disease 

12 

0 

12 

3 

5 

4 

.03 

Inflammation  of  Bladder 

74 

2 

76 

'24 

16 

36 

.20 

Disease  of  Bladder 

54 

1 

55 

24 

16 

15 

.15 

Hemorrhage  of  Bladder 

5 

0 

5 

1 

2 

2 

.01 

Eupture  of  Bladder 

'    1 

0 

1 

1 

. . 

Urinary  Calculi 

20 

1 

21 

4 

ii 

6 

.06 

Gravel 

13 

0 

13 

8 

0 

5 

.03 

3 

Disease  of  Prostate     ) 
Gland                         f 

39 

0 

39 

16 

13 

10 

.10 

1 

Stricture  of  Urethra 

5 

0 

5 

4 

1 

.01 

a 

Gangrene  of  Scrotum 

1 

0 

1 

1 

,  , 

,  , 

S 

09 

Other  Urinary 

66 

5 

71 

16 

25 

30 

.19 

» 

Childbirth  and  Puer- ) 
peral  Diseases           ) 

Diseases  of  Breast        ) 
and  Uterus                  [ 

•' 

197 

197 

61 

73 

63 

.52 

110 

110 

29 

53 

28 

.29 

Debility,  Exhaustion    [ 
and  Prostration         \ 

377 

28 

405 

145 

136 

124 

1.08 

Abscess 

117 

5 

122 

43 

38 

41 

.32 

Hemorrhage 

66 

9 

75 

18 

33 

24 

.20 

Tumors 

55 

3 

58 

21 

23 

14 

.15 

Inflammation  of  Joints 

15 

0 

15 

8 

2 

5 

.04 

Old  Age 

87 

12 

99 

63 

18 

18 

.26 

Accidents  and  Injuries 

2,678 

34 

2,712 

806 

1,019 

887 

7.21* 

Suicides 

475 

7 

482 

150 

180 

152 

1.28 

! 

Causes  unknown  or      ) 
ill  defined                     \ 

508 

24 

532 

125 

161 

246 

1.42 

*Deaths  from  Accidents  Only  were  2,058  or  3.48  per  cent  of  59,008  total  deaths  to  the  year  1890. 


186 


TABLE     X. 


(A.)    DISEASES  AND  DURATIONS  OF  POLICY  AT  DEATH  OF  35,442  INSURED  MALES. 


r~ 

Duration  or  Years  of  Insurance. 

Total. 

DISEASES. 

0-i 

i-H 

H-2|2|-4i 

H-n 

9|-19i 

19i-29^ 

[                 All  Causes. 

2,445 

842 

5,161 

4,651 

7,803 

10,062 

4,089 

1,197 

35,442 
6,356 

1 — 
1 

Zymotic  Disaases 

1,223 

943 

1,297 

1,424 

509 

118 

1^' 

Constitutional  Diseases 

226 

978 

1,124 

2,091 

2,635 

937 

182 

8,175 

iS 

Nervous  Diseases 

297 

620 

591 

1,078 

1,525 

745 

247 

5,107 

!» 

Circulatory  Diseases 

75 

190 

199 

411 

641 

330 

140 

1,986 

'8 
p 

Respiratory  Diseases 

312 

761 

626 

1,031 

1,322 

553 

165 

4,770 

CQ 

Digestive  Diseases 

216 

493 

461 

717 

949 

402 

105 

3,344 

Miscellaneous  Diseases 

477 

896 

707 

1,178 
468 

1,566 

613 

240 

5,704 

Typhoid,  Typhus  Fever 

316 

473 

357 

492 

160 

40 

2,306 

Malarial  Fever 

108 

163 

123 

176 

186 

62 

13 

831 

« 

Erysipelas 

22 

41 

54 

79 

113 

53 

12 

374 

1 

Dysentery 

92 

105 

75 

124 

124 

52 

15 

587 

1 

Diarrhcea 

27 

49 

52 

66 

74 

48 

12 

328 

Cholera 

102 

97 

67 

75 

67 

21 

2 

431 

Alcoholism 

8 

24 

13 

29 

26 

17 

. . 

117 

Other  Zymotic  Diseases 

167 

271 

202 

66 

280 

342 

96 

24 

1,382 
611 

^  1  Dropsy 

25 

74 

147 

180 

96 

23 

tJ    Cancer 

15 

55 

51 

155 

216 

95 

44 

632 

■i 

Consumption 

155 

790 

947 

1,691 

2,113 

689 

89 

6,474 

Other  Constitutional 

31 

59 

60 
208 

98 

126 

_   57 
250 

26 

458 

Apoplexy 

115 

210 

357 

468 

96 

1,705 

i 

Congestion  of  Brain 

64 

102 

85 

147 

179 

63 

15 

655 

Paralysis,      Softening  [ 
etc.,  of  Brain             \ 

101 

253 

234 

452 

724 

357 

112 

2,236 

^ 

Epilepsy,  Convulsions 

4 

15 

19 

35 

37 

17 

3 

130 

Other  Nervous 

13 
66 

40 
173 

45 

87 

117 

58 

21 

381 

!>• 

Diseases  of  Heart 

189 

386 

597 

313 

131 

1,855 

■H 

Other  Circulatory 

9 

17 

10 

25 

572 

44 

17 

9 

131 

.     Pneumonia 

188 

447 

355 

750 

310 

89 

2,711 

g     Congestion  of  Lungs 

44 

92 

81 

107 

149 

70 

25 

568 

g  j  Bronchitis  and  Pleurisy 

21 

87 

71 

154 

170 

76 

31 

610 

Abscess,   Hemorrhage^ 
etc.,  of  Lungs            ^ 

46 

102 

89 

159 

200 

75 

12 

683 

Other  Respiratory 

13 

33 

30 

39 

53 

22 

8 

198 

Diseases  of  Stomach 

36 

84 

91 

139 

160 

95 

23 

628 

_> 

Diseases  of  Bowels 

62 

118 

99 

163 

194 

85 

18 

739 

Peritonitis 

18 

51 

37 

48 

66 

18 

8 

246 

Diseases  of  Liver 

43 

134 

151 

232 

326 

122 

29 

1,038 

Other  Digestive 

57 
4 

106 

83 

135 

203 

82 

27 

693 

Diabetes 

17 

11 

33 

60 

19 

14 

158 

Diseases  of  Kidneys 

31 

85 

100 

178 

302 

140 

50 

886 

Other  Urinary 

8 

24 

26 

55 

85 

56 

28 

282 

Childbirth  and  Puer- 1 
per^il  Diseases             ' 

s 

•  • 

•  ■ 

*  • 

*  * 

e 

Diseases  of  Breast  and  ) 
Uterus                        ' 

PI 

•  • 

'  • 

S 

Abscess,  Hemorrhage,  [ 
Old  Age                           C 

11 

45 

30 

60 

78 

49 

66 

339 

IM 

Debility,   Exhaustion,  } 
Prostration,  etc.         f 

8 

40 

35 

75 

120 

61 

38 

378 

Accidents  and  Injuries 

334 

526 

384 

573 

639 

194 

28 

2,678 

Suicides 

37 

86 

68 

97 

139 

37 

11 

475 

Unknown  Causes 

44 

73 

53 

107 

143 

57 

5 

508; 

Note.     The  Total,  3.'5,442,  includes  26  more  unknown  and  8  above  29|  Years. 


TABLE    X 


187 


(B.)    DISEASES  AND  DURATIONS  OF  POLICY  AT  DEATH  OF  3,182  INSURED  FEMALES. 


Duration  or 

fears  of  Insurance. 

J 

DISEASES. 

0-i 

i-li 

H-2i 

2i-4i 

4i-9i 

9f-19i 

19i-29i 

Total. 

All  Causes. 

197 

403 

341 

467 

513 

190 

70 

2,182 

"^ 

Zymotic  Diseases 

48 

62 

48 

61 

57 

23 

4 

303 

ftH 

Constitutional  Diseases 

19 

86 

101 

118 

148 

65 

12 

549 

Nervous  Diseases 

16 

30 

31 

47 

35 

23 

12 

194 

d 

Circulatory  Diseases 

9 

11 

12 

24 

32 

9 

9 

106 

» 
g 

Respiratory  Diseases 

23 

62 

45 

-     65 

66 

20 

12 

293 

Digestive  Diseases 

28 

53 

37 

56 

67 

19 

9 

269 

Miscellaneous  Diseases 

54 

99 

67 

96 

108 

31 

12 

468 

Typhoid,  Typhus  Fever 

16 

24 

21 

26 

22 

7 

2 

118 

Malarial  Fever 

8 

12 

11 

7 

6 

5 

49 

d 

Erysipelas 

1 

1 

3 

4 

1 

10 

1 

Dysentery 

7 

1 

5 

6 

12 

3 

1 

35 

Diarrhoea 

4 

7 

3 

4 

3 

1 

22 

N 

Cholera 
Alchoholism 

4 

2 

3 
1 

4 

2 

•• 

•• 

15 
1 

Other  Zymotic  Diseases 

9 
2 

15 

3 

11 

8 

6 

i 

53 

. 

Dropsy 

8 

7 

8 

14 

6 

45 

^    Cancer 

2 

4 

9 

18 

8 

11 

3 

55 

1 

Consumption 

14 

68 

78 

85 

119 

41 

8 

413 

Other  Constitutional 

1 

6   . 

7 

7 

7 

7 

1 

36 
61 

Apoplexy 

7 

10 

8 

16 

13 

5 

2 

09 

Congestion  of  Brain 

2 

2 

4 

2 

3 

2 

1 

16 

1 

Paralysis,     Softening  i 
etc.,  of  Brain 

6 

13 

15 

19 

14 

11 

8 

86 

^ 

Epilepsy,  Convulsions 

1 

4 

3 

2 

,  , 

10 

Other  Nervous 

i 

4 

4 

6 

2 

3 

1 

21 

>. 

Diseases  of  Heart 

7 

11 

10 

23 

32 

9 

9 

101 

u 

Other  Circulatory 

2 

2 

1 

5 

Pneumonia 

19 

37 

24 

43 

37 

12 

5 

177 

^ 

Congestion  of  Lungs 

5 

5 

4 

9 

3 

2 

28 

+> 

Bronchitis  and  Pleurisy 

i 

5 

5 

10 

3 

2 

2 

28 

Abscess,  Hemorrhage) 
etc.,  of  Lungs           ) 

2 

15 

8 

6 

13 

1 

1 

46 

Other  Respiratory 

1 

3' 

2 

4 

2 

2 

14 

Diseases  of  Stomach 

6 

12 

6 

11 

14 

3 

2 

54 

> 

Diseases  of  Bowels 

7 

19 

10 

9 

17 

6 

2 

70 

9) 

Peritonitis 

5 

7 

9 

13 

4 

3 

41 

p 

Diseases  of  Liver 

2 

8 

6 

13 

15 

4 

48 

Other  Digestive 

8 

7 

6 

10 

17 
3 

6 

2 

56 

Diabetes 

,  , 

.. 

3 

Diseases  of  Kidneys 

3 

4 

4 

4 

9 

2 

1 

27 

Other  Urinary 

3 

2 

3 

1 

9 

3 

Childbirth  and  Puer- ) 
peral  Diseases           ) 

30 

51 

25 

45 

40 

6 

197 

s 

03 

Diseases  of  Breast  and } 
Uterus                       f 

6 

23 

20 

25 

28 

6 

2 

110 

:3 

Abscess,   Hemorrhage ) 
Old  Age                     j 

2 

3 

6 

5 

3 

6 

3 

28 

JM 

Debility,   Exhaustion,  ) 
Prostration,  etc.          ) 

2 

3 

4 

3 

9 

6 

2 

29 

Accidents  and  Injuries 

5 

7 

4 

7 

8 

1 

2 

34 

Suicides 

2 

1 

1 

2 

1 

. . 

7 

Unknown  Causes 

4 

4 

3 

3 

4 

4 

1 

24 

NoTB.    The  Total,  3,182,  includes  1  more  unknown. 


188 


TABLE     XI. 


(A.)    DISEASES  AND  AGES  AT  DEATH  OF  35,443  INSURED  MALES. 


Ages  at  Death. 

DISEASES. 
All  Causes. 

91-19^ 
133 

19i-29i 
3,476 

29f39i 

39i-49| 

49i-59| 

|59H9i 

69i-79| 

79i-89| 

Total. 

9,321 

10,840 

7,576 

3,357 

647 

92 

35,44^ 

Zymotic 

54 

903 

1,866 

1,943 

1,137 

390 

58 

5 

6,356 

pH* 

Constitutional 

22 

1,117 

2,691 

2,441 

1,342 

484 

76 

2 

8,175 

M 

Nervous 

9 

'238 

997 

1,576 

1,410 

733 

135 

8 

5,107 

» 

Circulatory 

3 

61 

328 

537 

582 

389 

81 

5 

1,986 

» 
g 

Respiratory 

11 

370 

1,168 

1,524 

1,117 

484 

88 

9 

4,770 

Digestive 

12 

216 

758 

1,134 

811 

361 

45 

7 

3,344 

Miscellaneous 

22 

571 

1,513 

1,685 

1,177 

516 

164 

56 

5,704 

Typhoid,Typhus 

28 

472 

702 

620 

361 

116 

7 

2,306 

Malarial  Fever 

4 

72 

252 

286 

154 

58 

5 

831 

^  'Erysipelas 

27 

86 

132 

85 

37 

6 

1 

374 

■^  Dysentery 

7 

62 

165 

160 

136 

44 

12 

1 

587 

a  Diarrhoea 

3 

27 

77 

98 

74 

37 

10 

2 

328 

N  Cholera 

5 

55 

134 

141 

73 

21 

2 

431 

1  Alcoholism 

6 

41 

55 

14 

1 

,  . 

117 

^ Other  Zymotic 

7 

182 

409 

451 

240 

76 

16 

1 

1,382 

.  Dropsy 

19 

103 

191 

183 

99 

15 

1 

611 

^  Cancer 

8 

72 

186 

239 

107 

20 

632 

Consumption 

21 

1,052 

2,406 

1,933 

819 

219 

23 

i 

6,474 

Other  Const'l 

1 

38 

110 

131 

101 

59 

18 

458 

Apoplexy 

1 

42 

238 

500 

598 

279 

46 

1 

1,705 

IB 

CongestionBrai  n 

3 

53 

190 

231 

130 

43 

5 

655 

§ 

^ 

Paralysis,  Soft- 1 
ening  Brain    1 

4 

109 

431 

663 

572 

355 

79 

6 

2,236 

^ 

Epilepsy    and  { 
Convulsions    ) 

10 

48 

48 

25 

13 

2 

130 

Other  Nervous 

1 

24 

90 

134 

85 

43, 

3 

1 

381 

-?;'  Diseasesof  Heart 

3 

59 

307 

.    488 

553 

362 

78 

5 

1,855 

■B 

Other  Circulat'y 

2 

21 

49 

29 

27 

3 

131 

Pneumonia 

6 

183 

594 

882 

689 

305 

49 

3 

2,711 

>> 

i^ 

Congest'n  Lungs 

2 

41 

132 

189 

130 

57 

16 

1 

568 

1 

Bronchitis  and  [ 
Pleurisy          ) 

2 

42 

152 

202 

132 

62 

15 

4 

610 

Abscess,  Hem- ) 
or'age  Lungs ) 

1 

90 

240 

192 

112 

42 

6 

•• 

683 

Other  Respirat'y 

14 

50 

59 

54 

18 

2 

1 

798 

. 

Dis.  of  Stomach 

3 

24 

124 

226 

159 

75 

16 

1 

628 

> 

Dis.  of  Bowels 

2 

72 

219 

206 

159 

73 

o 

3 

739 

Peritonitis 

2 

35 

73 

77 

42 

15 

1 

1 

246 

bo 
P 

Dis.  of  Liver 

2 

37 

209 

410 

,  266 

101 

11 

2 

1,038 

Other  Digestive 

3 

48 

133 

215 

185 

97 

12 

693 

Diabetes 

5 

32 

58 

26 

33 

4 

o      . 

158 

Dis.  of  Kidneys 

4 

59 

160 

291 

239 

107 

25 

1 

886 

Other  Urinary 

11 

31 

53 

78 

82 

25 

2 

282 

Childbirth.Pu-  } 

»     erperal  Dis.     f 

•  • 

'  • 

*  • 

g  Dis.  Breast       ) 
§    and  Uterus     ) 

•  * 

"3  Abscess,  Hem- ) 
S  or'age,01dAgef 

1 

16 

77 

77 

55 

37 

.   52 

25 

339 

1^ 

Debility,    Ex-  ) 
haustion,  etc.  \ 

21 

60 

88 

102 

79 

25 

2 

378 

Accid'ts,  Injuries 

16 

365 

894 

820 

449 

119 

15 

^,678 

Suicides 

1 

49 

126 

173 

106 

18 

2 

475 

1  UnknownCauses 

45 

133 

125 

122 

41 

16 

26 

508 

TABLE    XI. 


189 


(B.)    DISEASES  AND  AGES  AT  DEATH  OF  2,183  INSURED  FEMALES. 


Ages  at  Death.                                                 ' 

DISEASES. 

9f  19i  19f  29i 

29^-39139^491 

49f59i 

59^69^ 

69|-79| 

79^89^ 

Total. 

AH  Causes. 

18 

360 

698 

563 

317 

164 

51 

11 

2,182 

Zymotic 

6 

48 

98 

75 

51 

17 

6 

2 

303 

tM 

Constitutional 

5 

99 

195 

158 

70 

20 

2 

0 

549 

pS 

Nervous 

26 

45 

44 

40 

29 

9 

2 

194 

< 

Circulatory 

5 

22 

34 

23 

18 

5 

106 

» 

Respiratory 

36 

78 

78 

48 

34 

12 

1 

293 

^ 

Digestive 

3 

33 

89 

73 

47 

24 

5 

269 

Miscellaneous 

4 

113 

171 

101 

39 

22 

12 

6 

468 

Typhoid,  Typhus 

2 

25 

33 

32 

21 

5 

118 

Malarial  Fever 

1 

2 

15 

15 

9 

5 

i 

i 

49 

d 

Erysipelas 

1 

2 

1 

5 

1 

,  , 

10 

o 

Dysentery 

4 

11 

7 

5 

5 

3 

1 

35 

n 

Diarrlicea 

i 

4 

14 

2 

1 

. . 

22 

N 

Cholera 
Alcoholism 

1 

4 

5 

4 

1 
1 

•• 

•• 

•  • 

15 
1 

Other  Zymotic 

1 

8 

18 

14 

8 

1 

2 

53 

Dropsy 

2 

12 

15 

15 

4 

.  , 

45 

^ 

Cancer 

1 

5 

24 

16 

4 

2 

55 

s 

o 

Consumption 

3 

91 

165 

105 

38 

10 

, . 

413 

o 

Other  Const'l 

2 

5 

13 

14 

1 

2 

36 

Apoplexy 

4 

10 

14 

19 

9 

3 

1 

61 

n 

CongestionBrain 

3 

8 

2 

2 

2 

16 

1 

Paralysis,  Soft-  ( 
ening  Brain    i 

12 

21 

22 

15 

12 

6 

1 

86 

^ 

Epilepsy    and  [ 

1 

1 

3 

2 

1 

10 

Convulsions    ) 

Other  Nervous 

6 

5 

3 

2 

5 

21 

>. 

Diseasesof  Heart 

5 

21 

31 

22 

17 

5 

101 

b  [Other  Circulat'7 

1 

3 

1 

5 

Pneumonia 

18 

45 

53 

26 

27 

7 

177 

>> 

S 

Congest'n  Lungs 

4 

8 

6 

4 

1 

3 

1 

28 

4^ 

Bronchitis  and } 
Pleurisy          ) 

4 

9 

6 

5 

4 

1 

28 

OB 

Abscess,  Hem- ) 
or'age  Lungs ) 

8 

13 

11 

8 

2 

•• 

46 

Other  Respirat'y 

2 

3 

2 

5 

1 

14 

Dis.  of  Stomach 

6 

19 

11 

5 

7 

5 

54 

•-< 

Dis.  of  Bowels 

1 

9 

27 

15 

14 

5 

. , 

70 

1 

Peritonitis 

1 

9 

17 

7 

5 

'    2 

. . 

41 

bo 

Dis.  of  Liver 

,   , 

3 

16 

20 

9 

3 

48 

Other  Digestive 

1 

6 

10 

20 

14 

7 

56 

Diabetes 

,  , 

2 

1 

, , 

3 

Dis.  of  Kidneys 

5 

9 

8 

4 

1 

27 

Other  Urinary 

1 

3 

4 

1 

9 

Childbirth.Pu-  / 

3 

66 

94 

34 

197 

1^ 

erperal  Dis.     j" 

o 

Dis.  Breast       ) 
and  Uterus     ) 

1 

22 

34 

33 

15 

4 

1 

110 

1 

Abscess,  Hem- } 
or'age.OldAgef 

1 

7 

5 

•• 

5 

5 

4 

28 

u 

Debility,    Ex-  | 
haustion,  etc.  f 

4 

7 

4 

3 

8 

1 

2 

29 

Accid'ts,  Injuries 

6 

13 

6 

6 

3 

1 

. . 

34 

Suicides 

, , 

3 

2 

2 

7 

UnknownCauses 

•• 

5 

4 

7 

4 

1 

3 

•• 

24 

190 


TABLE     XII. 


(A)  MALE  LIFE.    DISEASES  AND  NUMBER  OF  DEATHS  BY  STATES  AND  TERRITORIES. 


1. 

_6 

o 
B 

o 

1 
B 

i 

i 

i  . 

§1 

>> 

3 
O 
t 

1 

O 

1 

O 

.2 
o  • 
o 

1 

■ft 

u 
a> 

1 

>, 

1 
.1 

00 

C 

i 

CD  <0 

< 

1 

p 

1 

o 

i 
1 

(5 

O 

P 

5 

^ 

Alabama 

10 

50 

26 

7 

10 

23 

12 

20 

22 

40 

5 

26 

3 

6 

260 

Arkansas 

21 

6 

3 

2 

8 

4 

11 

1 

10 

11 

5 

82 

California 

38 

78 

121 

38 

47 

84 

67 

63 

38 

65 

20 

92 

24 

30 

805 

Colorado 

1 

1 

3 

1 

2 

1 

1 

2 

2 

2 

6 

1 

1 

24 

Connecticut 

179 

165 

314 

96 

67 

148 

131 

108 

71 

122 

42 

103 

19 

83 

1648 

Delaware 

4 

11 

10 

4 

3 

3 

2 

7 

2 

11 

3 

60 

Dist.  of  Col'bia 

7 

23 

50 

7 

9 

21 

9 

19 

13 

17 

4 

8 

4 

12 

203 

Florida 

1 

10 

10 

4 

6 

3 

3 

2 

7 

2 

48 

Georgia 

8 

45 

20 

*6 

i2 

20 

7 

16 

14 

25 

2 

14 

1 

7 

197 

Idaho 

1 

1 

4 

6 

Illinois 

151 

270 

398 

106 

92 

233 

105 

235 

134 

261 

46 

206 

25 

76 

2338 

Indiana 

63 

135 

181 

37 

24 

92 

38 

126 

68 

98 

11 

83 

12 

28 

996 

Iowa 

33 

65 

97 

28 

19 

73 

36 

46 

38 

62 

11 

39 

9 

22 

578 

Kansas 

11 

21 

19 

7 

1 

14 

3 

13 

5 

13 

4 

22 

4 

4 

141 

Kentucky 

19 

73 

93 

24 

33 

49 

26 

53 

33 

49 

8 

57 

19 

21 

557 

Louisiana 

9 

112 

54 

12 

18 

44 

13 

15 

14 

50 

10 

31 

2 

14 

398 

Maine 

74 

114 

158 

47 

18 

79 

34 

48 

50 

64 

12 

73 

12 

33 

816 

Maryland 

54 

104 

176 

57 

59 

113 

66 

82 

57 

91 

22 

49 

6 

43 

979 

Massachusetts 

297 

392 

857 

229 

182 

379 

244 

245 

207 

275 

136 

359 

51 

255 

4108 

Michigan 

69 

105 

162 

41 

40 

77 

51 

91 

55 

95 

13 

88 

21 

37 

945 

Minnesota 

43 

20 

70 

9 

21 

29 

20 

30 

25 

30 

9 

40 

2 

8 

356 

Mississippi 

7 

54 

26 

9 

13 

14 

9 

20 

10 

24 

2 

19 

1 

12 

220 

Missouri 

75 

277 

178 

49 

66 

122 

49 

101 

71 

120 

16 

99 

17 

62 

1302 

Mon.Neb.ISTev. 

9 

13 

11 

5 

2 

14 

2 

10 

6 

14 

1 

16 

1 

4 

108 

New  Hamps're 

58 

60 

110 

22 

33 

65 

23 

40 

40 

56 

13 

41 

5 

34 

600 

New  Jersey 

54 

97 

249 

44 

49 

97 

74 

73 

46 

95 

32 

52 

11 

56 

1029 

New  Mexico 

1 

3 

1 

,  , 

1 

6 

New  York 

449 

643 

143i 

395 

424 

768 

474 

572 

473 

66i 

290 

422 

95 

346 

7443 

N.  Carolina 

7 

39 

25 

7 

6 

14 

8 

17 

11 

29 

3 

9 

6 

181 

Ohio 

140 

232 

408 

91 

111 

203 

91 

166 

160 

233 

38 

185 

33 

95 

2186 

Oregon 

2 

3 

8 

3 

3 

1 

1 

3 

3 

3 

5 

1 

36 

Pennsylvania 

199 

264 

575 

167 

135 

291 

195 

174 

157 

326 

85 

174 

35 

170 

2947 

Rhode  Island 

15 

38 

80 

24 

26 

42 

29 

30 

11 

35 

10 

16 

3 

18 

377 

S.  Carolina 

3 

13 

14 

6 

10 

10 

4 

9 

7 

17 

3 

2 

3 

101 

Tennessee 

8 

160 

63 

8 

24 

22 

16 

27 

16 

46 

4 

27 

6 

14 

441 

Texas 

7 

51 

20 

10 

9 

18 

6 

20 

13 

34 

1 

21 

5 

10 

225 

Utah 

1 

3 

1 

1 

2 

1 

9 

Vermont 

25 

33 

58 

8 

13 

24 

17 

23 

15 

29 

1 

21 

2 

12 

281 

Virginia 

15 

33 

34 

5 

13 

17 

17 

14 

9 

17 

3 

20 

1 

7 

205 

Washington 

1 

1 

1 

1 

2 

, . 

6 

West  Virginia 

5 

6 

13 

i 

10 

10 

2 

< 

5 

15 

5 

i 

4 

84 

Wisconsin 

121 

142 

227 

71 

46 

106 

51 

114 

86 

145 

17 

139 

33 

64 

1362 

Unknown 

1 

5 

2 

1 

4 

1 

1 

1 

4 

1 

24 

45 

Brit'h  America 

29 

37 

73 

9 

23 

45 

24 

35 

45 

39 

10 

46 

5 

19 

439 

Other  Foreign 

6 

33 

41 

11 

25 

21 

17 

16 

17 

22 

2 

33 

3 

17 

264 

Total 

2307 

4049 

6472 

1705 

1703j3403 

1987 

2711 

2056 

3345 

887 

2678474 

1665 

35442 

TABLE     XII, 


191 


(B)  FEMALE  LIFE.    DISEASES  AND  NUMBER  OF  DEATHS  BY  STATES  AND  TEBBITOEIES 


o  a. 

o 

o 

a 
o 

a 
o 

ft 

a 

§ 

3 

1-3 

5 
o 

1 

< 

3 
O 

1 

1 

O 

o 

5 

a 
o 
B 
g 

o 

g 

1 
o 

O 

B 
o 

to 

CO 

1 
5 

6>> 

o 

5 

-d    a 

a    a) 

1  2 

e  2 

i" 
(5 

1 
5 

1 

o 

i    i 
1 

1   ^ 

Alabama 

2 

3 

3 

3 

2 

1 

3 

3 

1 

21 

Arkansas 

1 

1 

1 

3 

California 

2 

4 

2 

2 

2 

1 

1 

5 

6 

2 

-      0 

,       33 

Colorado 

,  , 

Connecticut 

14 

16 

36 

10 

6 

19 

7 

7 

10 

20 

2 

9 

5 

13 

174 

Delaware 

1 

2 

1 

1 

2 

1 

8 

Distof  Col'bia 

2 

3 

1 

2 

2 

, . 

1 

1 

12 

Florida 

1 

1 

Georgia 

7 

2 

1 

1 

3 

. . 

i;  .. 

. . 

2 

20 

Idaho 

. . 

Illinois 

11 

15 

35 

7 

2 

7 

9 

7 

10 

23 

19 

8 

16 

169 

Indiana 

11 

12 

9 

2 

4 

3 

4 

20 

5 

13 

10 

5 

5 

103 

Iowa 

5 

5 

11 

2 

1 

3 

4 

3 

4 

8 

1 

5 

3 

55 

Kansas 

1 

3 

1 

2 

2 

,  . 

1 

1 

2 

13 

Kentucky 

6 

3 

1 

4 

3 

3 

1 

4 

3 

28 

Louisiana 

. . 

2 

1 

1 

i 

i 

1 

2 

2 

11 

Maine 

1 

5 

1 

1 

. . 

2 

1 

2 

. . 

13 

Maryland 

2 

4 

16 

5 

4 

7 

4 

4 

2 

11 

4 

3 

3 

3 

72 

Massachusetts 

7 

15 

52 

17 

4 

12 

12 

14 

8 

23 

3 

29 

8 

16 

220 

Michigan 

4 

8 

19 

11 

3 

4 

4 

7 

5 

8 

1 

6 

7 

6 

93 

Minnesota 

1 

1 

1 

^  , 

3 

3 

6 

15 

Mississippi 

3 

3 

1 

1 

1 

1 

2 

3 

, . 

1 

i 

i 

18 

Missouri 

4 

6 

6 

4 

2 

2 

1 

7 

3 

10 

8 

2 

3 

58 

Mon.Neb.Nev. 

^  , 

,  , 

1 

1 

1 

1 

4 

New  Hamps're 

5 

15 

5 

1 

3 

2 

5 

3 

9 

1 

6 

1 

2 

58 

New  Jersey- 

5 

14 

3 

5 

3 

4 

4 

5 

5 

2 

5 

2 

5 

62 

New  Mexico 

. , 

New  York 

17 

33 

68 

31 

7 

28 

24 

33 

27 

45 

8 

21 

24 

19 

385 

N.  Carolina 

5 

2 

3 

2 

1 

1 

3 

1 

1 

19 

Ohio 

6 

14 

31 

10 

7 

11 

5 

21 

12 

16 

1 

18 

9 

10 

171 

Oregon 

,   , 

1 

1 

Pennsylvania 

8 

7 

30 

9 

4 

11 

10 

8 

4 

23 

9 

9 

8 

140 

Rhode  Island 

1 

6 

2 

3 

1 

2 

4 

1 

1 

21 

S.  Carolina 

1 

1 

1 

1 

4 

2 

1 

11 

Tennessee 

1 

3 

3 

1 

2 

1 

3 

4 

,  , 

1 

19 

Texas 

1 

,  , 

1 

1 

1 

1 

1 

3 

1 

10 

Utah 

,  , 

^  , 

,  , 

. , 

Vermont 

1 

1 

9 

2 

1 

1 

2 

1 

3 

3 

1 

2 

27 

Virginia 

2 

. . 

^  , 

1 

1 

1 

1 

6 

Washington 

. . 

West  Virginia 

i 

2 

1 

i 

5 

Wisconsin 

7 

3 

is 

4 

1 

4 

1 

5 

1 

8 

2 

9 

5 

3 

66 

Unknown 

1 

1 

li 

3 

Brit'h  America 

2 

,  , 

6 

1 

i 

3 

1 

4 

3 

3 

2! 

26 

Other  Foreign 

1 

3 

•• 

1 

•  • 

2 

1 

8 

Total 

118 

184 

409 

138 

63 

132 

105 

176 

116 

273 

27 

198 

110 

133 

2182 

192 


TABLE     XIII. 


MALE  LIFE  (A).     RATIO  OF  DEATHS  BY  EACH  DISEASE  TO  10,000  LIVING  EXPOSED  TO 
RISK,  AN  EQUAL  NUMBER  10,000  IN  EACH  STATED  PERIOD  OF  INSURANCE. 


Duration  or  Tears  of  Insurance. 

DISEASES. 

0-h 

fH 

If2i 

2Hi 

.4f9i 

H-^H 

19f29| 

r  Total. 

ActTD'th 

All  Causes. 

68.6 

80.4 

93.1 

102.5 

114.5 

140.9 

213.5 

102.0 

35,442 

Zymotic 

23.7 

19.0 

18.8 

17.1 

16.3 

17.5 

21.1 

18.3 

6,356 

>i  Constitutional 

6.3 

15.3 

22.5 

27.5 

30.0 

32.3 

32.4 

23.5 

8,175 

2§  Nervous 

8.3 

9.6 

11.8 

14.1 

17.2 

25.6 

43.8 

14.7 

5,107 

B   Circulatory 

2.1 

3.0 

4.0 

5.4 

7.3 

11.3 

25.0 

5.7 

1,986 

P   Respiratory 

8.9 

11.9 

12.6 

13.6 

15.0 

19.1 

29.4 

13.7 

4,770 

*"  i  Digestive 

6.0 

7.6 

9.2 

9.3 

10.7 

13.8 

18.7 

9.6 

3,344 

jMiscellaneous 

13.3 

14.0 

14.2 

15.5 

18.0 

21.3  1     43.1 

16.5 

5,704 

Typhoid,Typhus 

1     8.9 

7.4 

1       7.2 

6.2 

5.7 

5.6  1       7-2 

6.6 

2,306 

Malarial  Fever 

3.0 

2.5 

!       2.4 

2.3 

2.1 

2.1  i       2.3 

2.4 

831 

.s 

Erysipelas 

.6 

.6 

1.1 

1.0 

1.3 

1.8  1      2.1 

1.1 

374 

1 

Dysentery 

2.6 

1.6 

1.5 

1.6 

1.4 

1.8 

2.7 

1.7 

587 

Diarrhoea 

.8 

.8 

1.0 

.9 

.8 

1.6 

2.1 

1.0 

328 

Cholera 

2.8 

1.5 

1.3 

1.0 

.8 

.7 

.4 

1.2 

431 

Alcoholism 

.2 

.4 

.3 

.4 

.3 

.6 

.3 

117 

Other  Zymotic 

4.8 

4.2 

4.0 

3.7 

3.9 

3.3 

4.3 

4.0 

1,382 

.  ^Dropsy 

.7 

1.1 

1.3 

1.9 

2.0 

3.3 

4.1 

1.8 

611 

*j  Cancer 

.4 

.9 

1.0 

2.0 

2.5 

3.3 

7.8 

1.8 

632 

o  Consumption 

4.3 

12.4 

19.0 

22.3 

24.1 

23.7 

15.9 

18.6 

6,474 

Other  Const'l 

.9 

.9 

1.2 

1.3 

1.4 

2.0 

4.6 

1.3 

458 

Apoplexy 

3.2 

3.3 

4.1 

4.7 

5.3 

8.6 

17.0 

4.9 

1,705 

CongestionBrain 

1.8 

1.6 

1.7 

1.9 

2.0 

2.2 

2.7 

1.9 

655 

1 

Paralysis,  Soft-) 
ening  Brain    '' 

2.8 

3.9 

4.7 

5.9 

8.2 

12.2       19.9 

6.4 

2,236 

£ 

Epilepsy    and  } 
Convulsions    ) 

.1 

.2 

.4 

.5 

.4 

.6           .5 

.4 

130 

Other  Nervous 

.4 

.6 

.9 

1.1 

1.3 

2.0         3.7 

1.1 

381 

^  Diseasesof  Heart 

1.8 

2.7 

3.8 

5.1 

6.8 

10.7       23.4 

5.3 

1,855 

o  lOther  Circulat'y 

.3 

.3 

.2 

7.2 

.3 

.5 

.6  '       1.6 

.4 

131 

Pneumonia 

5.4 

7.0 

7.6 

8.6 

10.7       15.9 

7.8 

2,7U 

u  iCongest'n  Lungs 

1.2 

1.4 

1.6 

1.4 

1.6 

2.4  :       4.4 

1.6 

568 

<a 
'p. 

Bronchitis  and  | 
Pleurisy          j 

6. 

1.4 

1.4 

2.0 

1.9 

2,6         5.6 

1.7 

610 

00 

Abscess,  Hem-  / 

1.3 

1.6 

1.8 

2.1 

2.3 

2.6         2.1 

2.0 

683 

or'age  Lungs  f 

Other  Respirat'y 

.4 

.5 

.6 

.5 

.6 

.8         1.4 

.6 

198 

^  JDis.  of  Stomach 

1.0 

1.3 

1.8 

1.8 

1.8 

3.3  1       4.1 

1.8 

628 

.t  'Dis.  of  Bowels 

1.7 

1.8 

2.0 

2.1 

2.2 

2.9 

3.2 

2.1 

739 

S  1  Peritonitis 

.5 

.8 

.7 

.6 

.7 

.6 

1.4 

.7 

246 

g  Dis.  of  Liver 
1  Other  Digestive 

1.2 

2.1 

3.0 

•     3.0 

3.7 

4.2 

5.2 

3.0 

1,038 

1.6 

1.6 

1.7 

1.8 

2:3 

2.8 

4.8 

2.0 

693 

Diabetes 

.1 

.3 

.2 

.4 

.7 

.7 

2.5 

.5 

158 

Dis.  of  Kidneys 

.9 

1.3 

2.0 

2.3 

3.4 

4.8 

9.0 

2.5 

886 

Other  Urinary 

.2 

.4 

.5 

.7 

1.0 

1.9 

5.0 

.8 

282 

Childbirth,  Pu-( 
erperal  Dis.      ) 

S 

§  Dis.  Breast       )  1 
g     and  Uterus    J 

•  • 

•  • 

•  • 

•  • 

•  • 

•  • 

*  • 

*  • 

g   Abscess,  Hem-  ) 
.5  :Or'age,01(iAge  J 

.3 

.7 

.6 

.8 

.9 

1.7 

11.8 

1.0 

339 

*  Debility,  Ex-    ) 
haustion,  etc. ) 

.2 

.6 

.7 

1.0 

1.4 

2.1 

6.8 

1.1 

378 

Accid'ts,  Injuries 

9.4 

8.3 

7.7 

7.6 

7.4 

6.8 

5.1 

7.7 

2,678 

Suicides 

1.0 

1.3 

1.4 

1.3 

1.6 

1.3 

2.0 

1.4 

475 

UnknownCauses 

1.2 

1.1 

1.1 

1.4 

1.6 

2.0 

.9 

1.5 

508 

Actual  Deaths 

2,445 

5,161 

4,651 

7,803 

10,062 

4,089 

1,197  ; 

J5,442    [ 

J5,442 

E 

xposed  to  Risk 

356,210, 

640,900 

499,870 

757,120 

876.050 

290,150  j    56,035  |.' 

J,476,335  3,476,335| 

TABLE    XIII 


193 


(B.)    FEMALE  LIFE.     RATIO  OF  DEATHS  BY  EACH  DISEASE  TO  10,000  LIVING  EXPOSED 
TO  RISK,  AN  EQUAL  NUMBER  10,000  IN  EACH  STATED  PERIOD  OF  INSURANCE, 


1 

Duration  oi 

Years  of  Insurance 

DISEASES. 

Oi 

fH 

n-H 

2Hi 

4f9i 

9il9i  19i-29i 

Total. 

Actual 
Deaths. 

All  Causes. 

85.9 

103.9 

114.1 

109.2 

123.8 

148.3 

r/5.8 

114.9 

2,182 

Zymotic 

21.2 

15.6 

15.3 

14.3 

13.8 

16.8 

5.7 

16.1 

302 

{h"  Constitutional 

8.0 

22.4 

34.2 

28.0 

35.8 

51.7 

31.6 

28.8 

547 

P^  Nervous 

7.3 

7.5 

10.5 

10.1 

8.4 

18.3 

28.8 

10.2 

195 

< 

Circulatory 

4.0 

2.9 

4.1 

5.4 

7.7 

7.2 

25.9 

5.5 

105 

» 

Respiratory 

9.3 

16.2 

15.2 

15.4 

16.0 

15.1 

31.8 

15.3 

292 

^ 

Digestive 

12.3 

13.8 

12.4 

13.3 

16.2 

15.2 

26.0 

14.3 

273 

Miscellaneous 

23.8 

25.5 

22.4 

22.7 

25.9 

24.0 

26.0 

24.7 

468 

Typhoid,Typhu8 

7.0 

6.3 

7.0 

6.2 

5.3 

5.6 

5.7 

6.3 

118 

Malarial  Fever 

3.5 

3.1 

3.7 

1.6 

1.5 

4.0 

. . 

2.6 

49 

o 

Erysipelas 

. . 

.  . 

.7 

1.0 

, . 

.5 

10 

•;3 

o 

Dysentery 

3.1 

,  , 

i.6 

1.4 

2.9 

2.4 

. . 

1.9 

35 

9  [Diarrhoea 

1.8 

1.8 

1.0 

.9 

.7 

.  , 

, , 

1.2 

22 

N  Cholera 

1.8 

.5 

1.0 

.9 

.5 

,  , 

.8 

15 

Alcoholism 

.1 

1 

Other  Zymotic 

4.0 

3.9 

1.0 

2.6 

1.9 

4.8 

2.7 

52 

.  Dropsy 

.9 

2.1 

2.4 

1.9 

3.4 

4.8 

2.6 

49 

S  Cancer 

.9 

1.0 

3.0 

4.3 

1.9 

8.7 

8.6 

2.7 

51 

g  Consumption 

6.2 

17.7 

26.4 

20.1 

28.8 

32.6 

23.0 

21.5 

409 

"  [other  Const'l 

1.6 

2.4 

1.7 

1.7 

5.6 

2.0 

38 

Apoplexy 

3.1 

2.6 

2.7 

2.8 

3.1 

4.0 

5.8 

3.3 

63 

•» 

CongestionBrain 

.9 

.5 

1.3 

.5 

.7 

1.6 

.9 

16 

1 

Paralysis,  Soft- } 
ening  Brain   ) 

3.3 

3.4 

5.1 

4.5 

3.4 

8.7 

23.0 

4.5 

86 

!^ 

Epilepsy    and  ^ 
Convulsions    ^ 

.9 

.7 

1.6 

.4 

9 

Other  Nervous 

1.0 

1.4 

1.4 

.5 

2.4 

1.1 

21 

>% 

Diseasesof  Heart 

3.1 

2.9 

3.4 

5.4 

7.7 

7.2 

25.9 

5.2 

100 

U 

Other  Circulat'y 

.9 

.7 

.3 

5 

Pneumonia 

8.4 

9.7 

8.1 

10.2 

9.0 

9.5 

14.4 

9.3 

176 

>> 

Congest'n  Lungs 

.  , 

1.3 

1.7 

.9 

2.2 

2.4 

5.8 

1.5 

30 

u 

Pi 

Bronchitis  and ) 
Pleurisy          ) 

•,• 

1.3 

1.7 

2.4 

.7 

1.6 

5.8 

1.6 

31 

(0 

Abscess,  Hem- ) 
or'age  Lungs ) 

.9 

3.9 

2.7 

1.4 

3.1 

2.2 

.  42 

Other  Respirat'y 

1.0 

.5 

1.0 

l.,6 

5.8 

.7 

13 

Dis.  of  Stomach 

3.6 

3.1 

2.0 

2.6 

3.4 

2.4 

5.8 

2.7 

52 

•5 

Dis.  of  Bowels 

3.1 

5.0 

3.4 

2.1 

4.1 

4.8 

5.8 

3.6 

69 

Peritonitis 

2.2 

1.8 

3.0 

3.1 

1.0 

8.6 

2.1 

41 

bo 
P 

Dis.  of  Liver 

.9 

2.1 

2.0 

3.1 

3.6 

3.2 

2.8 

53 

Other  Digestive 

3.5 

1.8 

2.0 

2.4 

4.1 

4.8 

5.8 

3.1 

58 

Diabetes 

.7 

.2 

3 

Dis.  of  Kidneys 

1.3 

1.0 

i.3 

.9 

2.2 

i.6 

. . 

1.5 

27 

Other  Urinary 

.8 

.4 

.7 

.5 

9 

OQ 

Childbirth,Pu-  } 
erperal  Dis.     ) 

13.2 

13.3 

8.5 

10.7 

9.7 

4.8 

•• 

10.4 

198 

b 

a 

Dis.  Breast       ) 
and  Uterus    ) 

2.6 

6.0 

6.8 

5.9 

6.8 

4.8 

5.8 

5.8 

110 

Abscess,  Hem- ) 
or'age.OldAgey 

.9 

.8 

2.0 

1.2 

.7 

4.8 

8.6 

1.5 

28 

3 

Debility,    Ex-  ) 
haustion,  etc.  j 

.9 

.8 

1.4 

.7 

2.2 

4.8 

5.8 

1.6 

31 

Accid'ts,  Injuries 

2.2 

1.8 

1.4 

1.7 

1.9 

5.8 

1.7 

32 

Suicides 

.9 

.5 

.3 

7 

{UnknownCausea 

1.8 

1.0 

1.0 

.7 

1.0 

3.2 

1.2 

23 

Actual  Deaths 

197 

403 

341 

467 

513 

190 

70 

2,182 

2,182 

Exposed  to  Risk 

22,610 

38,142 

29,431 

43,032 

41,124 

12,529 

3,458 

189.340 

189,340 

194 


TABLE     XIT. 


MALE  LIFE  (A).      RATIO  OF  DEATHS  BY  EACH  DISEASE  TO  10,000  LIVING  EXPOSED 
TO  RISK,  AN  EQUAL  NUMBER  10,000  IN  EACH  PERIOD  OF  AGE. 


75.7 

Ages  of  Expoi 

nire. 

DISEASES. 

19i-29^ 

29f39| 

39f  49i  49|-59i  59f  69^ 

69^-79^ 

79^-891 

1389. 7 

AllAges 

il02.0 

All  Causes. 

74.8 

76.0 

97.5 

146.0 

270.4 

538.0 

Zymotic 

30.7 

19.5 

15.2 

17.5 

21.9 

31.4 

48.2 

75.5 

18.3 

>i 

Constitutional 

12.6 

24.0 

22.0 

22.0 

25.9 

39.0 

63.2 

30.2 

!  23.5 

P4 

Nervous 

5.1 

5.1 

8.1 

14.2 

27.2 

59.0 

112.3 

120.9 

14.7 

Circulatory 

1.7 

1.3 

2.7 

4.8 

11.2 

31.3 

67.4 

75.5 

5.7 

?^ 

Respiratory 

6.3 

8.0 

9.5 

13.7 

21.5 

39.0 

73.2 

135.9 

13.7 

03 

Digestive 

6.8 

4.7 

6.2 

10.2 

15.6 

29.1 

37.4 

105.7 

9.6 

Miscellaneous 

12.5 

12.3 

12.3 

15.1 

22.7 

41.6 

136.4 

845.8 

16.5 

Typhoi(l,Typlius 

15.9 

10.2 

5.7 

5.6 

7.0 

9.3 

5.8 

.. 

6.6 

Malarial  Fever 

2.3 

1.6 

2.1 

2.6 

3.0 

4.7 

4.2 

2.4 

u 

Erysipelas 

.6 

.7 

1.2 

1.6 

3.0 

5.0 

15.1 

1.1 

i 

Dysentery 

4.0 

1.3 

1.3 

1.4 

2.6 

3.5 

10.0 

15.1 

1.7 

i 

Diarrhoea 

1.7 

.6 

.6 

.9 

1.4 

3.0 

8.3 

30.2 

1.0 

N 

Cholera 

2.8 

1.2 

1.1 

1.3 

1.4 

1.7 

1.7 

1.2 

Alcoholism 

.1 

.3 

.5 

.3 

.1 

. . 

.3 

Other  Zymotic 

4.0 

3.9 

3.3 

4.1 

4.6 

6.1 

13.3 

15.1 

4.0 
1.8 

Dropsy 

,   ^ 

.4 

.8 

1.7 

3.5 

8.0 

12.5 

15.1 

4A 

Cancer 

.   , 

.2 

.6 

1.7 

4.6 

8.6 

16.6 

1.8 

g 

Consumption 

12.0 

22.7 

19.6 

17.4 

15.8 

17.6 

19.1 

15.1 

18.6 

1 

Other  Const'l 

.6 

.8 

.9 

1.2 

2.0 

4.8 

15.0 

1.3 

Apoplexy 

.6 

.9 

1.9 

4.5 

11.5 

22.5 

38.3 

15.1 

'  4.9 

to 

CongestionBrain 

1.7 

1.1 

1.5 

2.1 

2.5 

3.5 

4.2 

1.9 

> 

Paralysis,  Soft-) 
ening  Brain    J 

2.3 

2.3 

3.5 

6.0 

11.0 

28.6 

65.7 

90.6 

6.4 

»z; 

Epilepsy    and 
Convulsions 

.2 

.4 

.4 

.5 

1.1 

1.7 

.4 

Other  Nervous 

.6 

.5 

.7 

1.2 

1.6 

3.5 

2.5 

15.1 

1.1 

y  jDiseasesof  Heart 
<S  1  Other  Circulat'y 

1.7 

1.3 

2.5 

4.4 

10.7 

29.2 

64.9 

75.5 

5.3 

.2 

.4 

.6 

2.2 

2.5 

.4 

Pneumonia 

3.4 

3.9 

4.8 

7.9 

13.3 

24.6 

40.8 

45.3 

7.8 

^ 

Congest'n  Lungs 

1.1 

.9 

1.1 

1.7 

2.5 

4.6 

13.3 

15.1 

1.6 

Bronchitis  and  | 
Pleurisy          j 

1.1 

.9 

1.2 

1.8 

2.6 

5.0 

12.5 

60.4 

1.7 

•p, 

S 
M 

Abscess,  Hem- ) 
or' age  Lungs  ^ 

.6 

1.9 

2.0 

1.7 

2.2 

3.4 

5.0 

•• 

2.0 

Other  Respirat'y 

.3 

.4 

.5 

1.0 

1.5 

1.7 

.6 

1 

Dis.  of  Stomach 

1.7 

.5 

1.0 

2.0 

3.1 

6.0 

13.3 

15.1 

1.8  I 

>    \ 

Dis.  of  Bowels 

1.1 

1.0 

1.8 

1.9 

3.1 

5.9 

4.2 

45.3 

2.1 

S 

Peritonitis 

1.1 

.8 

.6 

.7 

.8 

1.2 

.7 

bo 

Dis.  of  Liver 

1.1 

.8 

1.7 

3.7 

5.1 

8.1 

9.1 

30.2 

3.0 

Other  Digestive 

1.7 

1.0 

1.1 

1.9 

3.6 

7.8 

10.0 

2.0 

Diabetes 

,  , 

.1 

.3 

.5 

.5 

2.6 

3.3 

0.5 

Dis.  of  Kidneys 

2.3 

1.3 

1.3 

2.6 

4.6 

8.6 

20.8 

15.1 

2.5 

i 

Other  Urinary 

.2 

.3 

.5 

1.5 

6.6 

20.8 

30.2 

.8 

Childbirth,  Pu-/ 
erperal  Dis.      j 

^ 

e 

Dis.  Breast       ) 
and  Uterus    ) 

•  • 

•  • 

•  • 

• ' 

*  • 

Abscess,  Hem-  ) 
or'age,01dAge  ) 

.6 

.3 

.6 

.7 

1.1 

3.0 

43.2 

377.6 

1.0 

i4 

Debility,  Ex-    { 
haustion,  etc.  \ 

.5 

.5 

.8 

2.0 

6.4 

20.8 

30.2 

1.1 

Accid'ts,  Injuries 

9.1 

7.9 

7.3 

7.4 

8.7 

9.6 

12.5 

7.7 

Suicides 

.6 

1.1 

1.0 

1.6 

2.0 

1.5 

1.7 

1.4 

UnknownCauses 

1.0 

1.1 

1.1 

2.4 

3.3 

13.3 

392.7 

1.5 

Actual  Deaths 

133 

3,476 

9,321 

10,840 

7,576 

3,357 

647 

92   ; 

55,442 

Exposed  to  Risk 

17,576 

464,444 

1,226,542 

1,113,191 

518.747 

134,148 

12,025 

663 

3.476,335 

TABLE     XIY. 


195 


FEMALE  LIFE  (B).     RATIO  OF  DEATHS  BY  EACH  DISEASE  TO  10,000  LIVING  EXPOSED 
TO  RISK,  AN  EQUAL  NUMBER  10,000  IN  EACH  PERIOD  OF  AGE. 


Ages  of 

Ezposare. 

DISEASES. 

19f29i|29f39i 

39H9i  1 49f  59i 

59f69i 

69i-79^ 

All  Ages.  I  Act'l  Deaths 

All  Causes. 

104.7 

101.4 

106.5 

i    134.7 

262.7 

630.2 

114.9       2,182 

Zymotic 

14.1 

14.2 

14.2 

i      21.6 

27.2 

74.2 

16.1   1       302 

JM 

Constitutional 

28.7 

28.4 

29.9 

29.8 

32.0 

24.6 

28.8          547 

Nervous 

7.6 

6.5 

8.3 

17.1 

46.5 

111.3 

10.2           195 

s 

Circulatory 

1.4 

3.3 

6.5 

9.4 

28.8 

61.8 

5.5           105 

M 

p 

Respiratory 

10.5 

11.3 

14.7 

20.3 

54.4 

148.3 

15.3           292 

oa 

Digestive 

9.5 

12.9 

13.8 

19.9 

38.5 

61.8 

14.3          273 

Miscellaneous 

32.9 

24.8 

'    19.1 

16.6 

35.3 

148.2 

24.7          468 

Typhoid,Typhu8 

7.3 

4.7 

6.0 

8.9 

8.0 

6.3          118 

Malarial  Fever 

.6 

2.2 

2.7 

3.9 

8.0 

12.4 

2.6 

49 

u 

Erysipelas 

.3 

.3 

.2 

2.1 

1.6 

.5 

10 

1 

Dyse  ntery 

1.2 

1.6 

1.4 

2.1 

8.0 

37.1 

1.9 

35 

Diarrhoea 

1.3 

2.0 

.4 

.4 

1.2 

22 

N 

Cholera 
Alcoholism 

1.2 

.8 

.8 

.4 
.4 

.8 
.1 

15 
1 

Other  Zymotic 

2.3 

2.6 

2.7 

3.4 

i.6 

24.7 

2.7 

52 

Dropsy 

.6 

1.7 

2.8 

6.4 

6.4 

2.6 

49 

la 

Cancer 

.3 

.8 

4.6 

6.8 

6.4 

24.6 

2.7 

51 

i 

Consumption 

26.4 

24.0 

19.8 

16.2 

16.0 

, . 

21.5   '       409  1 

C9 

Other  Const'l 

1.4 

1.9 

2.7 

.4 

3.2 

2.0 

38 

Apoplexy 

1.2 

1.4 

2.6 

8.0 

14.5 

37.1 

3.3 

63 

B 

CongestionBrain 

.9 

1.2 

.4 

.9 

3.2 

.9 

16 

0 
O 

t 

Paralysis,  Soft-) 
ening  Brain    J 

3.5 

3.0 

4.1 

6.4 

19.2 

74.2 

4.5 

86 

^ 

Epilepsy    and  ) 
Convulsions    ) 

.3 

.2 

.6 

.9 

1.6 

.4 

9 

Other  Nervous 

1.7 

.7 

.6 

.9 

8.0 

1.1 

21 

•^  Diseasesof  Heart 

1.4 

3.1 

5.9 

9.4 

27.2 

61.8 

5.2          1 

00 

3   Other  Circulat'y 

.2 

.6 

1.6 

.3 

5 

. 

Pneumonia 

5.2 

6.5 

10.0 

11.0 

43.2 

86.6 

9.3          1 

76 

o 

Congest'n  Lungs 

1.2 

1.2 

1.1 

1.7 

1.6 

37.1 

1.5 

30 

(8 

>4 

Bronchitis  and  ) 
Pleurisy    ■       j 

].2 

1.3 

1.1 

2.1 

6.4 

12.3 

1.6 

31 

■a 

Abscess,  Hem- } 
or'age  Lungs  f 

2.3 

1.9 

2.1 

3.4 

3.2 

•• 

2.2    . 

42 

Other  Respirat'y 

.6 

.4 

.4 

2.1 

12.3 

.7 

13 

^-  Dis.  of  Stomach 

1.7 

2.7 

2.1 

2.1 

11.2 

61.8 

2.7 

52 

.5  Dis.  of  Bowels 

2.6 

3.9 

2.8 

5.9 

8.0 

3.6 

69 

S   Peritonitis 

2.6 

2.5 

1.4 

2.1 

3.3 

,  , 

2.1 

41 

2  |Di8.  of  Liver 

.9 

2.3 

3.8 

3.9 

4.8 

,  , 

2.8 

53 

lOther  Digestive 

1.7 

1.5 

3.7 

5.9 

11.2 

3.1 

58 

Diabetes 

.4 

.4 

.2 

3 

Dis.  of  Kidneys 

i.4 

1.3 

1.6 

1.7 

12.3 

1.5 

27 

Other  Urinary 

.3 

.4 

1.7 

1.6 

.5 

9 

3 

Childbirth, Pu-  i 
erperal  Dis.     j 

19.3 

13.6 

6.3 

10.4          1 

98 

S  Dis.  Breast       ) 
§     and  Uterus     f 

6.4 

5.0 

6.2 

6.4 

6.4 

12.3 

5.8          1 

10 

g   Abscess,  Hem-  ) 
.2  'or'age,01dAge  ' 

.3 

1.0 

.9 

8.1 

61.8 

1.5 

?,8 

^ 

Debility,  Ex-    } 
haustion,  etc. ) 

1.2 

1.0 

.8 

1.3 

12.8 

12.4 

1.6 

31 

Accid'ts,  Injuries 

1.7 

1.9 

1.1 

2.5 

4.8 

12.3 

1.7 

32 

Suicides 

.9 

.4 

.9 

.3 

7 

1  UnknownCauses 

1.4 

6 

1.4 

1.7 

1.6 

37.1 

1.2 

23 

Actual  Deaths 

360 

698 

563 

317 

164 

51 

2,182       2,1 

32 

Exposed  to  Risk 

34,427 

68,769 

52,783 

23,536 

6,245 

809 

189,340      189,3 

40 

196 


TABLE     XY. 


(A.)    MALE  LIFE.    PERCENTAGE   DISTRIBUTION   OF    DISEASES    AMONG   100  DEATHS, 
THE    SAME  NUMBER  100  IN  EACH  PERIOD  OF   INSURANCE. 


'~ 

1 

Dtiration  or  Years  of  Insurance. 

DISEASES. 

3-i 

^-li 

H-2i 

2^-4i 

H-9i 

H-19i 

I9i-29i 

Total. 

'                 All  Causes. 

100.0 

100.0 

100.0 

100.0 

100.0 

100.0 

100.0 

100.0 

Zymotic  Diseases 

34.5 

23.6 

20.3 

16.7 

14.1 

12.5 

9.9 

17.9 

r>H 

Constitutional  Diseases 

9.2 

18.9 

24.2 

26.8 

26.1 

23.0 

15.2 

23.1 

< 

Nervous  Diseases 

12.1 

12.1 

12.7 

13.8 

15.2 

18.1 

20.6 

14.4 

Circulatory  Diseases 

3.1 

3.6 

4.3 

5.2 

6.3 

8.1 

11.7 

5.6 

to 

Respiratory  Diseases 

12.8 

14.8 

13.3 

13.2 

13.1 

13.5 

13.^ 

13.5. 

s 

Digestive  Diseases 

8.8 

9.6 

10.0 

9.2 

9.5 

9.8 

8.8 

9.5 

Miscellaneous  Diseases 

19.5 

17.4 

15.2 

15.1 
6.0 

15.7 

15.0 

20.0 

16.0 

Typhoid,  Typhus  Fever 

13.0 

9.2 

7.7 

4.9 

3.9 

3.3 

6.5 

Malarial  Fever 

4.4 

3.1 

2.7 

2.3 

1.8 

1.5 

1.1 

2.3 

« 

Erysipelas 

.9 

.8 

1.2 

1.0 

1.1 

1.3 

1.0 

1.1 

1 

Dysentery 

3.8 

2.0 

1.6 

1.6 

1.2 

1.3 

1.3 

1.7 

t 

Diarrhoea 

1.1 

.9 

1.1 

.8 

.7 

1.2 

1.0 

.9 

N 

Cholera 

4.2 

1.9 

1.4 

1.0 

.7 

.5 

.2 

1.2 

Alcoholism 

.3 

.5 

.3 

.4 

.3 

.4 

,  , 

.3 

Other  Zymotic  Diseases 

6.8 

5.2 

4.3 

3.6 

3.4 

2.4 

2.0 

3.9 

Dropsy 

1.0 

1.4 

1.4 

1.9 

1.8 

2.4 

1.9 

1.7 

'^ 

Cancer 

.6 

1.1 

1.1 

2.0 

2.1 

2.3 

3.7 

1.8 

1 

Consumption 

6.3 

15.3 

20.4 

21.6 

21.0 

16.9 

7.4 

18.3 



Other  Constitutional 

1.3 

1.1 

1.3 
4.5 

1.3 

1.2 

1.4 
6.1 

2.2 

1.3 

Apoplexy 

4.7 

4.1 

4.6 

4.6 

8.0 

4.8 

^ 

CongestiQn  of  Brain 

2.6 

2.0 

1.8 

1.9 

1.8 

1.5 

1.3 

1.8 

1 

Paralysis,     Softening  \ 
etc.,  of  Brain            ) 

4.1 

4.9 

5.0 

5.8 

7.2 

8.7 

9.3 

6.3 

^ 

Epilepsy,  Convulsions 

.2 

.3 

.4 

.4 

.4 

.4 

.2 

.4 

Other  Nervous 

.5 

.8 

1.0 

1.1 

1.2 

1.4 

1.8 

1.1 

>. 

Diseases  of  Heart 

2.7 

3.3 

4.1 

4.9 

5.9 

7.7 

10.9 

5.2 

S 

Other  Circulatory 

.4 

.3 

.2 

.3 

7.3 

.4 

.4 

.8 

.4 

Pneumonia 

7.7 

8.7 

7.6 

7.4 

7.6 

7.4 

7.7 

^ 

Congestion  of  Lungs 

1.8 

1.8 

1.7 

1.4 

1.5 

1.7 

2.1 

1.6 

Bronchitis  and  Pleurisy 

.9 

1.7 

1-5 

2.0 

1.7 

1.9 

2.6 

1.7 

"ft    Abscess,  Hemorrhage 
5        etc.,  of  Lungs 

1.9 

2.0 

.  1.9 

2.0 

2.0 

1.8 

1.0 

1.9 

Other  Respiratory 

.5 

.6 
1.6 

.6 

.5 

1.8 

.5 
1.6 

.5 

.7 

.6 

-    Diseases  of  Stomach 

1.5 

2.0 

2.3 

1.9 

1.8 

,  .5     Diseases  of  Bowels 

2.5 

2.3 

2.1 

2.1 

1.9 

2.1 

1.5 

2.1  1 

•    Peritonitis 

.7 

1.0 

.8 

.6 

.7 

.4 

.7 

.7  1 

g     Diseases  of  Liver 

1.8 

2.6 

3.3 

3.0 

3.3 

.  3.0 

2.4 

2.9 

Other  Digestive 

2.3 

2.1 
.3 

1.8 

1.7 

2.0 

2.0 

2.3 

2.0 

Diabetes 

.2 

.2 

.4 

.6 

.5 

1.2 

.4 

Diseases  of  Kidnevs 

1.3 

1.6 

2.1 

2.3 

3.0 

3.4 

4.2 

2.5 

Other  Urinary 

.3 

.5 

.6 

.7 

.9 

1.4 

2.6 

.8 

Childbirth  and  Puer- / 
peral  Diseases           \ 

3 

• 

% 

Diseases  of  Breast  and 
Uterus 

S 

Abscess,  Hemorrhage, 
Old  Age 

.4 

.9 

.6 

.8 

.8 

1.2 

5.5 

1.0 

"^ 

Debility,   Exhaustion,  ] 
Prostration,  etc.        f 

.3 

.8 

.8 

1.0 

1.2 

1.5 

3.2 

1.1 

x\ccidents  and  Injuries 

13.7 

10.2 

8.3 

7.3 

6.4 

4.7 

2.3 

7.5 

Suicides 

1.5 

1.7 

1.5 

1.2 

1.4 

.9 

.9 

1.3 

Unknown  Causes 

1.8 

1.4 

1.1 

1.4 

1.4 

1.4 

.4 

1.4 

\               Actual  Deaths 

2,445 

5,161 

4,651 

7,803 

10,062 

4,089 

1,197 

35,442 

TABLE     XY. 


197 


(B).    FEMALE  LIFE.    DURATIONS.    PERCENTAGE  DISTRIBUTION  OF  DISEASES  AMONG 

100  DEATHS,  THE  SAME  NUMBER  100  IN  EACH  STATED 

PERIOD  OF  INSURANCE. 


All  Causes. 

Duration  or  Years  of  Insurance. 

0-i 

Hi 

H-H 

H-H 

4f  9i  1  9f  19i 

19f29i 

Total, 

100.0 

100.0 

100.0 

100.0 

100.0 

100.0 

100.0 

100.0 

Typhoid  and  Typhus 

8.1 

6.0 

6.2 

5.6 

4.3 

3.7 

2.9 

5.4 

Other  Zymotic  Diseases 

16.3 

9.4 

7.9 

7.5 

6.8 

8.4 

2.8 

8.5 

Consumption 

7.1 

16.9 

22.9 

18.2 

23.2 

21.6 

11.4 

18.9 

Other  Constitutional 

2.5 

4.4 

6.7 

7.1 

5.6 

12.6 

5.7 

6.3 

Apoplexy 

3.6 

2.5 

2.3 

3.4 

2.5 

2.6 

2.9 

2.8 

Other  Nervous  Diseases 

4.5 

4.9 

6.8 

6.6 

4.3 

9.5 

14.3 

6.1 

Diseases  of  Heart 

3.6 

2.7 

2.9 

4.9 

6.2 

4.7 

12.9 

4.6 

Pneumonia 

9.6 

9.2 

7.0 

9.2 

7.2 

6.3 

7.1 

8.1 

Other  Respiratory 

2.1 

6.2 

6.2 

4.7 

5.7 

4.2 

10.0 

5.3 

Digestive  System 

14.2 

13.2 

10.9 

12.0 

13.1 

10.0 

12.8 

12.3 

Childbirth  and   Puer-  { 
peral  Diseases            ) 

15.2 

12.7 

7.3 

9.6 

7.8 

3.2 

9.0 

Diseases  of  Breast  and ) 
Uterus                         f 

3.1 

5.7 

5.9 

5.4 

5.5 

3.2 

2.9 

5.1 

All  other  Diseases 

10.1 

6.2 

7.0 

5.8 

7.8 

10.0 

14.3 

7.6 

TABLE   XTL 

(B.)    FEMALE  LIFE.     AGES.     PERCENTAGE   DISTRIBUTION   OF  DISEASES  AMONG   100 

DEATHS,  THE  SAME  NUMBER  100  IN  EACH  STATED 

PERIOD  OF  AGE, 


All  Causes. 

Ages  of  Death. 

19^-291 

29f39| 

39H9i 

100.0 

49f59i 

59f69^ 

69^-79i 

Total. 
100.0 

Act'lD'ths. 

100.0 

100.0 

100.0 

100.0 

100.0 

2,182 

Typhoid  and  Typhus 

6.9 

4.7 

5.7 

6.6 

3.1 

5.4 

118 

Other  Zymotic  Diseases 

6.4 

9.3 

7.6 

9.5 

7.3 

11.8 

8.4 

184 

Consumption 

25.3 

23.6 

18.7 

12.0 

6.1 

18.8 

409 

Other  Constitutional 

2.2 

4.3 

9.4 

10.1 

6.1 

4.0 

6.3 

138 

Apoplexy 

1.1 

1.4 

2.5 

6.0 

5.5 

5.9 

2.9 

63 

Other  Nervous  Diseases 

6.1 

5.1 

5.3 

6.6 

12.2 

11.7 

6.1 

132 

Diseases  of  Heart 

1.4 

3.0 

5.5 

6.9 

10.4 

9.8 

4.6 

100 

Pneumonia 

5.0 

6.5 

9.4 

8.2 

16.5 

13.7 

8.0 

176 

Other  Respiratory 

5.0 

4.7 

4.5 

7.0 

4.2 

9.8 

5.3 

116 

Digestive  System 

9.2 

12.7 

13.0 

14.8 

14.6 

9.8 

12.5 

273 

Childbirth   and  Puer-  [ 
peral  Diseases            \ 

18.3 

13.5 

6.0 

9.1 

198 

Diseases  of  Breast  and ) 
Uterus                       ij 

6.1 

4.9 

5.9 

4.7 

2.4 

2.0 

5.0 

110 

All  other  Diseases 

7.0 

6.3 

6.5 

7.6 

11.6 

21.5 

7.6 

165 

198 


TABLE    XYI. 


(A.)    MALE  LIFE.    PERCENTAGE   DISTRIBUTION   OF    DISEASES    AMONG   100  DEATHS, 
THE    SAME   NUMBER  100  IN   EACH  PERIOD  OF   INSURANCE. 


DTRF.ASES. 

Ages  of  Exposure. 

1 

i9hm 

29H9i  39H9^  49f  59i  59^-691 

69f79i 

Total. 

All  Causes. 

100,0 

100.0 

100.0 

100.0 

100.0 

100.0 

100.0 

Zymotic  Diseases 

26.0 

20.0 

17.9 

15.1 

11.6 

9.0 

17.8 

^    Constitutional  Diseases 

32.1 

28.9 

22.5 

17.7 

14.4 

11.7 

23.1 

P^    Nervous  Diseases 
S     Circulatory  Diseases 

6.8 

10.7 

14.5 

18.6 

21.9 

20.9 

14.5 

1.7 

3.5 

5.0 

7.7 

11.6 

12.5 

5.6 

^     Respiratory  Diseases 

10.7 

12.5 

14.0 

14.8 

14.4 

13.6 

13.4 

«o     Digestive  Diseases 

6.3 

8.1 

10.5 

10.7 

10.8 

6.9 

9.5 

Miscellaneous  Diseases 

16.4 

16.3 

15.6 

15.4 

15.3 

25.4 

16.1 

Typhoid,  Typhus  Fever 

13.5 

7.5 

5.7 

4.8 

3.5 

1.1 

6.5 

Malarial  Fever 

2.1 

2.7 

2.6 

2.0 

1.7 

.8 

2.3 

«     Erysipelas 

.8 

.9 

1.2 

1.1 

1.1 

.9 

1.1 

o     Dysentery 

1.8 

1.8 

1.5 

1.8 

1.3 

1.9 

1.6 

P.    Diarrhoea 

.8 

.8 

.     .9 

1.0 

1.1 

1.5 

.9 

•^     Cholera 

1.6 

1.4 

1.3 

1.0 

.6 

.3 

1.2 

Alcoholism 

.2 

.5 

.5 

.2 

, , 

.3 

Other  Zymotic  Diseases 

5.2 

4.4 

4.2 

3.2 

2.3 

2.5 

3.9 

^    Dropsy 

.5 

1.1 

1.8 

2.4 

2.9 

2.3 

1.8 

*J     Cancer 

.2 

.8 

1.7 

3.2 

3.2 

3.1 

1.7 

o     Consumption 

30.3 

25.8 

17.8 

10.8 

6.5 

3.5 

18.3 

Other  Constitutional 

1.1 

1.2 

1.2 

1.3 

1.8 

2.8 

1.3 

Apoplexy 

1.2 

2.6 

4.6 

7.9 

8.3 

7.1 

4.8 

g     Conprestion  of  Brain 

1.5 

2.0 

2.1 

1.7 

1.3 

.8 

1.9 

^     Paralysis,     Softening  { 
^        etc.,  of  Brain             J 

3.1 

4.6 

6.1 

■  7.6 

10.6 

12.2 

6.3 

^    Epilepsy,   Convulsions 

.3 

.5 

.5 

.3 

.4 

.3 

.4 

Other  Nervous 

.7 

1.0 

1.2 

1.1 

1.3 

.5 

1.1 

^    Diseases  of  Heart 

1.6 

3.3 

4.5 

7.3 

10.8 

12.0 

5.2 

"o     Other  Circulatory 

.1 

.2 

.5 

.4 

.8 

.5 

.4 

.    Pneumonia 

5.3 

6.4 

8.1 

9.1 

9.1 

7.6- 

7.6 

g     Congestion  of  Lungs 

1.2 

1.4 

1.7 

1.7 

1.7 

2.5 

1.6 

oa     Bronchitis  and  Pleurisy 
'g»    Abscess,   Hemorrhage ) 
|S        etc.,  of  Lungs            f 

1.2 

1.6 

1.9 

1.8 

1.8 

2.3 

1.7 

2.6 

2.6 

1.8 

1.5 

1.3 

.9 

,    1.9 

Other  Respiratory 

.4 

,5 

.5 

.7 

.5 

.3 

.6 

•    Diseases  of  Stomach 

.7 

1.3 

2.1 

2.1 

2.2 

2.5 

1.8 

.5     Diseases  of  Bowels 

2.1 

2.4 

1.9 

2.1 

2.2 

.8 

2.1 

S     Peritonitis 

1.0 

.8 

.7 

.6 

.5 

.7 

g     Diseases  of  Liver 

1.1 

2.2 

3.8 

3.5 

3.0 

1.7 

2.9 

Other  Digestive 

1.4 

1.4 

2.0 

2.4 

2.9 

1.9 

2.0 

Diabetes 

.1 

.4 

.5 

.3 

1.0 

.6 

.5 

Diseases  of  Kidneys 

1.7 

1.7 

2.7 

3.2 

3.2 

3.9 

2.5 

Other  Urinary 

.3 

.3 

.5 

1.0 

2.4 

3.9 

.8 

Ciiildbirth  and  Puer-/ 
g        peral  Diseases            J 

§     Diseases  of  Breast  and 
g         Uterus                         ■ 

•3    Abscess,  Hemorrhage, 
S        Old  Age 

.5 

.8 

.7 

.7 

1.1 

8.0 

1.0 

S     Debility,   Exhaustion,  / 
Prostration,  etc*.         f 

.6 

.7 

.8 

1.3 

2.4 

3.9 

1.1 

Accidents  and  Injuries 

10.5 

9.6 

7.6 

5.9 

3.5 

2.3 

7.5 

Suicides 

1.4 

'   1.4 

1.6 

1.4 

.5 

.3 

1.3 

Unknown  Causes 

1.3 

1.4 

1.2 

1.6 

1.2 

2.5 

1.4 

Actual  Deaths 

3,476 

9,321 

'  10,840 

7,576 

3,357 

647 

35,442 

TABLE    XYII. 


199 


(A).    CLIMATIC  DISTRIBUTION  OP  DEATHS  AND  DISEASES   AMONG    100  DEATHS  OP 
INSURED  MALES  AND  PEMALES. 


Ages,  : 

20-75. 

Besidence  at  Death. 

North  of  ae-'SO' 

South  36"  30'.  j 

Foreign 
Male. 

XJnited  States. 

TJ.  S.  Census  1870. 

SEX. 

Male.     Fern. 

Male. 

Fem. 

Male. 
100.0 

Fem. 

ioo7o 

14.0 

Male. 
100.0 

Fem. 

Too.o^ 

Deaths  from  all  Causes. 

100.0  100.0 

100.0 

100.0 

100.0 

Zymotic  Diseases 

17.3    13.3 

28.4 

22.5 

15.0 

17.8 

:     15.9 

14.5 

{H 

Constitutional  Diseases 

23.6    25.6 

15.4 

16.5 

19.1 

23.1 

24.9 

i     32.1 

37.4 

Nervous  Diseases 

14.5 

8.9 

13.1 

11.3 

16.1 

14.5 

8.9 

,       9.5 

8.1 

s 

Circulatory  Diseases 

5.8 

5.0 

4.0 

3.8 

5.8 

5.6 

4.8 

!       5.9 

5.9 

>i 

Respiratory  Diseases 

13.4 

13.4 

12.6 

12.8 

16.1 

13.4 

13.4 

13.3 

11.4 

<a 

Digestive  Diseases 

9.2 

12.2 

12.9 

14.3 

8.7 

9.5 

12.6 

6.5 

6.6 

Miscellaneous  Diseases 

16.2 

21.6 

13.6 

18.8 

19.2 

16.1 

21.4 

16.8 

16.1 

Typhoid,  Typhus  Fever 

6.8 

5.5 

2.8 

4.5 

5.0 

6.5 

5.4 

6.8 

6.6 

Malarial  Fever 

2.1 

1.8 

6.9 

9.0 

1.1  i 

2.3 

2.3 

2.5 

2.4 

u 

Erysipelas 

1.1 

.5 

.9 

.9 

1.1 

.5 

!         .6 

.6 

1 

Dysentery 

1.5 

1.5 

3.4 

2.2 

1.7 

1.6 

1.6 

.9 

.9 

Diarrhoea 

.9 

1.0 

2.1 

1.5 

1.0 

.9 

1.0 

i.7 

1.4 

Cholera 

1.2 

.7 

1.4 

.6 

1.2 

.7 

.1 

.1 

Alcoholism 

.3 

.1 

.2 

.   , 

.6 

.3 

.1 

1.1 

.3 

Other  Zymotic  Diseases 

3.4 

2.2 
2.2 

10.7 
1.3 

5.3 
3.0 

4.1 

3.9 

3.4 

2.2 

2.2 

^ !  Dropsy 

1.8 

1.3 

1.8 

2.2 

2.1 

3.0 

1 

Cancer 

1.8 

2.4 

.7 

2.3 

.7 

1.7 

2.3 

1.7 

2.5 

Consumption 

18.7 

19.3 

12.3 

9.0 

16.2 

18.3 

18.7 

26.2 

29.7 

Other  Constitutional 

1.3 

1.7 

1.1 

2.2 

.9 

1.3 

1.7 

2.1 

2.2 

Apoplexy 

4.8 

2.8 

4.8 

4.5 

6.8 

4.8 

2.9 

2.2 

1.8 

f? 

Congestion  of  Brain 

1.8 

.6 

2.9 

3.0 

1.7 

1.9 

.7 

.3 

.3 

i 

Paralysis,      Softening  I 
etc.,  of  Brain             f 

6.4 

4.0 

4.4 

3.0 

5.8 

6.3 

3.9 

4.0 

3.4 

!4 

Epilepsy,   Convulsions 

.4 

.0 

.4 

.7 

.4 

.4 

.7 

.8 

Other  Nervous 

1.1 

1.0 

.6 

.8 

1.1 
4.5 

1.1 

1.0 

2.3 

1.8 

t>^ 

Diseases  of  Heart 

5.4 

4.7 

3.9 

3.8 

5.2 

4.6 

I    5.9 

5.9 

•H 

Other  Circulatory 

.4 

7.7 

.3 

.1 

1.3 
7.3 

.4 

.2 

Pneumonia 

7.9 

7.4 

9.8 

7.6 

8.1 

ilO.2 

8.3 

s 

Congestion  of  Lungs 

1.6 

1.5 

1.3 

. , 

1.6 

1.6 

1.4 

1 

Bronchitis  and  Pleurisy 

1.7 

1.4 

2.0 

1.5 

2.1 

1.7 

1.4 

1.1 

1.0 

Abscess,    Hemorrhage } 
etc.,  of  Lungs            f 

1.9 

2.0 

1.1 

.8 

4.3 

1.9 

1.9 

1    2.0 

2.1 

Other  Respiratory 

.5 

.6 
2.4 

.8 

.7 

.8 
1.6 

.6 
1.8 

.6 

Diseases  of  Stomach 

1.7 

3.0 

1.5 

2.4 

1,0 

1.1 

> 

Diseases  of  Bowels 

2.0 

3.0 

3.4 

5.3 

1.7 

2.1 

3.2 

2.6 

2.4 

1 

Peritonitis 

.7 

1.9 

.3 

.8 

1.0 

.7 

1.9 

.2 

.5 

r? 

Diseases  of  Liver 

2.9 

2.2 

2.8 

4.5 

2.8 

2.9 

2.4 

2.0 

1.7 

Other  Digestive 

1.9 

2.7 

3.4 

2.2 

1.6 
.3 

2.0 

2.7 

.7 

.9 

Diabetes 

.5 

.2 

.1 

.5 

.1 

.4 

.1 

Diseases  of  Kidneys 

2.6 

1.3 

1.4 

1.7 

2.5 

1.2 

1.9 

.8 

Other  Urinary 

.8 

.4 

•  .7 

.3 

.8 

.4 

.4 

.1 

i 

Childbirth  and  Puer- 
peral Diseases 

9.0 

' 

9.0 

9.1 

6.5 

Diseases  of  Breast  and  _ 
Uterus                        1 

5.0 

5.3 

5.0 

2.4 

9 

Abscess,  Hemorrhage,  | 
Old  Age                       ) 

Debility,   Exhaustion,  } 
Prostration,  etc.         f 

1.0 
1.1 

1.4 

1.4 

.6 

.7 

1.5 

1.0 

.7 

1.0 
1.1 

1.3 

1.4 

[    2.7 

2.7  i 

Accidents  and  Injuries 

7.5 

1.5 

7.8 

1.5 

11.2 

7.5 

1.5 

9.1 

1.4 

Suicides 

1.4 

.4 

.8 

1.1 

1.3 

.3 

.9 

.3 

Unknow^n  Causes 

1.3 
82,544 

1.0 
2,012 

1.5 

1.5 

2.9 
1    703 

1.4 

1.1 

1.4 

1.8 
91.898 

■   ■- — 1 

Actual  Deaths 

2.153 

133 

35,442 

2.182 

104,531 

^00 


TABLE    XVII. 


(B).    PROPORTIONAL  DEATHS  AND  DISEASES  TO  100  TOTAL  DEATHS  OP 
INSURED  MALES  IN  EACH  GROUP  OF  STATES 


Group  of  States. 

L* 

XL 

III. 

IV. 

V. 

VI. 

VII. 

Mean 
Group. 

Groups. 

All  Causes. 

100.0 

100.0 

100.0 

100.0 

100.0  100.0 

100.0 

Zymotic 

16.7 

19.0 

15.5 

17.9 

21.1 

28.4 

14.2 

19.0 

I  * 

§ 

Constitutional 

25.0 

21.9 

26.0 

22.0 

20.9 

15.4 

19.8 

21.6 

Nervous 

14.7 

11.8 

14.4 

13.8 

15.4 

13.1 

16.4 

14.2 

New  England. 

Circulatory 

6.3 

4.5 

6.8 

4.4 

5.1 

4.0 

8.2 

5.6 

New  York. 

a 

Respiratory 

13.6 

14.9 

11.3 

15.9 

13.9 

12.6 

13.0 

13.5 

^ 

Digestive 

8.2 

10.2 

10.5 

10.7 

9.1 

12.9 

8.1 

10.0 

II. 

Miscellaneous 

16.5 

17.7 

15.5 

15.3 

14.5 

13.6 

20.3 

16.2 

Northwest. 
Michigan. 

Typhoid.Typlius 

7.2 

8.8     6.4 

6.4 

5.3 

2.8 

4.6 

5.9 

Malarial  Fever 

1.5 

2.4     1.7 

3.2 

2.9 

6.9 

1.7 

2.9 

Wisconsin. 

u 

Erysipelas 

1.0 

1.3 

.9 

1.2 

1.0 

.9 

2.0 

1.2 

Minnesota. 

o 

Dysentery 

1.6 

1.4 

.8 

1.4 

2.8 

3.4 

1.3 

1.8 

Nebraska. 

I 

Diarrhoea 

.9 

.7 

.9 

.7 

1.2 

2.1 

.2 

1.0 

in. 

N  Cholera 

.8 

.8 

1.0 

1.9 

2.7 

1.4 

.8 

1.3 

Alcoholism 

.3 

.3 

.3 

.4 

.4 

.2 

.5 

.3 

New  Jersey. 

Other  Zymotic 

3.4 

3.3 

3.5 

2.7 

4.8 

10.7 

3.1 

4.5 

Pennsylvania. 
IV 

.  j  Dropsy 

1.7 

1.7 

2.4 

1.8 

1.7 

1.3 

1.7 

1.8 

*> 

Cancer 

2.0 

1.6 

2.0 

1.5 

1.7 

.7 

1.7 

1,6 

13 

o 

Consumption 

19.7 

17.3 

20.7 

17.7 

16.4 

12.3 

15.1 

17.0 

Ohio. 

U 

Other  Const'] 

1.6 

1.3 

.9 

1.0 

1.1 

1.1 

1.3 

1.2 
4.9 

Indiana. 
Illinois. 

Apoplexy 

5.0 

4.0 

4.6 

4.0 

5.5 

4.8 

6.1 

1 

Congestions  rain 

Paralysis,  Soft-  i^ 

ening  Brain   f 

1.4 
6.9 

1.5 
5.3 

2.0 
6.1 

2.4 
5.9 

2.2 

6.0 

2.9 
4.4 

1.5 

6.5  . 

2.0 
5.9 

Iowa. 
Kansas. 

V. 

Delaware. 
Maryland. 
Dist.  Columbia. 

in 

Epilepsy    and  I 
Convulsions    J 
Other  Nervous 

.3 
1.1 

.3 

.7 

.6 
1.1 

.4 
1.1 

.4 
1.3 

.4 

.6 

3.9 

1.3 
1.0 

.5 
1.0 

>» 

Diseasesof  Heart 

5.8. 

4.2 

6.6 

4.2 

4.8 

6.6 

5.2 

a 

w 

Other  Circulat'y 

.5 

.3 

.2 

.2 

.3 

.1 

1.6 

.5 

Virginia. 
Kentucky. 

Pneumonia 

7.0 

8.7 

6.2 

9.4 

8.3 

7.4 

8.0 

7.9 

^ 

Congest'n  Lungs 

1.7 

1.7 

1.1 

1.6 

1.7 

1.3 

.8 

1.4 

Missouri. 

o 

Bronchitis  and  | 
"  Pleurisy          ) 

1.7 

2.0 

1.4 

1.9 

1.4 

2.0 

2.0 

1.8 

VI. 

« 

Abscess,  Hem-  { • 

or'age  Lungs  \ 

Other  Respirat'y 

1.8 
.4 

2.1 

^.4 

1.9 

.7 

2.3 

.7 

1.8 

.7 

1.1 

.8 

1.6 
.6 

•1.8 
.6 

South  of  36°  30'. 
North  Carolina, 

, 

Dis.  of  Stomach 

1.5 

2.4 

1.9 

1.8 

1.6 

3.0 

1.2 

1.9 

Tennessee. 

> 

Dis.  of  Bo  web 

1.8 

2.2 

2.3 

2.4 

1.9 

3.4 

1.4 

2.2 

Georgia. 

a 
e 

Peritonitis 

.7 

.8 

.9  1     .8 

.5 

.3 

.3 

.6 

Florida. 

bo 
P 

Dis.  of  Liver 

2.6 

2.5 

3.5 

3.5 

3.0 

2.8 

3.7 

3.1 

Alabama. 

Other  Digestive 

1.6. 

2.3 

1.9 

2.2 

2.1 

3.4 

1.5 

2.1 

Mississippi. 
Arkansas. 

Diabetes 

.5 

.5 

.5 

.4 

.6 

.1 

.5 

.4 

Dis.  of  Kidneys 

3.3 

1.4 

2.9 

1.8 

1.6 

1.4 

2.3 

2.1  , 

Louisiana. 

Other  Urinary 

.9 

.8 

l.O 

.5 

.7' 

.7 

.6 

.7 

Texas. 

Childbirth.Pu-  ) 

VII. 

" 

erperal  Dis.     f 

•  • 

'  " 

•  * 

•  * 

S 

Dis.  Breast 
and  Uterus 

Pacific,  etc. 

g 

•  • 

•  * 

5 
o 
m 

Abscess,  Hem-  [ 
or'age.OldAgej" 

1.1 

.8 

1.0 

1.0 

1.0 

.6 

.3 

.8 

Washington. 
Oregon. 

» 

Debility,    Ex- 
haustion, etc. 

1.0 

1.0 

2.2 

.7 

1.0 

.7 

1.1 

1.1 

California. 
Utah. 

Accid'ts,  Injuries 

6.8 

10.1 

5.7 

8.6 

7.1 

7.8 

11.4 

8.2 

Dakota. 

Suicides 

1.2 

2.1 

1.2 

1.3 

1.4 

.8 

2.9 

1.6 

New  Mexico. 

UnknownCauses 

i     1.7 

1.0 

1.0 

1.0 

1.1 

1.5 

1.2 

1.2 

Actual  Deaths 

15,273 

j2,7ie 

3,976|6,239 

|3,306 

j2,153 

863 

.. 

TABLE    XYII. 


201 


(O-     PROPORTIONAL  DEATHS  AND  DISEASES  TO  10,000  MALES  LIVING  IN  EACH 

GROUP  OP  STATES. 


Group  of  States. 

I.* 

11. 

HI. 

IV. 

V. 

VI. 

VII. 

Mean 
Group. 

Groups. 

All  Causes. 

105.3 

97.7 

107.1 

104.5 

130.5 

170.5 

113.2 

Zymotic 

17.6 

18.5 

16.6 

18.7 

27.5 

48.4 

15.9 

23.3 

L* 

i 

Constitutional 

26.4 

21.4 

27.9 

33.0 

37.3 

26.3 

22.1 

34.9 

Nervous 

15.4 

11.5 

15.4 

14.4 

30.1 

22.3 

18.4 

16.8 

New  England. 

< 

Circulatory 

6.6 

4.4 

7.3 

4.6 

6.7 

6.8 

9.2 

6.5 

New  York. 

s 

Respiratory 

13.3 

14.6 

12.1 

16.6 

18.1 

21.5 

14.6 

15.8 

II. 

^ 

Digestive 

8.6 

10.0 

11.2 

11.2 

11.9 

22.0 

9.1 

12.0 

Miscellaneous 

17.4 

17.3 

16.6 

16.0 

18.9 

23.2 

22.9 

18.9 

Northwest. 
Michigan. 

Typhoid,Typhus 

7.6 

8.5 

6.8 

6.7 

6.9 

4»-8 

5.2 

6.6 

Malarial  Fever 

1.7 

2.3 

1.8 

3.3 

3.8 

11.8 

1.9 

3.8 

Wisconsin. 

o 

Erysipelas 

1.0 

1.3 

1.0 

1.3 

1.3 

1.5 

2.2 

1.4 

Minnesota. 

Dysentery 

1.7 

1.4 

.9 

1.4 

3.6 

5.8 

1.5 

2.3 

Nebraska. 

I 

Diarrhoea 

.9 

.7 

1.0 

.8 

1.6 

3.6 

.2 

1.3 

in. 

N 

Cholera 

.9 

.8 

1.1 

2.0 

3.5 

2.4 

.9 

1.7 

Alcoholism 

.3 

.3 

.3 

.4 

.5 

.3 

.6 

.4 

New  Jersey. 

Other  Zymotic 

5.6 

3.2 

3.7 

2.8 

6.3 

18.2 

3.4 

5.9 

Pennsylvania. 
IV 

Dropsy 

1.8 

1.6 

2.6 

1.9 

2.2 

2.2 

1.9 

2.0 

^ 

Cancer 

2.1 

1.5 

2.1 

1.6 

2.2 

1.1 

1.9 

1.8 

§ 

Consumption 

20.8 

16.9 

22.2 

18.5 

21.5 

21.0 

16.9 

19.7 

Ohio. 

u 

Other  Const'l 

1.7 

1.4 

1.0 

1.0 

1.4 

2.0 

1.4 

1.4 

5.8 

Indiana- 
Illinois. 
Iowa. 
Kansas. 

V. 

Delaware. 
Maryland. 
Dist.  Columbia. 

Apoplexy 

5.2 

3.8 

5.0 

4.2 

7.2 

8.2 

6.8 

i 

CongestionBrain 

Paralysis,  Soft-  / 

ening  Brain   ) 

1.5 

7.2 

1.5 
5.2 

2.1 

6.5 

2.5 

6.2 

2.9 

7.8 

4.9 

7.5 

1.7 
7.3 

2.4 
6.8 

^ 

Epilepsy    and  ) 

Convulsions    ) 

Other  Nervous 

.3 
1.2 

.3 

.7 

.6 
1.2 

.4 
1.1 

.5 
1.7 

.7 
1.0 

1.5 
1.1 

.6 
1.1 

►. 

Diseasesof  Heart 

6.1 

4.1 

7.1 

4.4 

6.3 

6.6 

7.4 

6.0 

Other  Circulat'y 

.5 

.3 

.2 

.2 

.4 

.2 

1.8 

.5 

Virginia. 
Kentucky. 

Pneumonia 

7.3 

8.5 

6.6 

9.8 

10.8 

12.6 

9.0 

9.2 

>> 

Congest'n  Lungs 

1.8 

1.7 

1.2 

1.7 

2.2 

2.2 

.9 

1.7 

Missouri. 

1 

.a 

Bronchitis  and ) 
Pleurisy          ) 

1.8 

2.0 

1.5 

2.0 

1.8 

3.4 

2.2 

2.1 

VI. 

09 

Abscess,  Hem- ) 

or' age  Lungs ) 

Other  Respirat'y 

1.9 
.4 

2.0 
•4 

2.0 

.8 

2.4 

.7 

2.4 

.9 

1.9 
1.4 

1.8 

.7 

2.1 

.8 

South  op  36°  30'. 

North  Carolina. 
South  Carolina. 
Tennessee. 

. 

Dis.  of  Stomach 

1.6 

2.3 

2.0 

1.9 

2.1 

5.1 

1.3 

2.3 

> 

Dis.  of  Bowels 

1.9 

2.2 

2.5 

2.5 

2.5 

5.8 

1.6 

2.7 

Georgia. 

s 

Peritonitis 

.7 

.8 

1.0 

.8 

.7 

.5 

.3 

.7 

Florida. 

bo 
P 

Dis.  of  Liver 

2.7 

2.4 

3.7 

3.7 

3.9 

4.8 

4.2 

3.6 

Alabama. 

Other  Digestive 

1.7 

2.3 

2.0 

2.3 

2.7 

5.8 

1.7 

2.6 

Mississippi. 
Arkansas. 

Diabetes 

.5 

.5 

.5 

.4 

.8 

.3 

.6 

.5 

Dis.  of  Kidneys 

3.5 

1.4 

3.1 

1.9 

3.1 

2.4 

2.6 

2.4 

Louisiana. 

Other  Urinary 

.9 

.8 

1.1 

.5 

.9 

1.2 

.7 

.9 

Texas. 

S 

Childbirth,Pu-  ) 
erperal  Dis.     J 

•• 

•• 

•• 

•• 

VII. 

s 

Dis.  Breast 
and  Uterus     ' 

'. , 

Pacific,  etc. 

r"! 

Abscess,  Hem- 
or'age.OldAge 

1.2 

.8 

1.1 

1.1 

1.3 

1.0 

.3 

1.0 

Washington. 
Oregon. 

M 

Debility,    Ex-  | 
haustion,  etc.  | 

1.0 

1.0 

2.4 

.7 

1.3 

1.1 

1.2 

1.2 

California. 
Utah. 

Accid'ts,  Injuries 

7.2 

9.7 

6.0 

9.0 

9.3 

13.3 

12.8 

9.6 

Dakota. 

Suicides 

1.3 

2.1 

1.3 

1.3 

1.8 

1.4 

3.3 

1.8 

New  Mexico. 

UnknownCauses 

1.8 

1.0 

1.1 

1.1 

1.4 

2.5 

1.3 

863 

1.5 

Actual  Deaths 

15,273 

2,716 

3,976 

6,239 

3,306 

2,153 

303 


TABLE     XYIII. 


CALENDAR  AND  DECIMAL  PARTS  OF  A  YEAR. 


Days, 
0 

Cal. 

Decimal. 

Days. 

Cal. 

Decimal. 

Da3r8. 

Cal.   Decimal. 

Days. 

Cal. 

Decimal. 

Jan.  0 

.00000000 

50 

Fb*19 

.13698630 

100 

Apr.lO.  27397260 

150 

May  30 

.41095890 

1 

*1 

.00273973 

51 

20 

.13972603 

101 

11 

.27671233 

151 

31 

.41369863 

2 

2 

.00547945 

52 

21 

.14246575 

102 

12 

.27945205 

162 

June  1 

.41643836 

3 

3 

.00821918 

53 

22 

.14520548 

103 

13 

.28219178 

153 

2 

.41917808 

4 

4 

.01095890 

54 

23 

.14794521 

104 

14 

.28493151 

154 

3 

.42191781 

5 

5 

.01369863 

55 

24 

.15068493 

105 

15 

.28767123 

155 

*4 

.42465753 

6 

6 

.01643836 

56 

25 

.15342466 

106 

*16 

.29041096 

156 

6 

.42739726 

7 

7 

.01917808 

57 

*26 

.15616438 

107 

17 

.29315068 

157 

6 

.43013699 

8 

*8 

.02191781 

58 

27 

.15890411 

il08 

18 

.29589041 

158 

7 

.43287671 

9 

9 

.02465753 

59 

28 

.16164384 

109 

19 

.29863014 

159 

8 

.43561644 

10 

10 

.02739726 

60 

Mar.  1 

.16438356  110 

20 

.30136986 

160 

9 

.43835616 

11 

11 

.03013699 

61 

2 

.16712329 

111 

21 

.30410959 

161 

10 

.44109589 

12 

12 

.03287671 

62 

3 

.16986301 

112 

22 

.30684932 

162 

*11 

.44383562 

13 

13 

.0.3561644 

1  63 

4 

.17260274 

113 

*23 

.30958904 

163 

12 

.44(:57534i 

14 

14 

.03835616 

64 

*5 

.17534247 

114 

24 

.31232877 

164 

13 

.44931507| 

15 

*15 

.04109589 

!  65 

6 

.17808219 

115 

25 

.31506849 

165 

14 

.45205479 

16 

16 

.04383562 

66 

7 

.18082192 

116 

26 

.31780822 

166 

15 

.45479452 

17 

li 

.04657534  67 

8 

.18356164 

117 

27 

.32054795 

167 

16 

.45753425 

18 

18 

.04931507 

68 

9 

.18630137 

118 

28 

.32328767 

168 

17 

.46027397 

19 

19 

.05205479 

69 

10 

.18904110 

119 

29 

.32602740 

169 

*18 

.46301370 

20 

20 

.05479452 

70 

11 

.19178082 

120 

*30 

.32876712 

170 

19 

.46575342 

21 

21 

.05753425 

71 

*12 

.19452055 

121 

May  1 

.33150685 

171 

20 

.46849315 

22 

*22 

.06027397 

72 

13|.  19726027] 

122 

2 

.33424658 

172 

21 

.47123288 

23 

23 

.06301370 

73 

14 

.20000000 

123 

3 

.33698630 

173 

22 

.47397260 

24 

24 

.06575342 

74 

15 

.20273973 

124 

4 

.33972603 

174 

23 

.47671233 

25 

25 

.06849315 

75 

16 

.20547945 

125 

5 

.34246575 

176 

24 

.47945205 

26 

26 

.07123288 

76 

17 

.20821918 

126 

6 

.34520548 

176 

*25 

.48219178 

27 

27 

.07397260 

77 

18 

.21095890 

127 

*7 

.34794521 

177 

26 

.48493151 

28 

28 

.07671233 

78 

*19 

.21369863 

128 

8 

'.35068493 

178 

27 

.48767123. 

29 

*29 

.07945205 

79 

20 

.21643836 

129 

9 

.35342466 

179 

28 

.49041096 

30 

30 

.08219178 

80 

21 

.21917808 

130 

10 

.35616438 

180 

29 

.49315068 

31 

31 

.08493151 

81 

22 

.22191781 

131 

11 

.35890411 

181 

30 

.49589041 

32 

Feb.  1 

.08767123 

82 

23 

.22465753 

132 

12 

.36164384 

182 

July  1 

.49863014 

33 

2 

.09041096 

83 

24 

.22739726 

133 

13 

.36438356 

183 

*2 

.50136986 

34 

3 

.09315068 

84 

25 

.23013699 

134 

*14 

.36712329 

184 

3i.50410959| 

35 

4 

.09589041 

85 

*  *26 

.23287671 

135 

15 

.36986301 

186 

4 

.50684932 

36 

*5 

.09863014 

86 

27 

.23561644 

136 

16 

.37260274 

186 

5 

.50958904 

37 

6 

.10136986 

87 

28 

.23835616 

137 

17 

.37534247 

187 

6 

.51232877 

38 

7 

.104109591 

88 

29 

.24109589 

138 

18 

.37808219 

188 

7 

.51506849 

39 

8 

.10684932 

89 

30 

.24383562 

139 

19 

.38082192 

189 

8 

.51780822 

40 

9 

.10958904 

90 

31 

.24657534 

140 

20 

.38356164 

190 

*9;.52054795| 

41 

10 

.11232877 

91 

April  1 

.24931507 

141 

*21 

.38630137 

191 

10 

.52328767 

42 

11 

.11506849 

92 

*2 

.25205479 

142 

22 

.38904110 

192 

11 

.52602740 

43 

*12 

.11780822 

93 

3 

.254794521 

143 

23 

.39178082 

193 

12 

.52876712 

44 

13 

.12054795 

1  94 

4j.  25753425 

144 

24 

.39452055 

194 

13 

.53150685 

45 

14 

.12328767 

i  95 

5{. 26027397 

145 

25 

.39726027 

196 

14 

.53424658 

46 

15 

.12602740 

96 

61.26301370 

146 

26 

.40000000 

196 

15 

..53698630 

47 

16 

.12876712 

1  97 

71.26575342 

147 

27 

.40273973 

197 

*16 

..53972603 

48 

17 

.13150685 

98 

8 

.26849315 

148 

*28 

.40547945 

198 

17 

.54246575 

49 

18 

.13424658 

99 

*9 

.27123288 

149 

29 

.40821918 

199 

18 

.54520548 

TABLE    XYill. 

CALENDAR  AND  DECIMAL  PARTS  OF  A  TEAR. 


203 
204  205 
206  207 


Days. 


200 
201 
202 
203 
204 

205 
206 
207 
208 
209 

210 
211 
212 
213 
214 

215 
216 
217 
218 
219 

220 
221 
222 
223 
224 

225 
226 
227 
228 
229 

230 
231 
232 
233 
234 

235 
236 
237 
238 
239 

240 

241 

1242 

243 

244 

245 
246 
247 
248 
249 


Cal. 

Decimal. 

Julyi9 

.54794521 

20 

.55068493 

21 

.55342466 

22 

.55616438 

*23 

.55890411 

24 

.56164384 

25 

,56438356 

26 

.56712329 

27 

.56986301 

28 

.57260274 

29 

.57534247 

*30 

.57808219 

31 

.58082192 

Au?.  1 

.58356164 

2 

.58630137 

3 

.58904110 

4 

.59178082 

5 

.59452055 

*6 

.59726027 

7 

.60000000 

8 

.60273973 

9 

.60547945 

10 

.60821918 

11 

.61095890 

12 

.61369863 

*13 

.61643836 

14 

.61917808 

15 

.62191781 

16 

.62465753 

17 

.62739726 

18 

.63013699 

19 

.63287671 

*20 

.63561644 

21 

.63835616 

22.64109589 


23 
24 
25 
26 
*27 

28 
29 
30 
31 
Sept.  1 

2 

*3 
4 
5 

6 


64383562 
64657534 
64931507 
65205479 
65479452| 

65753425 
66027397 
66301370 
66575342 
66849315 

67123288 
67397260 
67671233 
,67945205 
,68219178 


Days. 

Cal. 

250 

Sept.  7 

251 

8 

252 

9 

253 

*10 

254 

11 

255 

12 

256 

13 

257 

14 

258 

15 

259 

16 

260 

*17 

261 

18 

262 

19 

263 

20 

264 

21 

265 

22 

266 

23 

267 

*24 

268 

25 

269 

26 

270 

27 

271 

28 

272 

29 

273 

30 

274 

Oct.  *1 

275 

2 

276 

3 

277 

4 

278 

5 

279 

6 

280 

7 

281 

*8 

282 

9 

283 

10 

284 

11 

285 

12 

286 

13 

287 

14 

288 

*15 

289 

16 

290 

17 

291 

18 

292 

19 

293 

20 

294 

21 

295 

*22 

296 

23 

297 

24 

298 

25 

299 

26 

Decimal. 


.68493151 
,68767123 
,69041096 
,69315068 
,69589041 

,69863014 
,70136986 
,70410959 
,70684932 
,70958904 

,71232877 
,71506849 
.71780822 
,72054795 
,72328767 
72602740 
72876712 
73150685 
73424658 
73698630 

73972603 
74246575 
74520548 
74794521 
75068493 

,75342466 
75616438 
75890411 
76164384 
76438356 

76712329 
76986301 

77260274 
77534247 
77808219 

78082192 
78356164 
78630137 
78904110 

79178082 

79452055 
79726027 
80000000 
80273973 
80547945 

80821918 
81095890 
81369863 
81643836 
81917808 


Days, 


300 
301 
302 
303 
304 

305 
306 
307 
308 
309 

310 
311 
312 
313 
314 

315 
316 
317 
318 
319 

320 
321 
322 
323 
324 

325 
326 
327 
328 
329 

330 
331 
332 
333 
334 

335 
336 
337 
338 
339 

340 
341 
342 
343 
344 

345 
346 
347 
348 
349 


Cal. 


Oct.  27 

28 

*29 

30 

31 

m,  1 

2 

3 

4 

*5 

6 

7 

8 

9 

10 

11 
*12 
13 
14 
15 

16 

17 

18 

*19 

20 

21 
22 
23 
24 
25 

*26 

27 
28 
29 
30 

Dec.  1 
2 

*3 
4 

5 

6 

7 

8 

9 

*10 

11 
12 
13 
14 
15 


Decimal. 


.82191781 
.82465753 
.82739726 
.83013699 
.83287671 
.83561644 
.83835616 
.84109589 
.84383562 
.84657534 

.84931507 
.85205479 
.85479452 
.85753425 
.86027397 

.86301370 
.86575342 
.86849315 

.87123288 
.87397260 

.87671233 
.87945205 
.88219178 
.88493151 

.88767123 

.89041096 
.89315068 
.89589041 
.89863014 
.90136986 

.90410959 
.90684932 
.90958904 

.91232877 
.91506849 

.91780822 
.92054795 
.92328767 
.92602740 
.92876712 

.93150685 
.93424658 
.93698630 
.93972603 
.94246575 

•94520548 
•94794521 
•95068493 
.95342466 
.95616438 


Days. 

Cal. 

350 

Dec.  16 

351 

*17 

352 

18 

353 

19 

354 

20 

355 

21 

356 

22 

357 

23 

358 

*24 

359 

25 

360 

26 

361 

27 

362 

28 

363 

29 

364 

30 

365 

*31 

Decimal. 


.95890411 
.96164384 
.96438356 
.96712329 
.96986301 

.97260274 
.97534247 
.97808219 
.98082192 
.98356164 

.98630137 
.98904110 

.99178082 
.99452055 

.99726027 

1.00000000 


YEAR  AND  DAY  OF  THE 
WEEK  DENOTED  BY  *. 


1881  Saturday. 

1882  Sunday. 

1883  Monday. 

1884  *Tues(iay.  Wcdn. 

1885  Thursday. 

1886  Friday. 

1887  Saturday. 

1888  *Sunday.  Mond. 

1889  Tuesday. 

1890  Wednesday. 

1891  Thursday. 

1892  *Friday.  Satur. 

1893  Sunday. 

1894  Monday. 

1895  Tuesday. 

1896  *Wedn.  Thurs. 

1897  Friday. 

1898  Saturday. 

1899  Sunday. 

1900  Monday. 

1901  Tuesday. 

1902  Wednesday. 

1903  Thursday. 

1904  I  *Friday.  Satur. 

1905  Sunday. 

1906  '  Monday. 

1907  Tuesday. 

1908  *Wedn.  Thurs. 

1909  Friday. 

1910  Saturday. 


*  In  1884  and  other  leap  years,  the  first  star  day  applies  only  in  January  and  February,  and  the  laat 
applies  only  in  the  remaining  ten  months. 


208 


TABLE      XX. 


THE  AMOUNT  OF  $1  AT  THE  END  OF  ANY  NUMBER  OF  TEARS. 


si       2 

2\ 

3 

U 

4 

4^      i 

tM 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent, 

Per  Cent. 

Ver  Cent.    ^ 

1 

1.02000000 

1.02500000 

1.03000000 

1.03500000 

1.04000000 

1.04500000'  1 

2 

1.04040000 

1.05062500  1.06090000 

1.07122500 

1.08160000 

1.09202500  i  2 

3 

1.06120800 

1.07689063  1.09272700 

1.10871787 

1.12486400 

1.14116613   3 

4 

1.08243316 

1.10381289 

1.12550881 

1.14752300 

1.16985856 

1.19251860 

4 

5 

1.10408080 

1.13140821 

1.15927407 

1.18768631 

1.21665290 

1.24618194 

6 

6 

1.12616242 

1.15969342 

1.19405230 

1.22925533 

1.26531902 

1.30226012 

6 

7 

1.14868567 

1.18868575 

1.22987387 

1.27227926 

1.31593178 

1.36086183 

7 

8 

1.17165938 

1.21840290 

1.26677008 

1.31680904 

1.36856905 

1.42210061 

8 

9 

1.19509257 

1.24886297 

1.30477318 

1.36289735 

1.42331181 

1.48609514 

9 

10 

1.21899442 

1.28008454 

1.34391638 

1.41059876 

1.48024428 

1.55296942 

10 

11 

1.24337431 

1.31208666 

1.38423387 

1.45996972 

1.53945406 

1.62285305 

11 

12 

1.26824179 

1.34488882 

1.42576089 

1.51106866 

1.60103222 

1.69588143 

12 

13 

1.29360663 

1.37851104 

1.46853371 

1.56395606 

1.66507351 

1.77219610 

13 

14 

1.31947876 

1.41297382 

1.51258972 

1.61869452 

1.73167645 

1.85194492 

14 

15 

1.34586834 

1.44829817 

1.55796742 

1.67534883 

1.80094351 

1.93528244 

15 

16 

1.37278571 

1.48450562 

1.60470644 

1.73398604 

1.87298125 

2.02237015 

16 

17 

1.40024142 

1.52161826 

1.65284763 

1.79467555 

1.94790050 

2.11337681 

17 

18 

1.42824625 

1.55965872 

1.70243306 

1.85748920 

2.02581652 

2.20847877 

18 

19 

1.45681117 

1.59865019 

1.75350605 

1.92250132 

2.10684918 

2.30786031 

19 

20 

1.48594740 

1.63861644 

1.80611123 

1.98978886 

il9113314 

2.41171402 

20 

21 

1.51566634 

1.67958185 

1.86029457 

2.05943147 

2.27876807 

2.52024116 

21 

22 

1.54597967 

1.72157140 

1.91610341 

2.13151158 

2.36991879 

2.63365201 

22 

23 

1.57689926 

1.76461068 

1.97358651 

2.20611448 

2.46471554 

2.75216635 

23 

24 

1.60843725 

1.80872595 

2.03279411 

2.28332849 

2.56330416 

2.87601383 

24 

25 

1.64060599 

1.85394410 

2.09377793 

2.36324498 

2.66583633 

3.00543446 

25  j 

26 

1.67341811 

1.90029270 

2.15659127 

2.44595856 

2.77246978 

3.14067901 

26 

27 

1.70688648 

1.94780002 

2.22128901 

2.53156711 

2.88336858 

3.28200956 

27 

28 

1.74102421 

1.99649502 

2.28792768 

2.62017196 

2.99870332 

3.42969999 

28 

29 

1.77584469 

2.04640739 

2.35656551 

2.7118779€ 

3.11865145 

3.58403649 

29 

30 

1.81136158 

2.09756758 

2.42726247 

2.80679370 

3.24339751 

3.74531813 

30 

31 

1.84758882 

2.15000677 

2.50008035 

2.90503148 

3.37313341 

3.91385745 

31 

32 

1.88454059 

2.20375694 

2.57508276 

3.00670759 

3.50805875 

4.08998104 

32 

33 

1.92223140 

2.25885086 

2.65233524 

3.11194235 

3.64838110 

4.27403018 

33 

34 

1.96067603 

2.31532213 

2.73190530 

3.22086033 

3.79431634 

4.46636154 

34 

35 

1.99988955 

2.37320519 

2.81386245 

3.33359045 

3.94608899 

4.66734781 

35 

36 

2.03988734 

2.43253532 

2.89827833 

3.45026611 

4.10393255 

4.87737846 

36 

37 

2.08068509 

2.49334870 

2.98522668 

3.57102542 

4.26808986 

5.09686049 

37 

38 

2.12229879 

2.55568242 

3.07478348 

3.69601131 

4.43881345 

5.32621921 

38 

39 

2.16474477 

2.61957448 

3.16702698 

3.82537171 

4.61636599 

5.56589908 

39 

40 

2.20803966 

2.68506384 

3.26203779 

3.95925972 

4.80102063 

5.81636454 

40 

41 

2.25220046 

2.75219043 

3.35989893 

4.09783381 

4.99306145 

6.07810094 

41 

42 

2.29724447 

2.82099520 

3.46069589 

4.24125799 

5.19278391 

6.35161548 

42 

43 

2.34318936 

2.89152008 

3.56451677 

4.38970202 

5.40049527 

6.63743818 

43 

44 

2.39005314 

2.96380808 

3.67145227 

4.54334160 

5.61651508 

6.93612290 

44 

45 

2.43785421  1 

3.03790328 

3.78159584 

4.70235855 

5.84117568 

7.24824843 

45 

46 

2.48661129 

3.11385086 

3.89504372 

4.86694110 

6.07482271 

7.57441961 

46 

47 

2.53634352 

3.19169713 

4.01189503 

5.03728404 

6.31781562 

7.91526849 

47 

48 

2.58707039 

3.27148956 

4.13225188  ' 

5.21358898 

6.57052824 

8.27145557 

48 

49 

2.63881179 

3.35327680 

4.25621944  1 

5.39606459 

6.83334937 

8.64367107 

49 

50 

2.69158803 

3.43710872 

4.38390602 

5-58492686 

7.10668335 

9.03263627 

50 

1 

Formula,  Amount  =  (1  +  *)"• 


TABLE     XX.  ^09 

THE  AMOUNT  OF  $1  AT  THE  END  OF  ANY  NUMBER  OF  YEARS, 


i 

5 

6 

7 

8 

9 

10 

e 

tS 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

^ 

1 

1.05000000 

1.06000000 

1.07000000 

1.08000000 

1.09000000 

1.10000000 

1 

2 

1.10250000 

1.12360000 

1.14490000 

1.16640000 

1.18810000 

1.21000000 

2 

3 

1.15762500 

1.19101600 

1.22504300 

1.25971200 

1.29502900 

1.33100000 

3 

4 

1.21550625 

1.26247696 

1.31079601 

1.36048896 

1.41158161 

1.46410000 

4 

5 

1.27628156 

1.33822558 

1.40255173 

1.46932808 

1.53862395 

1.61051000 

5 

6 

1.34009564 

1.41851911 

1.50073035 

1.58687432 

1.67710011 

1.77156100 

6 

7' 

1.40710042 

1.50363026 

1.60578148 

1.71382427 

1.82803912 

1.94871710 

7 

8 

1.47745544 

1.59384807 

1.71818618 

I  1.85093021 

1.99256264 

2.14358881 

8 

9 

1.55132822 

1.68947896 

1.83845921- 

:  1.99900463 

2.17189328 

2.35794769 

9 

10 

1.62889463 

1.79084770 

1.96715136 

i  2.15892500 

2.36736367 

2.59374246 

10 

11 

1.71033936 

1.89829856 

2.10485195 

1  2.33163900 

2.58042641 

2.85311671 

11 

12 

1.79585633 

2.01219647 

2.25219159 

2.51817012 

2.81266478 

3.13842838 

12 

13 

1.88564914 

2.13292826 

2.40984500 

2.71962373 

3.06580461 

3.45227121 

13 

14 

1.97993160 

2.26090396 

2.57853415 

2.93719362 

3.34172703 

3.79749834 

14 

15 

2.07892818 

2.39655819 

2.75903154 

3.17216911 

3.64248246 

4.17724817 

15 

16 

2.18287459 

2.54035168 

2.95216375 

3.42594264 

3.97030588 

4.59497299 

16 

17 

2.29201832 

2.69277279 

3.15881521 

3.70001805 

4.32763341 

5.05447028 

17 

18 

2.40661923 

2.85433915 

3.37993228 

\   3.99601950 

4.71712042 

5.55991731 

18 

19 

2.52695020 

3.02559950 

3.61652753 

4.31570106 

5.14166125 

6.11590904 

19 

20 

2.65329771 

3.20713547 

3.86968446 

4.66095714 

5.60441077 

6.72749995 

20 

21 

2.78596259 

3.39956360 

4.14056237 

5.03383372 

6.10880774 

7.40024994 

21 

22 

2.92526072 

3.60353742 

4.43040174 

5.43654041 

6.65860043 

8.14027494 

22 

23 

3.07152376 

3.81974966 

4.74052986 

5.87146365 

7.25787447 

8.95430243 

23 

24 

3.22509994 

4.04893464 

5.07236695 

6.34118074 

7.91108317 

9.84973268 

24. 

25 

3.38635494 

4.29187072 

5.42743264 

6.84847520 

8.62308066 

10.83470594 

25 

26 

3.55567269 

4.54938296 

5.80735292 

7.39635321 

9.39915792 

11.91817654 

26 

27 

3.73345632 

4.82234594 

6.21386763 

7.98806147 

10.24508213 

13.10999419 

27 

28 

3.92012914 

5.11168670 

6.64883836 

8.62710639 

11.16713952 

14.42099361 

28 

29 

4.11613560 

5.41838790 

7.11425705 

9.31727490 

12.17218208 

15.86309297 

29  ! 

30 

4.32194238 

5.74349117 

7.61225504 

10.06265689 

13.26767847 

17.44940227 

30 

31 

4.53803949 

6.08810064 

8.14511290 

10.86766944 

14.46176953 

19.19434250 

31 

32 

4.76494147 

6.45338668 

8.71527080 

11. 73708300 

15.76332879 

21.11377675 

32 

33 

5.00318854 

6.84058988 

9.32533975 

12.67604963 

17.18202838 

23.22515442 

33 

34 

5.25334797 

7.25102528 

9.97811354 

13.69013361 

18. 72841093 

25.54766986 

34 

35 

5.51601537 

7.68608679 

10.67658148 

14. 78534429 

20.41396792 

28.10243685 

35 

36 

5.79181614 

8.14725200 

11.42394219 

15.96817184 

22.25122503 

30.91268053 

36 

37  6.08140694 

8.63608712 

12.22361814 

17.24562558 

24.25383528 

34.00394859 

37 

38 

6.38547729 

9. 15425235 

13.07927141 

18.62527563 

26.43668046 

37.40434344 

38  1 

39 

6.70475115 

9.70350749 

13. 99482041 

20.11529768 

28.81598170 

41.14477779 

39 

40 

7.03998871 

10.28571794 

14.97445784 

21.72452150 

31.40942005 

45.25925557 

40  1 

41 

7.39198815 

10.90286101 

16.02266989 

23.46248322 

34.23626786 

49.78518112  41 

42 

7.76158756 

11.55703267 

17.14425678 

25.33948187 

37.31753197 

54.763699241  42  i 

|43 

8.14966693 

12.25045463 

18.34435475 

27.36664042 

40.  67610984 

60.24006916  43  1 

44 

8.55715028 

12.98548191 

19.62845959 

29.55597166 

44.33695973 

66.26407608 

44 

l45 

8.98500779 

13.76461083 

21.00245176 

31.92044939 

48.32728610 

72.89048369 

46 

46 

9.4,3425818 

14.59048748 

22.47262338 

34.47408534 

52.67674185 

80.17953205 

46 

47 

9.90597109 

15.46591673 

24.04570702 

37.23201217 

57.41764862 

88.19748526 

47 

48 

10.40126965 

16.39387173 

25.72890651 

40.21057314 

62.58523700 

97.01723378 

48 

49 

10.92133313 

17.37750403 

27.52992997 

43.42741899 

68.21790833 

106.71895716 

49 

50 

11.46739979 

18.42015427 

29.45702506 

46.90161251 

74.35752008 

117.39085288  60 

1 

210  TABLE      XX. 

THE  AMOUNT  OF  $1  AT  THE  END  OF  ANY  NUMBER  OF  TEARS. 


51 
62 
53 
54 
55 

56 
57 
58 
59 
60 

61 
62 
63 
64 
65 

66 
67 
68 
69 
70 

71 
72 
73 
74 
75 

76 
77 
78 
79 
80 

81 
82 
83 
84 
85 

86 
87 
88 
89 
90 

91 
92 
93 
94 
95 

96 
97 
98 
99 
100 


2 
Per  Cent. 


2.74541979 
2.80032819 
2.85633475 
2.91346144 
2.97173067 

3.03116529 
3.09178859 
3.15362436 
3.21669685 
3.28103079 

3.34665140 
3.41358443 
3.48185612 
3.55149324 
3.62252311 

3.69497357 
3.76887304 
3.84425050 
3.92113551 
3.99955822 

4.07954939 
4.16114038 
4.24436318 
4.32925045 
4.41583546 

4.50415216 
4.59423521 
4.68611991 
4.77984231 
4.87543916 

4.97294794 
5.07240690 
5.17385504 
5.27733214 

5.38287878 

5.49053636 
5.60034708 
5.71235402 
5.82660110 
5.94313313 

6.06199579 
6.18323570 
6.30690042 
6.43303843 
6.56169920 

6.69293318 
6.82679184 
6.96332768 
7.10259423 
7.24464612 


2| 
Per  Cent. 


3 
Per  Cent. 


3.52303644  4.51542320 

3.61111235  4.65088590 

3.70139016  4.79041247 

3.79392491  4.93412485 

3.88877303  5.08214859 

3.98599236  5.23461305 

4.08564217  5.39165144 

4.18778322  5.55340098 

4.29247780  5.72000301 

4.39978975  5.89160310 

4.50978449;  6.06835120 

4.62252910  6.25040173 

4.73809233  6.43791378 

4.85654464  6.63105120 

4.97795826  6.82998273 

5.10240721  7.03488222 

5.22996739  7.24592868 

5.36071658  7.46330654 

5.494734491  7.68720574 

5.632102861  7.91782191 

5.77290543,'  8.15535657 

5.91722806  8.40001727 

6.06515876  8.65201778 

6.21678773  8.91157832 

6.372207431  9.17892567 

6.5315126l|  9.45429344 

6.69480043;  9.73792224 
6.8621704410.03005991 
7.0337247010.33096170 
7.2095678210.64089056 

7.3898070110.96011727 


3| 
Per  Cent. 


7.57455219 
7.76391599 
7.95801389 
8.15696424 


11.28892079 
11.62758841 
11.97641607 
12.33570855 


8. 36088834!l2. 70577981 
8.56991055113.08695320 
8.7841583213.47956180 
9.0037622813.88394865 
9.2288563314.30046711 

9.4595777414.72948112 
9.6960671815.17136556 


9. 93846886 
10.18693058 
10.44160385 

10.70264395 
10.97021004 
11.24446530 


15.62650652 
16.09530172 
16.57816077 

17.07550559 

17.58777076 
18.11540388 


11.52557693118.65886600 
11.8137163519.21863198 


5.78039930 
5.98271327 
6.19210823 
6.40883202 
6.63314114 

6.86530108 
7.10558662 
7.35428215 
7.61168203 

7.87809090 

8.15382408 
8.43920792 
8.73458020 
9.04029051 
9.35670068 

9.68418520 
10.02313168 
10.37394129 
10.73702924 
11.11282526 

11.50177414 
11.90433624 
12.32098801 
12.75222259 
13.19855038 

13.66049964 
14.13861713 
14.63346873 
15.14564013 
15.67573754 


16.22438835 
16.79224194 
17.37997041 

17.98826938  26. 
18.61785880  28. 


4 
Per  Cent. 


^ 

Per  Cent. 


7.39095068  9.43910490 
7.686588711  9.86386463 
7.9940522610.30773853 
8.31381435110.77158677 
8.6463669211.25630817 

8.9922216011.76284204 

9.35191046{12.29216993 

9.7259868812.84531758 

10.11502635'l3.42335687 

10.51962741114.02740793 


10.9404125014. 
11.3780290015. 
11.83315016jl6. 
12.3064761716. 
12.79873522|l7. 


65864129 
31828014 
00760275 
72794487 
48070239 


13.31068463 
13.84311201 
14.39683649 
14.97270995 


18.26733400 
19.08936403 
19.94838541 
20.84606276 


15.57161835  21.78413558 


1944830822. 
84226241123. 
51595290i24. 
2I659IO2I25. 
94525466127. 


76442168 
78882066 
85931759 
97798688 
14699629 


19.70306485  28.36861112 
20.49118744  29.64519862 


21.31083494 
22.16326833 
23.04979907 


23. 
24. 

25. 


30.97923256 
32.37329802 
33.83009643 


97179103  35. 
93066267i36. 
92788918{38. 
96500475140. 
04360494  42. 


19.26948386  29 
19.94391580  30 


20.64195285 
21.36442120 
22.11217594 

22.88610210 
23.68711567 
24.51616472 
25.37423049 
26.26232856 

27.18151005 
28.13286291 
29.11751311 
30.13662607 


16534913 
33196310 
54524162 
80705129 
11933334 


35245077 
94331106 
60576006 
34301926 
15845513 


44.05558561 
46.03808696 
48.10980087 
50.27474191 
52.53710530 


48410667  54 
90347094|57, 
37960978:59, 
91479417:62. 
51138594|65. 

43.17I84137I68, 
44.89871503  71 


46.69466363 
48.56245017 


31.19140798|50.50494818,81 


90127503 
37183241 
95356487 
65147529 
47079168 

41697730 
49574128 
71304964 
07513687 
58851803 


TABLE     XX. 

THE  AMOUNT  OF  $1  AT  THE  END  OF  ANY  NUMBER  OF  YEARS. 


2X1 


§ 

5 

6 

7 

8 

10 

1 

^ 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

^ 

51 

12.04076978 

19.53536353 

31.51901683 

50.65374151 

139.13993817 

51 

52 

13.64380836 

30.69688534 

33.73534799 

54.70604083 

143.04393198 

52 

53 

13.37494868 

31.93869846 

36.08613335 

59.08252410 

156.24722518 

53 

54 

13.93869611 

23.25502037 

38.61315092 

63.80912603 

171.87194770 

54 

55 

14.63563093 

24.65032159 

41.31500148 

68.91385611 

189.05914247 

55 

56 

15.36741346 

26.12934089 

44.20705159 

74.42696460 

207.96505672 

56 

57 

16.13578309 

37.69710134 

47.30154520 

80.38112177 

228.76156239 

57 

58 

16.94357334 

39.35893742 

50.61265336 

86.81161151 

251.63771863 

58 

59 

17.78970085 

31.12046307 

54.15553910 

93.75654043 

276.80149049 

59 

60 

18.67918589 

32.98769085 

57.94643683 

101.25706367 

304.48163954 

60 

61 

19.61314519 

34.96695230 

63.00367671 

109.35762876 

334.92980350 

61 

62 

30.59380345 

37.06496944 

66.34386408 

118.10623906 

368.42378385 

62 

63 

31.63349357 

39.28886761 

70.98686457 

127.55473819 

405.36506333 

63 

64 

33.70466730 

41.64619966 

75.95594509 

137.75911734 

445.79156845 

64 

65 

33.83990056 

44.14497164 

81.37386134 

148.77984662 

-  490.37073530 

65 

66 

35.03189559 

46.79366994 

86.96196153 

160.68223435 

539.40779783 

66 

67 

36.38349037 

49.60129014 

93.04939884 

173.53681310 

593.34857761 

67 

68 

37.59766488 

52.57736755 

99.56374976 

187.41975814 

653.68343537 

68 

69 

38.97754813 

55.73300960 

106.53314334 

303.41333880 

717.95177891 

69 

70 

30.43643554 

59.07593018 

113.98939330 

318.60640590 

789.74695680 

70 

71 

31.94774681 

63.63048599 

131.96864965 

336.09491837 

868.73165348 

71 

72 

33.54513415 

66.37771515 

130.50645513 

254.98251184 

955.59381773 

72 

73 

35.33339086 

70.36037806 

139.64190699 

375.38111379 

1,051.15319950 

73 

74 

36.98351040 

74.58300074 

149.41684047 

397.41160181 

1,156.36851945 

74 

75 

38.83368593 

79.05693078 

159.87601931 

331.30453996 

1,271.89537140 

75 

76 

40.77433033 

83.80033603 

171.06734066 

346.90089335 

1,399.08490853 

76 

77 

43.81303633 

88.83835619 

183.04305450 

374.65396374 

1,538.99339939 

77 

78 

44.95368804 

94.15805756 

195.85499833 

404.63520084 

1,692.89273933 

78 

79 

47.30137344 

99.80754103 

309.56484820 

436.99531691 

1,862.18201336 

79 

80 

49.56144107 

105.79599348 

224.23438758 

471.95483436 

2,048.40021459 

80 

81 

53.03951313 

113.14375309 

239.93079471 

509.71133100 

2,253.34033604 

81 

82 

54.64148878 

118.87337837 

256.72595034 

550.48811868 

3,478.56435965 

82 

83 

57.37356333 

136.00473097 

274.69676686 

594.53716818 

3,726.42068561 

83 

84 

60.34334138 

133.56500433 

393.93554054 

643.08934163 

3,999.06375418 

84 

85 

63.25435344 

141.57890448 

314.50032838 

693.45648896 

3,398.96903959 

85 

86! 

66.41707113 

150.07363875 

336.51535136 

748.93300808 

3,638.86593355 

86 

87  1 

69.73793467 

159.07805708 

360.07142596 

808.84764873 

3,991.75353581 

87 

88 

73.33483091 

168.63374050 

385.27642578 

873.55546063 

4,390.92777839 

88 

89 

•  76.88606195 

178.74010493 

412.24577558 

943.43989747: 

4,830.02055633 

89 

90 

80.73036505 

189.46451133 

441.10297987 

1,018.91508937: 

5,313.03361185 

90 

91 

84.76688330 

300.83338190 

471.98018846 

1,100.43829641 

5,844.33487303 

91 

92 

89.00533747 

313.88333481 

505.01880166 

1,188.46356013 

6,438.75736034 

92 

93 

93.45548884 

335.65536430 

540.37011777 

1,383.53956494 

7,071.63309637 

93 

94 

98.13826328 

339.19458016 

578.19602602 

1,386.33373013 

7,778.79640601 

94 

95 

103.03467645 

353.54635497 

618.66974784 

1,497.13054854 

8,556.67604661 

95 

96 

108.18641027 

368.75903037 

661.97663019 

1,616.89019343 

9,412.34365127 

96 

97 

113.59573078 

384.88457308 

708.31499430 

1,746.34140783 

10,353.57801640 

97 

98 

119.27551733 

301.97764641 

757.89704390 

1,885.94073044 

11,388.93581804 

98 

99 

135.339393191330.09630519 

810.94983697 

3,036.81597808 

12,527.82939984 

99 

100 

131.50135785  339.30308351 

867.71632556 

3,199.76135633 

13,780.61233982 

100 

213  TABLE     XXI. 

THE  PRESENT  VALUE  OF  |1  DUE  AT  THE  END  OF  ANY  NUMBER  OF  YEARS. 


g 

2 

3i 

3 

n 

4 

H 

i 

^ 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

^ 

1 

.98039216 

.97560976 

.97087379 

.96618357 

.96153846 

.95693780 

1 

2 

.96116878 

.95181440 

.94259591 

.93351070 

.924556'21 

.91572995 

2 

3 

.94232233 

.92859941 

.91514166 

.90194270 

.88899636 

.87629660 

3  ! 

4 

.92384543 

.90595064 

.88848705 

.87144223 

.85480419 

.83856134 

4 

5 

.90573081 

.88385429 

.86260878 

.84197317 

.82192711 

.80245105 

5 

6 

.88797138 

.86229687 

.83748426 

.81350064 

.79031453 

.76789574 

6 

7 

.87056018 

.84126524 

.81309151 

.78599096 

.75991781 

.73482846 

7 

8 

.85349037 

.82074657 

.78940923 

.75941155 

.73069020 

.70318513 

8 

9 

.83675527 

.80072836 

.76641673 

.73373097 

.70258674 

.67290443 

9 

10 

.82034830 

.78119840 

.74409391 

.70891881 

.67556417 

.64392768 

10 

11 

.80426304 

.76214478 

.72242127 

.68494571 

.64958093 

.61619874 

11 

12 

.78849318 

.74355589 

.70137988 

.66178330 

.62459705 

.58966386 

12 

13 

.77303253 

•72542038 

.68095134 

.63940415 

.60057409 

.56427164 

13 

14 

.75787502 

.70772720 

.66111781 

.61778179 

.57747508 

.53997286 

14 

15 

.74301473 

.69046556 

.64186195 

.59689062 

.55526450 

.51672044 

15 

16 

.72844581 

.67362493 

.62316694 

.57670591 

.53390818 

.49446932 

16 

17 

.71416256 

.65719506 

.60501645 

.55720378 

.51337325 

.47317639 

17 

18 

.70015937 

.64116591 

.58739461 

.53836114 

.49362812 

.45280037 

18 

19 

.68643076 

.62552772 

.57028603 

.52015569 

.47464242 

.43330179 

19 

20 

.67297133 

.61027094 

.55367576 

.50256588 

.45638695 

.41464286 

20 

21 

.65977582 

.59538629 

.53754928 

.48557090 

.43883360 

.39678743 

21 

22 

.64683904 

.58086467 

.52189250 

.46915063 

.42195539 

.37970089 

22 

23 

.63415592 

.56669724 

.50669175 

.45328563 

.40572633 

.36335013 

23 

24 

.62172149 

.55287535 

.49193374 

.43795713 

.39012147 

.34770347 

24 

25 

.60953087 

.53939059 

.47760557 

.42314699 

.37511680 

.33273060 

25 

26 

.59757928 

.52623472 

.46369473 

.40883767 

.36068923 

.31840248 

26 

27 

.58586204 

.51339973 

.45018906 

.39501224 

.34681657 

.30469137 

27 

28 

.57437455 

.50087778 

.43707675 

.38165434 

.33347747 

.29157069 

28 

29 

.56311231 

.48866125 

.42434636 

.36874816 

.32065141 

.27901502 

29 

30 

.55207089 

.47674269 

.41198676 

.35627841 

.30831867 

.26700002 

30 

31 

.54124597 

.46511481 

.39998715 

.34423035 

.29646026 

.25550241 

31 

32 

.53063330 

.45377055 

.38833703 

.33258971 

.28505794 

.24449991 

32 

33 

.52022873 

.44270298 

.37702625 

.32134271 

.27409417 

.23397121 

33 

34 

.51002817 

.43190534 

.36604490 

.31047605 

.26355209 

.22389589 

34 

35 

.50002761 

.42137107 

.35538340 

.29997686 

.25341547 

.21425444 

35 

36 

.49022315 

.41109372 

.34503243 

.28983272 

.24366872 

.20502817 

36 

37 

.48061093 

.40106705 

.33498294 

.28003161 

.23429685 

.19619921 

37 

38 

.47118719 

.39128492 

.32522615 

.27056194 

.22528543 

.18775044 

38 

39 

.46194822 

.38174139 

.31575355 

.26141251 

.21662061 

.17966549- 

39 

40 

.45289042 

.37243062 

.30655684 

.25257247 

.20828904 

.17192870 

40 

41 

.44401021 

.36334695 

.29762800 

.24403137 

.20027793 

.16452507 

41 

42 

.43530413 

.35448483 

.28895922 

.23577910 

.19257493 

.15744026 

42 

43 

.42676875 

.34583886  . 

.28054294 

,22780590 

.18516820 

.15066054 

43 

44 

.41840074 

.33740376 

.27237178 

.22010232 

.17804635 

.14417276 

44 

45 

.41019680 

.32917440 

.26443862 

•21265924 

.17119841 

.13796437 

45 

46 

.40215373 

.32114576 

.25673653 

.20546787 

.16461386 

.13202332 

46 

47 

.39426836 

.31331294 

.24925876 

.19851968 

.15828256 

.12633810 

47 

48 

.38653761 

.30567116 

.24199880 

.19180645 

.15219476 

.12089771 

48 

49 

.37895844 

.29821576 

.23495029 

.18532024 

.14634112 

.11569158 

49 

50 

.37152788 

.29094221 

.22810708 

.17905338 

.14071261 

.11070965 

50 

FoBMULA,  Present  Value 


(1  +  0" 


=  v"*. 


TABLE     XXI.  213 

iTHE  PRESENT  VALUE  OF  $1  I^UE  AT  THE  END  OF  ANY  NUMBER  OP  YEARS. 


i 

5 

6 

7 

8 

9 

10 

1 

Sh 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

1 

1 

.95238095 

.94339623 

.93457944 

.92592593 

.91743119 

.90909091 

2 

-.90702948 

.88999644 

.87343873 

.85733882 

.84167999 

.82644628 

2 

3 

.86383760 

.83961928 

.81629788 

.79383224 

.77218348 

.75131480 

3 

4 

.82270247 

.79209366 

.76289521 

':   .73502985 

.70842521 

.68301346 

4 

5 

.78352617 

.7472581ir 

.71298618 

j  .68058320 

.64993139 

.62092132 

5 

6 

.74621540 

.70496054 

.66634222 

.63016963 

.59626733 

.56447393 

6 

7 

.71068133 

.66505711 

.62274974 

i  .58349040 

.54703424 

.51315812 

7 

8 

.67683936 

.62741237 

.58200910 

i  .54026888 

.50186628 

.46650738 

8 

9 

.64460892 

.59189846 

.54393374 

j  .50024897 

.46042778 

.42409762 

9 

10 

.61391325 

.55839478 

.50834929 

.46319349 

.42241081 

.38554329 

10 

11 

.58467929 

.52678752 

.47509280 

1  .42888286 

.38753285 

.35049390 

11 

12 

.55683742 

.49696936 

.44401196 

1  .39711376 

.35553473 

.31863082 

12 

13 

.53032135 

.46883902 

.41496445 

.36769792 

.32617865 

.28966438 

13 

14 

.50506795 

.44230096 

.38781724 

.34046104 

.29924647 

.26333125 

14 

15 

.48101710 

.41726506 

.36244602 

.31524171 

.27453804 

.23939205 

15 

16 

.45811152 

.39364628 

.33873460 

.29189047 

.25186976 

.21762914 

16 

17 

.43629669 

.37136442 

.31657439 

.27026895 

.23107318 

.19784467 

17 

18 

.41552065 

.35034379 

.29586392 

.25024903 

.21199374 

.17985879 

18 

19 

.39573396 

.33051301 

.27650833 

.23171206 

.19448967 

.16350799 

19 

20 

.37688948 

.31180473 

.25841900 

.21454821 

.17843089 

.14864363 

20 

21 

.35894236 

.29415540 

.24151309 

.19865575 

.16369806 

.13513057 

21 

22 

.34184987 

.27750510 

.22571317 

.18394051 

.15018171 

.12284597 

22 

23 

.32557130 

.26179726 

.21094688 

.17031528 

.13778139 

.11167816 

23 

24 

.31006791 

.24697855 

. 1971466a 

.15769934 

.12640494 

.10152560 

24 

25 

.29530277 

.23299863 

.18424918 

.14601790 

.11596784 

.09229600 

25 

26 

.28124073 

.21981003 

.17219549 

.13520176 

.10639251 

.08390545 

26 

27 

.26784832 

.20736795 

.16093037 

.12518682 

.09760781 

.07627768 

27 

28 

.25509364 

.19563014 

.15040221 

.11591372 

.08954845 

.06934335 

28 

29 

.24294632 

.18455674 

.14056282 

.10732752 

.08215454 

.06303941 

29 

30 

.23137745 

.17411013 

.13136712 

.09937733 

.07537114 

.05730855 

30 

31 

.22035947 

.16425484 

.12277301 

.09201605 

:06914783 

.05209868 

31 

32 

.20986617 

.15495740 

.11474113 

.08520005 

.06343838 

.04736244 

32 

33 

.19987254 

.14618622 

.10723470 

.07888893 

.05820035 

.04305676 

33 

34 

.19035480 

.13791153 

.10021934 

.07304531 

.05339481 

.03^14251 

34 

35 

.18129028 

.13010522 

.09366294 

.06763454 

.04898607 

.03558410 

36 

36 

.17265741 

.12274077 

.08753546 

.06262458 

.04494135 

.03234918 

36 

37 

.16443563 

.11579318 

.08180884 

.05798572 

.04123059 

.02940835 

37 

38 

.15660536 

.10923885 

.07645686 

.05369048 

.03782623 

.02673486 

38 

39 

.14914797 

.10305552 

.07145501 

.04971341 

.03470296 

.02430442 

39 

40 

.14204568 

.09722219 

.06678038 

.04603093 

.03183758 

.02209493 

40 

41 

.13528160 

.09171904 

.06241157 

.04262123 

.02920879 

.02008630 

41 

42 

.12883962 

.08652740 

.05832857 

.03946411 

.02679706 

.01826027 

42 

43 

.12270440 

.08162962 

.05451268 

.03654084 

.02458446 

.01660025 

43 

44 

.11686133 

.07700908 

.05094643 

.03383411 

.02255455 

.01509113 

44 

45 

.11129651 

.07265007 

.04761349 

.03132788 

.02069224 

.01371921 

45 

46 

.10599667 

.06853781 

.04449859 

.02900730 

.01898371 

.01247201 

46 

47 

.10094921. 

.06465831 

.04158747 

.02685861 

.01741625 

.01133819 

47 

48 

.09614211 

,06099840 

.03886679  , 

.02486908 

.01597821 

.01030745 

48 

49 

.09156391 

.05754566 

.03632410  , 

.02302693 

.01465891 

.00937041 

49 

50 

.08720373 

.05428836 

.03394776 

.02132123 

.01344854 

.00851855 

50 

214  TABLE     XXI. 

THE  PRESENT  VALUE  OF  $1  DUE  AT  THE  END  OF  ANY  NUMBER  OF  YEARS. 


g 

2 

2i 

3 

3i 

4 

4.1 

13 

^ 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

51 

.36424302 

.28384606 

.22146318 

.17299843 

.13530059 

.10594225 

51 

52 

.35710100 

.27692298 

.21501280 

.16714824 

.13009672 

.10138014 

52 

53 

.35009902 

.27016876 

.20875029 

.16149589 

.12509300 

.09701449 

53 

54 

.34323433 

.26357928 

.20267018 

.15603467 

.12028173 

.09283683 

54 

55 

.33650425 

.25715052 

.19676717 

.15075814 

.11565551 

.08883907 

55 

56 

.32990613 

.25087855 

.19103609 

.14566004 

.11120722 

.08501347 

56 

57 

.32343738 

.24475956 

.18547193 

!  .14073433 

.10693002 

.08135260 

57 

58 

.31709547 

.23878982 

.18006983 

.13597520 

.10281733 

.07784938 

58 

59 

.31087791 

.23296568 

.17482508 

.13137701 

.09886282 

.07449701 

59 

60 

.30478227 

.22728359 

.16973309 

.12693431 

.095016040 

.07128901 

60 

61 

.29880614 

.22174009 

.16478941 

.12264184 

.09140423 

.06821915 

61 

62 

.29294720- 

.21633179 

.15998972 

.11849453 

.08788868 

.06528148 

62 

63 

.28720314 

.21105541 

.15532982 

.11448747 

.08450835 

.06347032 

63 

64 

.28157170 

.20590771 

.15080565 

.11061591 

.08125803 

.05978021 

64 

65 

.27605069 

.20088557 

.14641325 

.10687528 

.07813272 

.05720594 

65 

66 

.27063793 

.19598593 

.14214879 

.10326114 

.07512761 

.05474253 

66 

67 

.26533130 

.19120578 

.13800853 

.09976922 

.07223809 

.05238519 

67 

68 

.26012873 

.18654223 

.13398887 

.09639538 

.06945970 

.05012937 

68 

69 

.25502817 

.18199241 

.13008628 

.09313563 

.06678818 

.04797069 

69 

70 

.25002761 

.17755358 

.12629736 

.08998612 

.06421940 

.04590497 

70 

1  71 

.24512511 

.17322300 

.12261879 

.08694311 

.06174942 

.04392820 

71 

72 

.24031874 

.16899805 

.11904737 

.08400300 

.05937444 

.04203655 

72' 

73 

.23560661 

.16487615 

.11557997 

.08116232 

.05709081 

.04022637 

73  1 

74 

.23098687 

.16085478 

.11221357 

.07841770 

.05489501 

.03849413 

74 

75 

.22645771 

.15693149 

.10894521 

.07576590 

.05278366 

.03683649 

75 

76 

.22201737 

.15310389 

.10577205 

.07320376 

.05075352 

.03525023 

76  i 

.  77 

.21766408 

.14936965 

.10269131 

.07072827 

.04880146 

.03373228 

77' 

78 

.21339616 

.14572649 

.09970030 

.06833650 

.04692449 

.03227969 

78, 

79 

.20921192 

.14217218 

.09679641 

.06602560 

.04511970 

.03088965 

79 

80 

.20510973 

.13870457 

.09397710 

.06379285 

.04338433 

.02955948 

80 

81 

.20108797 

.13532153 

.09123990 

.06163561 

.04171570 

.02828658 

81 

82 

.19714507 

.13202101 

.08858243 

.05955131 

.04011125 

.02706850 

82 

83 

.19327948 

.12880098 

.08600236 

.05753750 

.03856851 

.02590287 

83 

84 

.18948968 

.12565949 

.08349743 

.05559179 

.03708510 

.02478744 

84 

85 

.18577420 

.12259463 

.08106547 

.05371187 

.03565875 

.02372003 

85 

86 

.18213157 

.11960452 

.07870434 

.05189553 

.03428726 

.02269860 

86 

87 

.17856036 

.11668733 

.07641198 

.05014061 

.03296852 

.02172115 

87 

88 

.17505918 

.11384130 

.07418639 

.04844503 

.03170050 

.02078579 

88 

89 

.17162665 

.11106468 

.07202562 

.04680679 

.03048125 

.01989070 

89 

90 

.16826142 

.10835579 

.06992778 

.04522395 

.02930889 

.01903417 

90 

91 

.16496217 

.10571296 

.06789105 

.04369464 

.02818163 

.01821451 

91 

92 

.16172762 

.10313460 

.06591364 

.04221705 

.02709772 

.01743016 

92 

93 

.15855649 

.10061912 

.06399383 

.04078942 

.02605550 

.01667958 

93 

94 

.15544754 

.09816500 

.06212993 

.03941006 

.02505337 

.01596132 

94 

95 

.15239955 

.09577073 

.06032032 

.03807736 

.02408977 

.01527399 

95 

96 

.14941132 

.09343486 

.05856342 

.03678972 

.02316324 

.01461626 

96 

97 

.14648169 

.09115596 

.05685769 

.03554562 

.02227235 

.01398685 

97 

98 

.14360950 

.08893264 

.05520164 

.03434359 

.02141572 

.01338454 

98 

99 

.14079363 

.08676355 

.05359382 

.03318222 

.02059204 

.01280817 

99 

100 

.13803297 

.08464737 

.05203284 

.03206011 

.01980004 

.01225663 

100 

TABLE  XXI.  215 

THE  PRESENT  VALUE  OF  $1  DUE  AT  THE  END  OP  ANT  NUMBER  OF  YEARS. 


2 

5 

6 

7 

8 

9 

10 

1 

1 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

^ 

1 

1  51 

.08305117 

.05121544 

.03172688 

.01974188 

.01233811 

.00774414 

51 

52 

.07909635 

.04831645 

.02965129 

.C1827952 

.01131937 

.00704013 

52 

53 

.07532986 

.04558156 

.02771148 

.01692548 

.01038474 

.00640011 

53 

54 

.07174272 

.04300147 

.02589858 

.01567174 

.00952728 

.00581829 

54 

55 

.06832640 

.04056742 

.02420428 

.01451087 

.00874063 

.00528935 

55 

56 

.06507276 

.03827115 

.02262083 

.01343599 

.00801892 

.00480850 

56 

57 

.06197406 

.03610486 

.02114096 

.01244073 

.00735681 

.00437136 

57 

58 

.05902291 

.03406119 

.01975791 

.01151920 

.00674937 

.00397397 

58 

59 

.05621230 

.03213320 

.01846533 

.01066592 

.00619208 

.00361270 

59 

60 

.05353552 

.03031434 

.01725732 

.00987585 

.00568081 

.00328427 

60 

61 

.05098621 

.02859843 

.01612834 

.00914431 

.00521175 

.00298570 

61 

62 

.04855830 

.02697965 

.01507321 

.00846696 

.00478142 

.00271427 

62 

63 

.04624600 

.02545250 

.01408711 

.00783977 

.00438663 

.00246752 

63 

64 

.04404381 

.02401180 

.01316553 

.00725905 

.00402443 

.00224320 

64 

65 

.04194648 

.02265264 

.01230423 

.00672134 

.00369214 

.00203927 

65 

66 

.03994903 

.02137041 

.01149928 

.00622346 

.00338728 

.00185388 

66 

67 

.03804670 

.02016077 

.01074699 

.00576247 

.00310760 

.00168535 

67 

68 

.03623495 

.01901959 

.01004392 

.00533562 

.00285101 

.00153214 

68 

69 

.03450948 

.01794301 

.00938684 

.00494039 

.00261560 

.00139285 

69 

70 

.03286617 

.01692737 

.00877275 

.00457443 

.00239963 

.00126623 

70 

71 

.03130111 

.01596922 

.00819883 

.00423558 

.00220150 

.00115112 

71 

72 

.02981058 

.01506530 

.00766246 

.00392184 

.00201972 

.00104647 

72 

73 

.02839103 

.01421254 

.00716117 

.00363133 

.00185296 

.00095134 

73 

74 

.02703908 

.01340806 

.00669269 

.00336234 

.00169996 

.00086485 

74 

75 

.02575150 

.01264911 

.00625485 

.00311328 

.00155960 

.00078623 

75 

76 

.02452524 

.01193313 

.00584565 

.00288267 

.00143082 

.00071^75 

76 

77 

.02335737 

.01125767 

.00546323 

.00266914 

.00131268 

.00064978 

77 

78 

.02224511 

.01062044 

.00510582 

.00247142 

.00120430 

.00059070 

78 

79 

.02118582 

.01001928 

.00477179 

.00228835 

.00110486 

.00053700 

79 

80 

.02017697 

.00945215 

.00445962 

.00211885 

.00101363 

.00048819 

80 

81 

.01921617 

.00891713 

.00416787 

.00196190 

.00092994 

.00044381 

81 

82 

.01830111 

.00841238 

.00389520 

..00181657 

.00085315 

.00040346 

82 

83 

.01742963 

.00793621. 

.00364038 

.00168201 

.00078271 

.00036678 

83 

84 

.01659965 

.00748699 

.00340222 

.00155742 

.00071808 

.00033344 

84 

85 

.01580919 

.00706320 

.00317965 

'.00144205 

.00065879 

.00030313 

85 

86 

.01505637 

.00666339 

.00297163 

.00133523 

.00060440 

.00027557 

86 

.  87 

.01433940 

.00628622 

.00277723 

.00123633 

.00055449 

.00025052 

87 

88 

.01365657 

.00593040 

.00259554 

.00114475 

.00050871 

.00022774 

88 

89 

.01300626 

.00559471 

.00242574 

.00105995 

.00046670 

.00020704 

89 

90 

.01238691 

.00527803 

.00226704 

.00098144 

.00042817 

.00018822 

90 

91 

.01179706 

.00497928 

.00211873 

.00090874 

.00039282 

.00017111 

91 

92 

.01123529 

.00469743 

.00198012 

.00084142 

.00036038 

.00015555 

92 

93 

.01070028 

.00443154 

.00185058 

.00077910 

.00033063 

.00014141 

93 

94 

.01019074 

.00418070 

.00172952 

.00072138 

.00030333 

.00012855 

94 

95 

.00970547 

.00394405 

.00161637 

.00066795 

.00027828 

.00011687 

95 

96 

.00924330 

.00372080 

.00151063 

.00061847 

.00025530 

.00010624 

96 

97 

.00880315 

.00351019 

.00141180 

.00057266 

.00023422 

.00009658 

97 

98 

.00838395 

.00331150 

.00131944 

.00053024 

.00021488 

.00008780 

98 

99 

.00798471 

.00312406 

.00123312 

.00049096 

.00019714 

.00007982 

99 

100 

.00760449 

.00294722 

.00115245 

.00045459 

.00018086 

.00007257 

100 

216 


TABLE    XXII. 


THE  AMOUNT  OF  $1  ANNUITY  AT  THE  END  OF  ANY  NUMBER  OF  YEARS. 


§ 

2 

2h 

3 

H 

4 

^ 

§ 

^ 

Per  Cent, 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

tS 

1 

1.000000 

1.000000 

1.000000 

1.000000 

1.000000 

1.000000 

1 

2 

2.020000 

2.025000 

2.030000 

2.035000 

2.040000 

2.045000   2 

3 

3.060400 

3.075625 

3.090900 

3.106225 

3.121600 

3.137025 i  3 

4 

4.121608 

4.152516 

4.183627 

4.214943 

4.246464 

4.278191 

4 

5 

5.204040 

5.256329 

5.309136 

5.362466 

5.416323 

5.470710 

5 

6 

6.308121 

6.387737 

6.468410 

6.550152 

6.632975 

6.716892 

6 

7 

7.434283 

7.547430 

7.662462 

7.779408 

7.898294 

8.019152 i  7 

8 

8.582969 

8.736116 

8.892336 

9.051687 

9.214226 

9.3800141  8 

9 

9.754628 

9.954519 

10.159106 

10.368496 

10.582795 

10.802114'  9 

10 

10.949721 

11.203382 

11.463879 

11.731393 

12.006107 

12.288209!  10 

11 

12.168715 

12.483466 

12.807796 

13.141992 

13.486351 

13.841179  11 

12 

13.412090 

13.795553 

14.192030 

14.601962 

15.025805 

15.464032 i  12 

13 

14.680332 

15.140442 

15.617790 

16.113030 

16.626838 

17.159913 

13 

14 

15.973938 

16.518953 

17.086324 

17.676986 

18.291911 

18.932109 

1^  1 

15 

17.293417 

17.931927 

18.598914 

19.295681 

20.023588 

20.784054 

15 

16 

18.639285 

19.380225 

20.156881 

20.971030 

21.824531 

22.719337 

16 

17 

20.012071 

20.864730 

21.761588 

22.705016 

23.697512 

24.741707 

17 

18 

21.412312 

22.386349 

23.414435 

24.499691 

25.645413 

26.855084 

18 

19 

22.840559 

23.946007 

25.116868 

26.357181 

27.671229 

29.063562 

19 

20 

24.297370 

25.544658 

26.870374 

28.279682 

29.778079 

31.371423 

20 

21 

25.783317 

27.183274 

28.676486 

30.269471 

31.969202 

33.783137 

21 

22 

27.298984 

28.862856 

30.536780 

32.328902 

34.247970 

36.303378 

22 

23 

28.844963 

30.584427 

32.452884 

34.460414 

36.617889 

38.937030 

23 

24 

30.421862 

32.349038 

34.426470 

36,666528 

39.082604 

41.689196 

24 

25 

32.030300 

34.157764 

36.459264 

38.949857 

41.645908 

44.565210  25 

26 

33.670906 

36.011708 

38.553042 

41.313102 

44.311745 

47.570645 

26 

27 

35.344324 

37.912001 

40.709634 

43.759060 

47.084214 

50.711324 

27 

28 

37.051210 

39.859801 

42.930923 

46.290627 

49.967583 

53.993333 

28 

29 

38.792235 

41.856296 

45.218850 

48.910799 

52.966280 

57.423033 

29 

30 

40.568079 

43.902703 

47.575416 

51.622677 

56.084938 

01.007070 

30 

31 

42.379441 

46.000271 

50.002678 

54.429471 

59.328335 

64.752388 

31 

32 

44.227030 

48.150278 

52.502759 

57.334502 

62.701469 

68.666245 

32 

33 

46.111570 

50.354034 

55.077841 

60.341210 

66.209527 

72.756226 

33 

34 

48.033802 

52.612885 

57.730177  ' 

63.453152 

69.857909 

77.030256 

34 

35 

49.994478 

54.928207 

60.462082 

66.674013 

73.652225 

81.496618 

35 

36 

51.994367 

57.301413 

63.275944 

70.007603 

77.598314 

86.163906 

36 

37 

54.034255 

59.733948 

66.174223 

73.457869 

81.702246 

91.041344 

37 

38 

56.114940 

62.227297 

69.159449 

77.028895 

85.970336 

96.138205 

38 

39 

58.237238 

64.782979 

72.234233 

80.724906 

90.409150 

101.464424 

39 

40, 

60.401983 

67.402554 

75.401260 

84.550278 

95.025516 

107.030323 

40 

41 

62.610023 

70.087617 

78.663298 

88.509537 

99.826536 

112.846688 

41 

42 

64.862223 

72.839808 

82.023196  ! 

92.607371 

104.819598 

118.924789 

42 

43 

67.159468 

75.660803 

85.483892  ■ 

96.848629 

110.012382 

125.276404 

43 

44 

69.502657 

78.552323 

89.048409 

101.238331 

115.412877 

131.913842 

44 

45 

71.892710 

81.516131 

92.719861 \ 

105.781673 

121.029392 

138.849965 

45 

46 

74.330564 

84.554034 

96.501457; 

110.484031 

126.870568 

146.098214 

46 

47 

76.817176 

87.667885 

100.396501 

115.350973 

132.945300 

153.672633 

47 

48 

79.353519 

90.859582 

104.408396 

120.388257 

139.263206 

161.587902 

48  1 

49 

81.940590 

94.131072 

108.540648  \ 

125.601846 

145.833734 

169.859357 

49 

50 

84.579401 

97.484349 

112.796867 i 

130.997910 

152.667084 

178.503028 

50 

Formula,  Amount 


—  (1  +  ^')"  — 1 


l  +  (l  +  0+...  +  (l-fi)«-i. 


TABLE    XXII.  ai"? 

THE  AMOUNT  OF  $1  ANNUITY  AT  THE  END  OF  ANY  NUMBER  OF  YEARS. 


OB 

5 

6 

7 

8 

9 

10 

d 

« 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent, 

1 

1.000000 

1.000000 

1.000000 

1.000000 

1.000000 

1.000000 

1 

2 

2.050000 

2.060000 

2.070000 

2.080000 

2.090000 

2.100000 

2 

3 

3.152500 

3.183600 

3.214900 

3.246400 

3.278100 

3.310000 

3 

4 

4.310125 

4.374616 

4.439943 

4.506112 

4.573129 

4.641000 

4 

5 

5.525631 

5.637093 

5.750739 

5.866601 

5.984711 

6.105100 

5 

6 

G.801913 

6.975319 

7.153291 

7.335929 

7.523335 

7.715610 

6 

7 

8.142008 

8.393838 

8.654021 

8.922803 

9.200435 

9.487171 

7 

8 

9.549109 

9.897468 

10.259803 

10.636628 

11.028474 

11.436888 

8 

9 

11.026564 

11.491316 

11.977989  1 

12.487558 

13.021036 

13.579477 

9 

10 

12.577893 

13.180795 

13.816448 

1 

14.486562 

15.192930 

16.937425 

10 

1 
11 

14.206787 

14.971643 

15,783599 

16.645487 

17.560293 

18.631167 

11 

,   12 

15.917127 

16.869941 

17.888451 

18.977126 

20.140720 

21.384284 

12 

13 

17.712983 

18.882138 

20.140643 

21.495297. 

22.953385 

24.622712 

13 

i  14 

19.598632 

21.015066 

22.550488 

24.214920 

26.019189 

27.974983 

14 

15 

21.578564 

23.275970 

25.129022 

27.152114 

29.360916 

31.772482 

15 

16 

23.657492 

25.672528 

27.888054 

30.324283 

33.003399 

35.949730 

16 

17 

25.840366 

28.212880 

30.840217 

33.750226 

36.973705 

40.544703 

17 

i  18 

28.132385 

30.905653 

33.999033 

37.450244 

41.301338 

45.599173 

18 

19 

30.539004 

33.759992 

37.378965 

41.446263 

46.018458 

61.169090 

19 

20 

33.065954 

36.785591 

40.995492 

45.761964 

61.160120 

57.274999 

20 

21 

35.719252 

39.992727 

44.865177 

50.422921 

56.764530 

64.002499 

21 

22 

38.505214 

43.392290 

49.005739 

!  55.456755 

62.873338 

71.402749 

22 

23 

41.430475 

46.995828 

53.436141 

60.893296 

69.531939 

79.543024 

23 

24 

44.501999 

50.815577 

68.176671 

66.764759 

76.789813 

88.497327 

24 

25 

47.727099 

54.864512 

63.249038 

1  73.105940 

84.700896 

98.347059 

25 

.26 

51.113454 

59.156383 

68.676470 

79.954415 

93.323977 

109.181766 

26 

27 

54.669126 

63.705766 

74.483823 

87.350768 

102.723135 

121.099942 

27 

'  28 

58.402583 

68.528112 

80.697691 

1  95.338830 

112.968217 

134.209936 

28 

29 

62.322712 

73.639798 

87.346529 

103.965936 

124.135356 

148.630930 

29 

30 

66.438848 

79.058186 

94.460786 

113.283211 

136.307539 

164.494023 

30 

31 

70.760790 

84.801677 

102.073041 

123.345868 

149.575217 

181.943426 

31 

32 

75.298829 

90.889778 

110.218154 

134.213537 

164.036987 

201.137767 

32 

33 

80.063771 

97.343165 

118.933425 

i 145.950620 

179.800315 

222.251644 

33 

34 

85.066959 

104.183755 

128.258765 

158.626670 

196.982344 

245.476699 

34 

35 

90.320307 

111.434780 

138.236878 

172.316804 

215.710755 

271.024368 

35 

36 

95.836323 

119.120867 

148.913460 

187.102148 

236.124723 

299.126805 

36 

37 

101.628139 

127.268119 

160.337402 

203.070320 

258.375948 

330.039486 

37 

38 

107.709546 

135.904206 

172.561020 

220.315945 

282.629783 

364.043434 

38 

39 

114.095023 

145.058458 

185.640292 

238.941221 

309.066463 

401.447778 

39 

i  40, 

120.799774 

154.761966 

199.635112 

259.056519 

337.882445 

442.592656 

40 

41 

127.839763 

165.047684 

214.609570 

280.781040 

369.291865 

487.851811 

41 

42 

135.231751 

175.950545 

230.632240 

304.243523 

403.528133 

637.636992 

42 

43 

142.993339 

187.507577 

247.776496 

329.583005 

440.845665 

692.400692 

43 

.  44 

151.14.3006 

199.758032 

266.120851 

356.949646 

481.621775 

652.640761 

44 

45 

159.700156 

212.743514 

285.749311 

386.505617 

525.858734 

718.904837 

45  : 

46 

168.685164 

226.508125 

306.751763 

418.426067 

574.186021 

791.796321 

46 

47 

178.119422 

241.098612 

329.224386 

452.900152 

626.862762 

871.974863 

47 

48 

188.025393 

256.564529 

353.270093 

490.132164 

684.280411 

960.172338 

48 

49 

198.426663 

272.958401 

378.999000 

530.342737 

746.865648 

1057.189672 

49 

50 

209.347996 

290.335905 

406.528929 

573.770156 

815.083556 

1163.908529 

50 

218  TABLE    XXII. 

THE  AMOUNT  OF  SI  ANNUITY  AT  THE  END  OF  ANY  NUMBER  OF  YEARS. 


51 
52 
53 
54 
55 

56 
57 
58 
59 
60 

61 
62 
63 
64 
65 


2 
Per  Cent. 


87.270989 
90.016409 
92.816737 
95.673072 
98.586534 

101.558264 
104.589430 
107.681218 
110.834843 
114.051539 

117.332570 

120.679222 
124.092806 
127.574662 
131.126155 


Per  Cent. 


661134.748679 

67  '  138.443652 

68  '  142.212525 


69 
70 

71 
72 
73 

74 
75 

76 

77 
78 
79 
80 

81 
82 
83 
84 
85 

86 
87 
88 
89 
90 

91 
92 
93 
94 
95 

96 
97 
98 
99 
100 


146.056776 
149.977911 

153.977469 
158.057019 
162.218159 
166.462522 
170.791773 

175.207608 
179.711760 
184.305996 
188.992115 
193.771958 

198.647397 
203.620345 
208.692752 
213.866607 
219.143939 

224.526818 
230.017354 
235.617701 
241.330055 
247.156656 

253.099789 
259.161785 
265.345021 
271.651921 
278.084960 

284.646659 
291.339592 
298.166384 
305.129712 
312.232306 


100.921458 
104.444494 
108.055606 
111.756996 
115.550921 

119.439694 
123.425687 
127.511329 
131.699112 
135.991590 

140.391380 
144.901164 
149.523693 
154.261780 
159.118330 

164.096289 
169.198696 
174.428663 
179.789380 
185.284114 

190.916217 
196.689123 
202.600351 

208.671509 
214.888297 

221.260504 
227.792017 

234.486818 
241.348988 
248.382713 

255.592280 
262.982087 
270.556640 
278.320556 

286.278570 

294.435534 
302.796422 
311.366333 
320.150491 
329. 154253 

338.383110 
347.842687 
357.538755 
367.477223 
377.664154 

388.105758 
398.808402 
409.778612 
421.023077 
432.5486541 


3 
Per  Cent. 


117.180773 
121.696197 
126.347082 
131.137495 
136.071620 

141.153768 
146.388381 
151.780033 
157.333434 
163.053437 

168.945040 
175.013391 
181.263793 

187.701707 
194.332758 

201.162741 
208.197623 
215.443551 
222.900858 
230.594004 

238.511886 
246.067242 
255.067259 
263.719277 
272.630856 

281.809781 
291.264075 
301.001997 
311.032057 
321.363019 

332.003909 
342.964026 
354.252947 
365.880536 
377.850952 

390.192000 
402.898440 
415.985393 
429.404955 
443.348904 

457.049371 
472.378852 
487.550217 
503.170724 
519.272020 

535.850180 
552.925092 
570.513403 
588.628867 
607.287733 


Per  Cent. 


136.582837 
142.363236 
148.345950 
154.538058 
160.946890 

107.580031 
174.445332 
181.550919 
188.905201 
190.516883 

204.394974 

212.548798 
220.988006 
229.722586 
238.702876 

248.119577 
257.803702 
267.826894 
278.200835 
288.937865 

300.050690 
311.552464 
323.456800 

335.777788 
348.530011 

361.728561 
375.389061 
389.527678 
404.161147 
419.306787 

434,982524 
451.206913 
467.999155 
485.379125 
503.367394 

521.985253 
541.254737 
561.198653 
581.840606 
603.205027 

625.317203 
648.203305 
671.890421 
696.406585 

721.780816 

748.043144 
775.224654 
808.357517 
832.475030 
862.611657 


4 
Per  Cent. 


159.773767 
167.164718 
174.851306 
182.845359 
191.159173 

199.805540 

208.797762 
218.149072 
227.875059 
237.990085 

248.510313 
259.450725 
270.828754 
282.001904 
294.908380 

307.707110 
321.077800 
334.920912 
349.317749 
364.290459 

379.862077 
396.056500 
412.898823 
430.414770 
448.631367 

467.576621 
487.279086 
507.770873 
529.081708 
551.244977 

574.294770 
598.266567 
623.197230 
649.125119 
676.090123 


Per  Cent. 


704.133728 
733.299078 
763.63104] 
795.176282 
827.983334 

862.102667 
897.586774 
934.490244 
972.869854 
1012.784648 


187.535665 
196.974769 
206.838634 
217.146373 
227.917959 

239.174268 
250.937110 
263.229279 
276.074597 
289.497954 

303.525362 
318.184003 
333.502283 
349.509886 
366.237831 

383.718533 
401.985867 
421.075231 
441.023617 

461.869680 

483.653815 
506.4182371 
530.207057! 
555.066375 
581.044362 

608.191358 
636.559909 
066.205168 
697.184400 
729.557699 

763.387795 
798.740246 
835.683557 
874.289317 
914.632336 


956.790791 
1000.846377 
1046.884464 
1094.994265 
1145.269007 

1197.806112 
1252.707387 
1310.079219 
1370.032784 
1432.684259 


1054.296034J1498. 155051 
1097.467876:1566.572028 
1142.3665911638.067770 
1189.06125411712.780819 
1237. 623705J1790. 855956 


51 
52 
53 
54 
55 

56 
57 
58 
59 
60 

61 
62 
63 
64 
65 

66 
67 
68 
69 
70 

71 
72 
73 

74 
75 

76 
77 
78 
79 
80 

81 
82 
83 
84 
85 

86 
87 
88, 
89 

90  I 

91  I 
92 
93 
94 
95 

96 
97 
98 
99 
100 


TABLE    XXII.  219 

THE  AMOUNT  OF  |1  'ANNUITY  AT  THE  END  OF  ANY  NUMBER  OP  YEARS, 


.- 

5 

6 

7 

8 

10 

tS 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

51 

220.815396 

308.756059 

435.985955 

620.671769 

1281.299382 

51 

52 

232.856165 

328.281422 

467.504971 

671.325510 

1410.429320 

52 

53 

245.498974 

348.978308 

501.230319" 

726.031551 

\      1552.472252 

63 

54 

258.773922 

370.917006 

537.316442 

785.114075 

1708.719477 

54 

55 

272.712618 

394.172027 

575.928593 

848.923201 

1880.591425 

55 

56 

287.348249 

418.822348 

617.243594 

917.837058 

2069.650567 

56 

57 

302.715662 

444.951689 

661.450646 

1   992.264022 

2277.615624 

57 

58 

318.851445 

472.648790 

708.752191 

1072.645144 

2506.377186 

58 

59 

335.794017 

502.007718 

759.364844 

1159.456755 

2758.014905 

59 

60 

353.583718 

533.128181 

813.520383 

1253.213296 

3034.816395 

60 

61 

372.262904 

566.115872 

871.466810 

1354.470360 

3339.298035 

61 

62 

391.876049 

601.082824 

933.469487 

1463.827988 

3674.227838 

62 

63 

412.469851 

638.147793 

999.812351 

1581.934227 

4042.650622 

63 

64 

434.093344 

677.436661 

1070.799216 

1709.488966 

4447.915685 

64 

65 

456.798011 

719.082861 

1146.755161 

1847.248083 

4893.707253 

65 

66 

480.637912 

763.227832 

1228.028022 

1996.027929 

5384.077978 

66 

67 

505.669807 

810.021502 

1,314.989983 

2156.710164 

5923.485776 

67 

68 

531.953298 

859.622792 

1408.039282 

2330.246977 

6516.834354 

68 

69 

559.550963 

912.200160 

1507.602032 

2517.666735 

7169.517789 

69 

70 

588.528511 

967.932170 

1614.134174 

2720.080074 

7887.469568 

70 

71 

618.954936 

1027.008100 

1728.123566 

2938.686480 

8677.216525 

71 

72 

650.902683 

1089.628586 

1850.092216 

3174.781398 

9545.938177 

72 

73 

684.447817 

1156.006301 

1980.598671 

3429.763910 

10501.531995 

73 

74 

719.670208 

1226.366679 

2120.240578 

3705.145023 

11552.685195 

74 

75 

756.653719 

1300.948680 

2269.657419 

4002.556624 

12708.953714 

75 

76 

795.486404 

1380.005601 

2429.533438 

4323.761154 

13980.849085 

76 

77 

836.260725 

1463.805937 

2600.600779 

4670.662047 

15379.933994 

77 

78 

879.073761 

1552.634293 

2783.642833 

5045.315011 

16918.927393 

78 

79 

924.027449 

1646.792350 

2979.497831 

5449.940211 

18611.820133 

79 

80 

971.228821 

1746.599891 

3189.062680 

5886.935428 

20474.002146 

80 

81 

1020.790262 

1852.395885 

3413.297067 

6358.890263 

22522.402360 

81 

82 

1072.829776 

1964.539638 

3653.227862 

6868.601484 

24775.642596 

82 

83 

1127.471264 

2083.412016 

3909.953812 

7419.089602 

27254.206856 

83 

84 

1184.844828 

2209.416737 

4184.650579 

8013.616770 

29980.627542 

84 

85 

1245.087069 

2342.981741 

4478.576120 

8655.706112 

32979.690296 

85 

86 

1308.341422 

2484.560646 

4793.076448 

9349.162601 

36278.659326 

86 

87 

1374.758493 

2634.634285 

5129.591799 

10098.095609 

39907.525258 

87 

88 

1444.496418 

2793.712342 

5489.663225 

10906.943258 

43899.277784 

881 

"89 

1517.721239 

2962.335082 

5874.939651 

11780.498718 

48290.205562 

89 

90 

1594.607301 

3141.075187 

6287.185427 

12723.938616 

53120.226119 

90 

91 

1675.337666 

3330.539698 

6728.288407 

13742.853705 

58433.248730 

91 

92 

1760.104549 

3531.372080 

7200.268595 

14843.282002 

64277.573603 

92 

93 

1849.109777 

3744  254405 

7705.287397 

16031.744562 

70706.330964 

93 

94 

1942.565266 

3969.909669 

8245.657515 

17315.284127 

77777.964060 

94 

95 

2040.693529 

4209.104250 

8823.853541 

18701.506857 

85556.760466 

95 

96 

2143.728205 

4462.650505 

9442.523288 

20198.627405 

94113.436513 

96 

97 

2251.914616 

4731.409535 

10104.499919 

21815.517598 

103525.780164 

97 

98 

2365.510346 

5016.294107 

10812.814913 

23561.759006 

113879.358180 

98 

99 

2484.785864 

5318.271753 

11570.711957 

25447.699726 

125268.293998 

99 

100 

2610.025157 

5638.368059 

12381.661794 

27484.515704 

137796.123398 

100 

220 


TABLE     XXIII. 


THE  PRESENT  VALUE  OF  $1  PER  ANNUM  FOR  ANY  NUMBER  OF  YEARS. 


e 

2 

2i 

3 

H 

4 

H 

g 

tH 

Per  Cent, 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

1 

1 

.980392 

.975610 

.970874 

.966184 

.961538 

.956938 

2  1  1.941561 

1.927424 

1.913470 

1.899694 

1.886095 

1.872668 

2 

3 

2.883883 

2.856024 

2.828611 

2.801637 

2.775091 

2.748964 

3 

4 

3.807729 

3.761974 

3.717098 

3.673079 

3.629895 

3.587526 

4 

5 

4.713460 

4.645828 

4.579707 

4.515052 

4.451822 

4.389977 

5 

6 

5.601431 

5.508125 

5.417191 

5.328553 

5.242137 

5.157872 

6 

7 

6.471991 

6.349391 

6.230283 

6.114544 

6.002055 

5.892701 

7 

8 

7.325481 

7.170137 

7.019692 

6.873956 

6.732745 

6.595886 

8 

9 

8.162237 

7.970866 

7.786109 

7.607687 

r.  435332 

7.268790 

9 

10 

8.982585 

8.752064 

8.530203 

8.316605 

8.110896 

7.912718 

10 

11 

9.786848 

9.514209 

9.252624 

9.001551 

8.760477 

8.528917 

11 

12 

10.575341 

10.257765 

9.054004 

9.663334 

9.385074 

9.118581 

12 

13 

11.348374 

10.983185 

10.634955 

10.302738 

9.985648 

9.682852 

13 

14 

12.106249 

11.690912 

11.296073 

10.920520 

10.563123 

10.222825 

14 

15 

12.849264 

12.381378 

11.937935 

11.517411 

11.118387 

10.739546 

15 

16 

13.577709 

13.055003 

12.561102 

12.094117 

11.652296 

11.234015 

16 

17 

14.291872 

13.712198 

13.166118 

12.651321 

12.165669 

11.707191 

17 

18 

14.992031 

14.353364 

13.753513 

13.189682 

12.659297 

12.159992 

18 

19 

15.678462 

14.978891 

14.323799 

13.709837 

13.133939 

12.593294 

19 

20 

16.351433 

15.589162 

14.877475 

14.212403 

13.590326 

13.007936 

20 

21 

17.011209 

16.184549 

15.415024 

14.697974 

14.029160 

13.404724 

21 

22 

17.658048 

16.765413 

15.936917 

15.167125 

14.451115 

13.784425 

22 

23 

18.292204 

17.332111 

16.443608 

15.620410 

14.856842 

14.147775 

23 

24 

18.913926 

17.884986 

16.935542 

16.058368 

15.246963 

14.495478 

24 

25 

19.523456 

18.424376 

17.413148 

16.481515 

15.622080 

14.828209 

25 

26 

20.121036 

18.950611 

17.876842 

16.890352 

15.982769 

15.146611 

26 

27 

20.706898 

19.464011 

18.327031 

17.285365 

16.329686 

15.451303 

27 

28 

21.281272 

19.964889 

18.764108 

17.667019 

16.663063 

15.742874 

28 

29 

21.844385 

20.453550 

19.188455 

18.035767 

16.983715 

16.021889 

29 

30 

22.396456 

20.930293 

19.600441 

18.392045 

17.292033 

16.288889 

30 

31 

22.937702 

21.395407 

20.000428 

18.736276 

17.588494 

16.544391 

31 

32 

23.468335 

21.849178 

20.388766 

19.068865 

17.873552 

16.788891 

32 

33 

23.988564 

22.291881 

20.765792 

19.390208 

18.147646 

17.022862 

33 

34 

24.498592 

22.723786 

21.131837 

19.700684 

18.411198 

17.246758 

34 

36 

24.998619 

23.145157 

21.487220 

20.000661 

18.664613 

17.461012 

35 

36 

25.488842 

23.556251 

21.832252 

20.290494 

18.908282 

17.666041 

36 

37 

25.969453 

23.957318 

22.167235 

20.570525 

19.142579 

17.862240 

37 

38 

26.440641 

24.348603 

22.492462 

20.841087 

19.367864 

18.049990 

38 

39 

26.902589 

24.730344 

22.808215 

21.102500 

19.584485 

18.229656 

39 

40 

27.355479 

25.102775 

23.114772 

21.355072 

19.792774 

18.401584 

40 

41 

27.799489 

25.466122 

23.412400 

21.599104 

19.993052 

18.566109 

41 

42 

28.234794 

25.820607 

23.701359 

21.834883 

20.185627 

18.723550 

42 

43 

28.661562 

26.166446 

23.981902 

22.062689 

20.370795 

18.874210 

43 

44 

29.079963 

26.503849 

24.254274 

22.282791 

20.548841 

19.018383 

44 

45 

29.490160 

26.833024 

24.518713 

22.495450 

20.720040 

19.156347 

45 

46 

29.892314 

27.154170 

24.775449 

22.700918 

20.884654 

19.288371 

46 

47 

30.286582 

27.467483 

25.024708 

22.899438 

21.042936 

19.414709 

47 

48 

30.673120 

27.773154 

25.266707 

23.091244 

21.195131 

19.535607 

48 

49 

31.052078 

28.071369 

25.501657 

23.276564 

21.341472 

19.651298 

49 

50 

31.423606 

28.362312 

25.729764 

23.455618 

21.482185 

19.762008 

50 

FOEMULA.  I 

'resent  Valuf 

>  =  i-<i+ 

i)-"' 1—v 

n 

TABLE    XXIII. 


221 


THE  PRESENT  VALUE  OF  $1  PER  ANNUM  FOR  ANY  NUMBER  OF  YEARS, 


1 

5 

6 

7 

8 

9 

10 

§ 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

sS 

.952381 

.943396 

.934579 

.925926 

.917431 

.909091 

1 

2 

1.859410 

1.833393 

1.808018 

1.783265 

1.759111 

1.735537 

2 

3 

2.723248 

2.673012 

2.624316 

2.577097 

2.531295 

2.486852 

3  i 

4 

3.545951 

3.465106 

3.387211 

3.312127 

3.239720 

3.169865 

4 ; 

5 

4.329477 

4.212364 

4.100197 

3.992710 

3.889651 

3.790787 

5 

6 

5.075692 

4.917324 

4.766540 

4.622880 

4.485919 

4.355261 

6 

7 

5.786373 

5.582381 

5.389289 

5.206370 

5.032953 

4.868419 

7 

8 

6.463213 

6.209794 

5.971299 

5.746639 

5.534819 

5.334926 

8 

9 

7.107822 

6.801692 

6.515232 

6.246888 

5.995247 

5.759024 

9 

10 

7.721735 

7.360087 

7.023582 

6.710081 

6.417658 

6.144567 

10 

11 

8.306414 

7.886875 

7.498674 

7.138964 

6.805191 

6.495061 

11 

12 

8  863252 

8.383844 

7.942686 

7.536078 

7.160725 

6.813692 

12 

13 

9.393573 

8  852683 

8.357651 

7.903776 

7.486904 

7.103356 

13 

14 

9.898641 

9.294984 

8.745468 

8.244237 

7.786150 

7.366687 

14 

15 

10.379658 

9.712249 

9.107914 

8.559479 

8.060688 

7.606080 

15 

16 

10.837770 

10.105895 

9.446649 

8.-851369 

8.312558 

7.823709 

16 

17 

11.274066 

10.477260 

9.763223 

9.121638 

8.543631 

8.021553 

17 

18 

11.689587 

10.827603 

10.059087 

9.371887 

8.755625 

8.201412 

18 

19 

12.085321 

11.158116 

10.335595 

9.603599 

8.950115 

8.364920 

19 

20 

12.462210 

11.469921 

10.594014 

9.818147 

9.128546 

8.513564 

20 

21 

12.821153 

11.764077 

10.835527 

1  a.  016803 

9.292244 

8.648694 

21 

22 

13.163003 

12.041582 

11.061241 

10.200744 

9.442425 

8.771540 

22 

23 

13.488574 

12.303379 

11.272187 

10.371059 

9.580207 

8.883218 

23 

24 

13.798642 

12.550358 

11.469334 

10.528758 

9.706612 

8.984744 

24 

25 

14.093945 

12.783356 

11.653583 

10.674776 

9.822580 

9.077040 

25 

26 

14.375185 

13.003166 

11.825779 

10.809978 

9.928972 

9.160945 

26 

27 

14.643034 

13.210534 

11.986709 

10.935165 

10.026580 

9.237223 

27 

28 

14.898127 

13.406164 

12.137111 

11.051078 

10.116128 

9.306567  . 

28 

29 

15.141074 

13.590721 

12.277674 

11.158406 

10.198283 

9.369606 

29 

30 

15.372451 

13.764831 

12.409041 

11.257783 

10.273654 

9.426914 

30 

31 

15.592811 

13.929086 

12.531814 

11.349799 

10.342802 

9.479013 

31 

32 

15.802677 

14.084043 

12.646555 

11.434999 

10.406240 

9.526376 

32 

33 

16.002549 

14.230230 

12.753790 

11.513888 

10.464441 

9.569432 

33 

34 

16.192904 

14.368141 

12.854009  1 

11.586934 

10.517835 

9.608575 

34 

35 

16.374194 

14.498246 

12.947672  i 

j 

11.654568 

10.566821 

9.644159 

35 

36 

16.546852 

14.620987 

13.035208  i 

11.717193 

10.611763 

9.676508 

36 

37 

16.711287 

14.736780 

13.117017 

11.775179 

10.652993 

9.705917 

37 

38 

16.867893 

14.846019 

13.193473 

11.828869 

10.690820 

9.732651 

38 

39 

17.017041 

14.949075 

13.264928  ' 

11.878582 

10.725523 

9.756956 

39 

40 

17.159086 

15.046297 

13.331709 

11.924613 

10.757360 

9.779051 

40 

41 

17.294368 

15.138016 

13.394120 

11.967235 

10.786569 

9.799137 

41 

42 

17.423208 

15.224543 

13.452449 

12.006699 

10.813366 

9.817397 

42 

43 

17.545912 

15.306173 

13.506962 

12.043240 

10.837951 

9.833998 

43 

44 

17.662773 

15.383182 

13.557908  1 

12.077074 

10.860505 

9.849089 

44 

45 

17.774070 

15.455832 

13.605522 

12.108402 

10.881197 

9.862808 

45 

46 

17.880067 

15.524370 

13.650020 

12.137409 

10.900181 

9.875280 

46 

47 

17.981016 

15.589028 

13.691608 

12.164267 

10.917597 

9.886618 

47 

48 

18.077158 

15.650027 

13.730474 

12.189136 

10.933575 

9.896926 

48 

49 

18.168722 

15.707572 

13.766799 

12.212163 

10.948234 

9.906296 

49 

50 

18.255925 

15.761861 

13.800746 

12  233485 

10.961683 

9.914814 

50 

333  TABLE     XXIII. 

THE  PRESENT  VALUE  OF  $1  PER  ANNUM  FOR  ANT  NUMBER  OF  YEARS. 


TABLE     XXIII.  333 

THE  PRESENT  VALUE  OF  $1  PER  ANNUM  FOR  ANY  NUMBER  OF  YEARS. 


2 

5 

6 

7 

s 

9 

10 

i 

51 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

^ 

18.338977 

15.813076 

13.832473 

12.253227 

10.974021 

9.922559 

51 

52 

18.418073 

15.861393 

13.862124 

12.271506 

10.985340 

9.929599 

52 

53 

18.493403 

15.906974 

13.889836 

12.288432 

10.995725 

9.935999 

53 

54 

18.565146 

15.949976 

13.915735 

12.304103 

11.005252 

9.941817 

54 

55 

18.633472 

15.990543 

13.939939 

12.318614 

11.013993 

9.947107 

55 

56 

18.698545 

16.028814 

13.962560 

12.332050 

11.022012 

9.951915 

56 

57 

18.760519 

16.064919 

13.983701 

12.344491 

11.029369 

9.956286 

57 

58 

18.819542 

16.098980 

14.003459 

12.356010 

11.036118 

9.960260 

58 

59 

18.875754 

16.131113 

14.021924 

12.366676 

11.042310 

9.963873 

59 

60 

18.929290 

16.161428 

14.039181 

12.376552 

11.047991 

9.967157 

60 

61 

18.980276 

16.190026 

14.055309 

12.385696 

11.053203 

9.970143 

61 

62 

19.028834 

16.217006 

14.070383 

12.394163 

11.057984 

9.972857 

62 

63 

19.075080 

16.242458 

14.084470 

12.402003 

11.062371 

9.975325 

63 

64 

19.119124 

16.266470 

14.097635 

12.409262 

11.066395 

9.977568 

64 

65 

19.161070 

16.289123 

14.109940 

12.415983 

11.070087 

9.979607 

65 

66 

19.201019 

16.310493 

14.121439 

12.422207 

11.073475 

9.981461 

66 

67 

19.239066 

16.330654 

14.132186 

12.42796-9 

11.076582 

9.983147 

67 

68 

19.275301. 

16.349673 

14.]  42230 

:  12.433305 

11.079433 

9.984679 

68 

69 

19.309810 

16.367617 

14.151617 

12.438245 

11.082049 

9.986071 

69 

70 

19.342677 

16.384544 

14.160389 

1  12.442820 

11.084449 

9.987338 

70 

71 

19.373978 

16.400513 

14.168588 

12.447055 

11.086650 

9.988489 

71 

72 

19.403788 

16.415578 

14.176251 

12.450977 

11.088670 

9.989535 

72 

73 

19.432179 

16.429791 

14.183412 

12.454608 

11.090523 

9.990487 

73 

74 

19.459218 

16.443199 

14.190104  i 

12.457971 

11.092223 

9.991351 

74 

75 

19.484970 

16.455848 

14.196359 

12.461084 

11.093782 

9.992138 

75 

76 

19.509495 

16.467781 

14.202205 

12.463967 

11.095213 

9.992852 

76 

77 

19."532853 

16.479039 

14.207668 

12.466636 

11.096526 

9.993502 

77 

78 

19.555098 

16.489659 

14.212774 

12.469107 

11.097730 

9.994093 

78 

79 

19.576284 

16.499679 

14.217546 

12.471396 

11.098835 

9.994630 

79 

80 

19.596460 

16.509131 

14.222005 

12.473514 

11.099849 

9.995118 

80 

81 

19.615677 

16.518048 

14.226173 

12.475476 

11.100778 

9.995562 

81 

82 

19.633978 

16.526460 

14.230069 

12.477293 

11.101632 

9.995965 

82 

83 

19.651407 

16.534396 

14.233709 

!  12.478975 

11.102414 

9.996332 

83 

84 

19.668007 

16.541883 

14.237111 

12.480532 

11.103132 

9.990666 

84 

85 

19.683816 

16.548947 

14.240291 

:  12.481974 

11.103791 

9.996969 

85 

86 

19.698873 

16.555610 

14.243262 

12.483310 

11.104396 

9.997244 

86 

87 

19.713212 

16.561896 

14.246040 

12.484546 

11.104950 

9.997495 

87 

88 

19.726869 

16.567827 

14.248635 

12.485691 

11.105459 

9.997723 

88 

89 

19.739875 

16.573421 

14.251061 

12.486751 

U.  105926 

9.997930 

89 

90 

19.752262 

16.578099 

14.253328 

12.487732 

11.106354 

9.998118 

90 

91 

19.764059 

16.583679 

14.255447 

12.488641 

11.106746 

9.998289 

91 

92 

19.775294 

16.588376 

14.257427 

12.489482 

11.107107 

9.998444 

92 

93 

19.785994 

16.592808 

14.259277 

12.490261 

11.107438 

9.998586 

93 

94 

19.796185 

16.596988 

14.261007 

12.490983 

11.107741 

9.998714 

94 

95 

19.805891 

16.600932 

14.262623 

12.491651 

11.108019 

9.998831 

95 

96 

19.815134 

16.604653 

14.264134 

12.492269 

11.108274 

9.998938- 

96 

97 

19.823937 

16.608163 

14.265546 

12.492842 

11.108509 

9.999034 

97 

98 

19.832321 

16.611475 

14.266865 

12.493372 

11.108724 

9.999122 

98 

99 

19.840306 

16.614599 

14.268098 

12.493863 

11.108921 

9.999202 

99 

100 

Perp. 

19.847910 

16.617546 

14.269251 

12.494318 

11.109102 

9.999274 

100 

20.000000 

16.666667 

14.285714 

12.500000 

11.111111 

10.000000 

Perp. 

224 


TABLE     XXIV. 


THE  ANNUITY  WHICH  $1 

WILL  PURCHASE  FOR  . 

INT  NUMBER  OF  YEARS. 

2 

2| 

3 

3i                   4 

4.1 

i  '; 

^ 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

""       1 

1 

1.02000000 

1.02500000 

1.03000000 

1.03500000 

1.04000000 

1.04500000 

1   i 

2 

0.51504950 

0.51882716 

0.52261084 

0.52640049 

0.53019608 

0.53399756 

2  i 

3 

.34675467 

.35013717 

.35353036 

.35693418 

.36034854 

.36377336 

3 

.4 

.26262375 

.26581788 

.26902705 

.27225114 

-.27549005 

.27874365 

4 

5 

.21215839 

.21524686 

.21835457 

.22148137 

.22462711 

.22779164 

5 

6 

0.17852581 

0.18154997 

0.18459750 

0.18766821 

0.19076190 

0.19387839 

6 

7 

.15451195 

.15749543 

.16050635 

.16354449 

.16660961 

.16970147 

7 

8 

.13650980 

.13946735 

.14245639 

.14547665  .14852783 

.15160965  '  8  1 

9 

.12251544 

.12545689 

.12843386 

.13144601  .13449299 

.13757447 

9  1 

10 

.11132653 

.11425876 

.11723051 

.12024137  !  .12329094 

.12637882 

10  1 

11 

0.10217794 

0.10510596 

0.10807745 

0.11109197 

0.11414904 

0.11724818 

11 

12 

.09455960 

.09748713 

•10046209 

.10348395 

.10655217 

.10966619 

12 

13 

.08811835 

.09104827 

.09402954 

.09706157 

.10014373 

.10327535 

13 

14 

.08260197 

.08553653 

.08852634 

.09157073 

.09466897 

.09782032 

14 

15 

.07782547 

.08076648 

.08376658 

.08682507 

.08994110 

.09311381 

15 

16 

0.07365013 

0.07659899 

0.07961085 

0.08268483 

0.08582000 

0.08901537 

16 

17 

.06996984 

.07292777 

.07595253 

.07904313 

.08219852 

.08541758 

17 

18 

.06670210 

.06967008 

.07270870 

.07581684 

.07899333 

..08223690 

18 

19 

.06378177 

.06676062 

.06981388 

.07294033 

.07613862 

.07940734 

19 

20 

.06115672 

.06414713 

.06721571 

.07036108 

.07358175 

.07687614 

20 

21 

0.05878477 

0.06178733 

0.06487178 

0.06803659 

0.07128011 

0.07460057 

21 

22 

.05663140 

.05964660 

.06274739 

.06593207 

.06919881 

.07254565 

22 

23 

.05466810 

.05769638 

.06081390 

.06401880 

.06730906 

.07068249 

23 

24 

.05287110 

.05591282 

.05904742 

.06227283 

.06558683 

.06898703 

24 

25 

.05122044 

.05427592 

.05742787 

.06067404 

.06401196 

.06743903 

25 

26 

0.04969923 

0.05276875 

0.05593829  ' 

0.05920540 

0.06256738 

0.06602137 

26 

27 

.04829309 

.05137687 

.05456421  ^ 

.05785241 

.06123854 

.06471949 

27 

28 

.04698967 

.05008793 

.05329323  ' 

.05660265 

.06001298 

.06352081 

28 

29 

.04577835 

.04889127 

,05211467 

.05544538 

.05887993 

.06241461. 

29 

30 

.04464992 

.04777764 

.05101926  ' 

: 

.05437133 

.05783010 

.06139154 

30 

31 

0.04359635 

0.04673900 

0.04999893 

0.05337240 

0.05685535 

0.06044345 

31 

32 

.04261061 

.04576831 

.04904662 

!  .05244150 

.05594859 

.05956320 

32 

33 

.04168653 

.04485938 

.04815612 

.05157242 

.05510357 

.05874453 

33 

34 

.04081867 

.04400675 

.04732196  , 

.05075966 

.05431477 

.05798191 

34 

35 

.04000221 

.04320553 

.04653929 

.04999835 

.05357732 

.05727045 

35 

36 

0.03923285 

0.04245158 

0.04580379 

0.04928416 

0.05288688 

0.05660578 

36 

37 

.03850678 

.04174090 

.04511162 

.04861325 

.05223956 

.05598402 

37 

38 

.03782057 

.04107012 

.04445934 

.04798214 

.05163192 

.05540169 

38 

39 

.03717114 

.04043615 

.04384385 

1  .04738775 

.05106083 

.05485567 

39 

40 

.03655575 

.03983623 

.04326238 

.04682728 

.05052349 

.05434315 

40 

41 

0.03597188 

0.03926786 

0.04271241 

0.04629822 

0.05001738 

0.05386158 

41 

42 

.03541729 

.03872876 

.04219168 

.04579828 

.04954020 

.05340868 

42 

43 

.03488993 

.03821688 

.04169811 

.04532539 

.04908989 

.05298235 

43 

44 

.03438794 

.03773037 

.04122985 

.04487768 

.04866454 

.05258071 

44 

45 

.03390962 

.03726751 

.04078518 

.04445343 

.04826246 

.05220202 

45 

46 

0.03345342 

0.03682676 

0.04036254 

0.04405108 

0.04788205 

0.05184471 

46 

47 

.03301792 

.03640669 

.03996051 

.04366919 

.04752189 

.05150734 

47 

48 

.03260184 

.03600599 

.03957777 

.04330646 

.04718065 

.05118858 

48 

49 

.03220396 

.03562348 

.03921314 

.04296167 

.04685712 

.05088722 

49 

50 

.03182321 

.03525806 

.03886546 

.04263371 

1 

.04655020 

.05060215 

50 

Formula,  Annuity  := 


l_(l  +  t)-n       l_v« 


TABLE    XXIY. 


225 


THE  ANNUITY  WHICH  $1  WILL  PUB< 
\ 

:hase  for  any  number  op  tears. 

i 

5 

6 

7 

1     8 

9 

10 

i 

^ 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

^  Per  Cent. 

Per  Cent. 

^ 

1 

1.05000000 

1.06000000 

1.07000000 

1.08000000 

1.09000000 

1.10000000 

1 

2 

0.53780488 

0.54543689 

0.55309179 

,0.56076923 

0.56846890 

0.57619048 

2 

3 

.36720856 

.37410981 

.38105166 

.38803351 

.39505476 

.40211480 

3 

4 

.28201183 

.28859149 

.29522812 

.30192080 

.30866866 

.31547080 

4 

5 

.23097480 

.23739640 

.24389069 

.25045645 

.25709246 

.26379748 

5 

6 

0.19701747 

0.20336263 

0.20979580 

0.21631539 

0.22291978 

0.22960738 

6 

7 

.17281983 

.17913502 

.18555322 

.19207240 

.19869052 

.20540550 

7 

8 

.15472181 

.16103594 

.16746776 

.17401476 

.18067438 

.18744402 

8 

9 

.14069008 

.14702224 

.15348647 

.16007971 

.16679880 

.17364054 

9 

10 

.12950458 

.13586796 

.14237750 

.14902949 

.15582009 

.16274540 

10 

11 

0.12038889 

0.12679294 

0.13335690 

0. 14007634 

0.14694666 

0.15396314 

11 

12 

.11282541 

.11927703 

.12590199 

!  .13269502 

.13965066 

.14676332 

12 

13 

.10645577 

.11296011 

.11965085 

.12652181 

.13356656 

.14077852 

13 

14 

.10102397 

.10758491 

.11434494 

.12129685 

.12843317 

.13574622 

14 

15 

.09634229 

.10296276 

.10979462 

.11682954 

.12405888 

.13147378 

15 

16 

0.09226991 

0.09895214 

0.10585765 

0.11297687 

0.12029991 

0.12781662 

16 

17 

.08869914 

.09544480 

.10242519 

.10962943 

.11704625 

.12466413 

17 

18 

.08554622 

.09235654 

.09941260 

.10670210 

.11421229 

.12193022 

18 

19 

.08274501 

.08962086 

.09675302 

.10412763 

.11173041 

.11954687 

19 

20 

.08024259 

.08718456 

.09439293 

.10185221 

.10954648 

.11745962 

20 

21 

0.07799611 

0.08500455 

0. 09228900 

iO.  09983225 

0.10761663 

0.11562439 

21 

22 

.07597051 

.08304557 

.09040577 

.09803207 

.10590499 

.11400506 

22 

23 

.07413683 

.08127848 

.08871393  ! 

.09642217 

.10438188 

.11257181 

23 

24 

.07247090 

.07967901 

.08718902 

.09497796 

.10302256 

.11129978 

24 

25 

.07095246 

.07822672 

.08581052 

.09367878 

.10180625 

.11016807 

25 

26 

0.06956432 

0.07690435 

0.08456103 

0.09250713 

0.10071536 

0.10915904 

26 

27 

.06829186 

.07569717 

.08342573 

.09144810 

.09973491 

.10825764 

27 

28 

.06712253 

.07459255 

.08239193 

.09048890 

.09885205 

.10745101 

28 

29 

.06604551 

.07357961 

.08144865 

.08961854 

.09805572 

.10672807 

29 

30 

.06505144 

.07264891 

.08058640 

.08882743 

.09733635 

.10607925 

30 

31 

0.06413212 

0.07179222 

0.07979691 

0.08810728 

0.09668560 

0.10549621 

31 

32 

.06328042 

.07100234 

.07907292 

.08745081 

.09609619 

.10497172 

32 

33 

.06249004 

.07027293 

.07840807 

.08685163 

.09556173 

.10449941 

33 

34 

.06175549 

.06959843 

.07779674 

.08630411 

.09507660 

.10407371 

34 

35 

.06107171 

.06897386 

.07723396 

.08580326 

.09463584 

.10368971 

35 

36 

0.06043446 

0.06839483 

0.07671531 

0.08534467 

0.09423505 

0.10334306 

36 

37 

.05983979 

.06785743 

.07623685 

.08492440 

.09387033 

.10302994 

37 

38 

.05928423 

.06735812 

.07579505 

.08453894 

.09353820 

.10274692 

38 

39 

.05876462 

.06689380 

.07538676 

.08418513 

.09323555 

.10249098 

39 

40 

.05827816 

.06646153 

.07500914 

.08386016 

.09295961 

.10225941 

40 

41 

0.05782229 

0.06605886 

0.07465962 

0.08356149 

0.09270789 

0.10204980 

41 

42 

.05739471 

.06568342 

.07433591 

.08328684 

.09247814 

.10185999 

42 

43 

.05699333 

.06533312 

.07403590 

.08303414 

.09226837 

.10168805 

43 

44 

.05661625 

.06500606 

.07375769 

.08280152 

.09207675 

.10153224 

44 

45 

.05626173 

.06470050 

.07349957 

.08258728 

.09190165 

.10139100 

45 

46 

0.05592820 

0.06441485 

0.07325996 

0.08238991 

0.09174160 

0.10126295 

48 

47 

.05561421 

.06414768 

.07303744 

.08220799 

.09159525 

.10114682 

47 

48 

.05531843 

.06389766 

.07283070 

.08204027 

.09146139 

.10104148 

48 

49 

.05503965 

.06366356 

.07263853 

.08188557 

.09133893 

.10094590 

49 

50 

.05477674 

.06344429 

.07245985 

.08174286 

.09122687 

.10085917 

50 

\ 

Z26  TABLE    XXIY.  ■ 

THE  ANNUITY  WHICH  |1  WILL  PURCHASE  FOR  ANT  NUMBER  OF  TEARS. 


i 

3 

2i 

3 

H 

4 

^ 

S 

^ 

Per  Cent. 

Per  Cent.  ^ 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per.  Cent. 

H 

51 

0.03145856 

0.03490870 

0.03853382 

0.04333156 

0.04635885 

0.05033333 

51 

52 

.03110909 

.03457446 

.03821718 

.04202428 

.04598313 

.05007679  1  52 

53 

.03077392 

.03435449 

.03791471 

.04174100 

.04571915 

.04983469  i  53 

54 

.03045236  .03394799 

.03762558 

.04147090 

.04546910 

.04960519  54 

65 

.03014337  .03365419 

1 

.03734907 

.04121323 

.04533124 

.04938754  55 

56 

0.02984657 

0.03337243 

0.03708447 

0.04096730 

0.04500487 

0.04918105  56 

57 

.02956130 

.03310204 

.03683114 

.04073245 

.04478933 

.04898506  57 

58 

.02928667 

.03284344  '  .03658848 

.04050810 

.04458401 

.04879897  58 

59 

.02902243 

.03359307 

.03635593 

.04029366 

.04438836 

.04862221  ;  59 

60 

.02876797 

.03335340 

.03613296 

.04008862 

.04420185 

.04845426 

60 

61 

0.02852278 

0.03212294 

0.03591908 

0.03989249 

0.04402398 

0.04829462 

61 

62 

.02828643 

.03190126 

.03571385 

.03970480 

.04385430 

.04814284 

62 

63 

.02805848 

.03168790 

.03551682 

.03952513 

.04369237 

.04799848 

63 

64 

.02783855 

.03148249 

.03532760 

.03935308 

.04353780 

.04786115 

64 

65 

.02762634 

.03128463 

.03514581 

.03918826 

.04339019 

.04773047 

65 

66 

0.03742122 

0.03109398 

0.03497110 

0.03903031 

0.04324921 

0.04760608 

66 

67 

.02722316 

.03091021 

.03480313 

.03887892 

.04311451 

.04748765 

67 

68 

.02703173 

.03073300 

.03464159 

.03873375 

.04298578 

.04737487 

68 

69 

.02684665 

.03056206 

.03448618 

.03859453 

.04286272 

.04726745 

69 

70 

.02666765 

.03039712 

.03433663 

.03846095 

.04274506 

.04716511 

70 

71 

0.02649446 

O;  03023790 

0.03419266 

0.03833277  !o.  04263353 

0.04706760 

71 

72 

.02632683 

.03008417 

.03405404 

.03830973  :  .04353489 

.04697465 

72 

73 

.02616454 

.02993568 

.03392053 

1  .03809160 

.04242190 

.04688605 

73 

74 

.02600736 

.02979333 

.0,3379191 

.03797816 

.04232334 

.04680159 

74 

75 

.02585508 

.03965358 

.03366796 

.03786919 

.04222900 

.04672104 

76 

76 

0.03570751 

0.03951956 

0.033.54849 

0.03776450 

0.04213868 

0.04664423 

76 

77 

.03556447 

.03938997 

.03343331 

.03766390 

.04205221 

.04657094 

77 

78 

.03543576 

.03936463 

.03332224 

.03756731 

.04196939 

.04650104 

78 

79 

.03539128 

.03914338 

.03321510 

.03747436 

.04189007 

.04643434 

79 

80 

.02516071 

.03903605 

.03311176 

.03738489 

.04181408 

.04637069 

80 

81 

0.02503405 

0.03891248  0.0.3301201 

0.03739894 

0.04174127 

0.04630995 

81 

82 

.02491110 

.03880254 

.03391576 

.03731628 

.04167150 

.04625197 

82 

83 

.02479173 

.02869608 

.03283384 

.03713676 

.04160463 

.04619662 

83 

84 

.02467581 

.03859398 

.03373313 

.03706025 

.04154054 

.04614379 

84 

85 

.02456321 

.03849310 

.03364650 

.03698662 

.04147909 

.04609334 

85 

86 

0.02445381 

0.03839633 

0.03356384 

0.03691576 

0.04142018 

0.04604516 

86 

87 

.02434750 

.03830255 

.03348303 

.03684756 

.04136370 

.04599915 

87 

88 

.02424416 

,02821165 

.03340393 

.03678190 

.04130953 

.04595522 

88 

89 

.03414370 

.02812353 

.03333848 

.03671868 

.04125758  ,  .04591325 

89 

90 

.03404603 

.02803809 

.03335556 

.03665781 

.04120775  .04587316 

90 

91 

0.03395101 

0.02795523 

0.03318508 

0.03659919 

0.04115995  0.04583486 

91 

92 

.02385859 

.02787486 

.03311695 

.03654273 

.04111410 

.04579827 

92 

93 

.02376868 

.03779690 

.03305107 

.03648834 

.04107010 

.04576331 

93 

94 

.02368118 

.03772126 

.03198737 

.03643594 

.04102789 

.04572991 

94 

95 

.02359602 

.02764786 

.03192577 

.03638546 

.04098738 

.04569799 

95 

96 

0.02351313 

0.02757662 

0.03186619 

0.03633683 

0.04094850 

0.04566749 

96 

97 

.02343242 

.02750747 

.03180856 

.03638995 

.04091119 

.04563834 

97 

98 

.02335383 

.02744034  .03175281 

.03624478 

.04087538 

.04561048 

98 

99 

.0233W30 

.02737517  \   .03169886 

.03630134 

.04084100 

.04558385 

99 

100 

.03330374 

.02731188  i  .03164667 

.03615937 

.04080800 

.04555839 

100 

Perp. 

0.03000000 

0.02500000  0.03000000 

0.03500000 

6.04000000 

0.04500000 

Perp.j 

TABLE     XXIY,  m 

THE  ANNUITY  WHICH  $1  WILL  PURCHASE  FOR  ANY  NUMBER  OF  YEARS, 


s 

1 
5 

6 

7 

8 

9 

10 

§ 

^ 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

^ 

51 

0.05452867 

0.06323880 

0.07229365 

0.08161116 

0.09112430 

0.10078046 

51 

52 

.05429449 

.06304617 

.07213901  ! 

.08148959 

.09103041 

.10070900 

52 

53 

.05407334 

.06286551 

.07199509  1 

.08137735 

.09094443 

.10064413 

53 

54 

.05386438  .06269602 

.07186110  1 

.08127370 

.09086570 

.10058523 

54 

55 

.05366686  .06253696 

.07173633 

.08117796 

.09079359 

.10053175 

55 

56 

0.05348010  0.06238765 

0,07162011 

0.08108952 

0.09072754 

0.10048317 

56 

57 

.05330343 

.06224744 

.07151183 

.08100780 

.09066702 

.10043906 

57 

58 

.05313626 

.06211573 

.07141093 

.08093228 

.09061157 

.10039898 

58 

59 

.05297802 

.06199200 

.07131689 

.08086247 

.09056076 

.10036258 

59 

60 

.05282818 

.06187572 

.07122923 

.08079795 

.09051419 

.10032951 

60 

61 

0.05268627 

0.06176642 

0.07114749 

0.08073830 

0.09047151 

0.10029946 

61 

62 

.05255183 

.06166366  1 

.07107127 

.08068314 

.09043240 

.10027217 

62 

63 

.05242442  ! 

.06156703  ! 

.07100019 

.08063214 

.09039654 

.10024736 

63 

64 

.05230365 

.06147615 

.07093388 

.08058497 

.09036366 

.10022483 

64 

65 

.05218915 

.06139066 

.07087203 

.08054135 

.09033352 

.10020434 

65 

66 

0.05208057 

0.06131022 

0.07081431 

0.08050100 

0.09030589 

0.10018573 

66 

67 

.05197757 

.06123454 

.07076046 

.08046367 

.09028056 

.10016882 

67 

68 

.05187986 

.06116330 

.07071021 

.08042914 

.09025732 

.10015345 

68 

69 

.05178715 

.06109625 

.07066330 

.08039719 

.09023602 

.10013948 

69 

70 

.05169915 

.06103313 

.07061953 

.08036764 

.09021649 

.10012678 

70 

71 

0.05161563 

0.06097370 

0.07057866 

0.08034029 

0.09019857 

0.10011524 

71 

72 

.05153633 

.06091774 

.07054051 

.08031498 

.09018214 

.10010476 

72 

73 

.05146103 

.06086505 

.07050490 

.08029156 

.09016708 

.10009522 

73 

74 

.05138953 

.06081542 

.07047164 

.08026990 

.09015326 

.10008656 

74 

75 

.05132161 

.06076867 

.07044060 

.08024984 

.09014058 

.10007868 

75 

76 

0.05125709 

0.06072463 

0.07041160 

0.08023128 

0.09012896 

0.10007153 

76 

77 

.05119580 

.06068315 

.07038453 

.08021410 

.09011831 

.10006502 

77 

78 

.05113757 

.06064407 

.07035924 

.08019820 

.09010852 

.10005911 

78 

79 

.05108222 

.06060724 

.07033563 

.08018349 

.09009955 

.10005373 

79 

80 

.05102963 

.06057254 

.07031357 

.08016987 

.09009132 

.10004884 

80 

81 

0.05097963 

0.06053984 

0.07029297 

0.08015726 

0.09008377 

0.10004440 

81 

82 

.05093211 

.06050903 

.07027373 

.08014559 

.09007685 

.10004036 

82 

83 

.05088694 

.06047998 

.07025576 

.08013479 

.09007050 

.10003669 

83 

84 

.05084399 

.06045261 

.07023897 

.08012479 

.09006467 

.10003336 

84 

85 

.05080316 

.06042681 

.07022329 

.08011553 

.09005933 

.10003032 

85 

86 

0.05076433 

0.06040249 

0.07020863 

0.08010696 

0.09005443 

0.10002756 

86 

87 

.05072740 

.06037956 

.07019495 

.08009903 

.09004993 

.10002506 

87 

88 

.05069228 

.06035795 

.07018216 

.08009168 

.09004581 

.10002278 

88 

89 

.05065888 

.06033757 

.07017021 

.08008489 

.09004202 

.10002071 

89 

90 

.05062711 

.06031836 

.07015905 

.08007859 

.09003855 

.10001883 

90 

91 

0.05059689 

0.06030025 

0.07014863 

0.08007277 

0.09003537 

0.10001711 

91 

92 

.05056815 

.06028318 

.07013888 

.08006737 

.09003245 

.10001556 

92 

93 

.05054080 

.06026708 

.07012978 

.08006238 

.09'002977 

.10001414 

93 

94 

.05051478 

.06025190 

.07012128 

.08005775 

.09002731 

.10001286 

94 

95 

.05049003 

.06023758 

.07011333 

.08005347 

.09002505 

.10001169 

95 

96 

0.05046648 

0.06022408 

0.07010590 

0.08004951 

0.09002298 

0.10001063 

96 

97 

.05044407 

.06021135 

.07009897 

.08004584 

.09002109 

.10000966 

97 

98 

.05042274 

.06019935 

.07009248 

.08004244 

.09001934 

.10000878 

98 

99 

.05040245 

.06018803 

.07008643 

.08003930 

.09001775 

.10000798 

99 

100 

.05038314 

.06017736 

.07008076 

.08003638 

.09001628 

.10000726 

100 

Perp. 

0.05000000 

0.06000000 

0.07000000 

0.08000000 

0.09000000 

0.10000000 

Perp. 

^28 


TABLE    XXY. 


LOGARITHM  OF  THE  PRESENT  VALUE  OF  $1,  DUE  AT  THE  END  OF  ANY  NUMBER 

OF  YEARS. 


Years. 

2  Per  Cent. 

2|  Per  Cent. 

3  Per  Cent. 

3^  Per  Cent. 

4  Per  Cent. 

^  Per  Cent. 

Years. 

1 
0 

0.0000000 

0.0000000 

0.0000000  ; 

0.0000000 

0.0000000 

0.0000000 

0 

1 

1.9913998 

1.9892761 

1.9871628  i 

1.9850597 

1.9829667 

1.9808837 

1 

2 

.9827997 

.9785523 

.9743256  i 

.9701193 

.9659333 

.9617674 

2 

3 

.9741995 

.9678284 

.9614883  ! 

.9551790 

.9489000 

.9426511 

3 

4 

.9655993 

.9571045 

.9486511 

.9402386 

.9318666 

.9235348 

4 

5 

T.9569991 

1.9463807 

T.  9358139 

T.  9252983 

T.  9148333 

T.  9044185 

5 

6 

.9483990 

.9356568 

.9229767 

.9103579 

.8978000 

.8853023 

6 

7 

.9397988 

.9249329 

.9101394 

.8954176 

.8807666 

.8661860 

7 

8 

.9311986 

.9142091 

.8973022 

.8804';^72 

.8637333 

.8470697 

8 

9 

.9225985 

.9034852 

.8844650 

.8655369 

.8466999 

.8279534 

9 

10 

T.  9139983 

T.8927613 

T.  8716278 

T.  8505965 

T.  8296666 

T.8088371 

10 

11 

.9053981 

.8820375 

.8587905 

.8356562 

.8126333 

.7897208 

11 

12 

.8967979 

.8713136 

.8459533 

.8207158 

.7955999 

.7706045 

12 

13 

.8881978 

.8605897 

.8331161 

.8057755 

.7785666 

.7514882 

13 

14 

.8795976 

.8498659 

.8202789 

.7908351 

.7615332 

.7323719 

14 

15 

T.  8709974 

T.  8391420 

T.  8074416 

T.  7758948 

T.  7444999 

T.  7132556 

15 

16 

.8623973 

.8284182 

.7946044 

.7609544 

.7274666 

.6941394 

16 

17 

.3537971 

.8176943 

.7817672 

.7460141 

.7104332 

.6750231 

17 

18 

.8451969 

.8069704 

.7689300 

.7310737 

.6933999 

.6559068 

18 

19 

.8365967 

.7962466 

.7560927 

.7161334 

.6763666 

.6367905 

19 

20 

T.  82  79966 

1.7855227 

T.  7432555 

T.  7011930 

T.  6593332 

1.6176742 

20 

21 

.8193964 

.7747988 

.7304183 

.6862527 

.6422999 

.5985579 

21 

22 

.8107962 

.7640750 

.7175811 

.6713123 

.6252665 

.5794416 

22 

23 

.8021961 

'.7533511 

.7047438 

.6563720 

.6082332 

.56X)3253 

23 

24 

.7935959 

.7426272 

.6919066 

.6414316 

.5911999 

.5412090 

24 

25 

1.7849957 

1.7319034 

T.6790694 

1.6264913 

T.5741665 

1.5220927 

25 

26 

.7763955 

.7211795 

.6662322 

.6115509 

.5571332 

.5029764 

26 

27 

.7677954 

.7104556 

.6533949 

.5966106 

.5400998 

.4838602 

27 

28 

.7591952 

.6997318 

.6405577 

.5816702 

.5230665 

.4647439 

28 

29 

.7505950 

.6890079 

.6277205 

.5667299 

.5060332 

.4456276 

29 

30 

T.  7419948 

T.  6782840 

T.  6148833 

1.5517895 

T.4889998 

T.  4265113 

30 

31 

.7333947 

.6675602 

.6020460 

.5368492 

.4719665 

.4073950 

31 

32 

.7247945 

.6568363 

.5892088 

.5219088 

.4549331 

.3882787 

32 

33 

.7161943 

.6461124 

.5763716 

.5069685 

.4378998 

.3691624 

33 

34 

.7075942 

.6353886 

.5635344 

.4920281 

.4208665 

.3500461 

34 

35 

T.  6989940 

T.  6246647 

T.  5506971 

1.4770878 

T.4038331 

T.  3309298 

35 

36 

.6903938 

.6139409 

.5378599 

.4621474 

.3867998 

.3118135 

36 

37 

.6817937 

.6032170 

.5250227 

.4472071 

.3697664 

.2926973 

37 

38 

.6731935 

.5924931 

.5121855 

.4322667 

.3527331 

.2735810 

38 

39 

.6645933 

.5817692 

.4993482 

.4173264 

.3356998 

.2544647 

39 

40 

T.  6559931 

T.5710454 

1.4865110 

1.4023860 

1.3186664 

T.  2353484 

40 

41 

.6473930 

.5603215 

.4736738 

.3874457 

.3016331 

.2162321 

41 

42 

.6387928 

.5495977 

.4608366 

.3725053 

.2845997 

.1971158 

42 

43 

.6301926 

.5388738 

.4479993 

.3575650 

.2675664 

.1779995 

43 

44 

.6215924 

.5281499 

.4351621 

.3426246 

.2505331 

.1588832 

44 

45 

T.  6129923 

T.  5174261 

T.  4223249 

1.3276843 

T.2334997 

1.1397669 

45 

46 

.6043921 

.5067022 

.4094877 

.3127439 

.2164664 

.1206506 

46 

47 

.5957919 

.4959783 

.3966504 

.2978036 

.1994331 

.1015343 

47 

48 

.5871918 

.4852545 

.3838132 

.2828632 

.1823997 

.0824181 

48 

49 

.5785916 

.4745306 

.3709760 

.2679229 

.1653664 

.0633018 

49 

0-9 

T.  6129923 

1.5174260 

1.4223250 

T.  3276845 

T.2334997 

T.  1397669 

0-9 

1019 

2.7529751 

2.4450395 

2.1386025 

3.8336495 

3.5301658 

3.2281379 

10-19 

20-29 

3.8929580 

3.3726530 

4.8548800 

4.3396145 

5.8268319 

5.3165088 

20-29 

30-39 

3.0329408 

4.3002664 

5.5711575 

6.8455795 

6.1234979 

7.4048798 

30  39 

40-49 

4.1729236 

5.2278800 

6.2874350 

7.3515445 

8.4201640 

9.4932507 

40-49 

Formula,  Logan thm  =  At;«. 


TABLE    XXY. 


229 


LOGARITHM  OF  THE  PRESENT  VALUE  OF  $1,  DUE  AT  THE  END  OF  ANY  NUMBER 

OF  YEARS. 


rears. 

5  Per  Cent. 

6  Per  Cent. 

7  Per  Cent.  1 

8  Per  Cent. 

9  Per  Cent. 

10  Per  Cent. 

Years. 

0 

0.0000000 

0.0000000 

0.0000000 

0.0000000 

0.0000000 

0.0000000 

^  o'""i 

1 

1.9788107 

1.9746941 

1.9706162 

1.9665762 

1.9625735 

1.9586073 

1  1 

2 

.9576214 

.9493883 

.9412324 

.9331525 

.9251470 

.9172146 

2 

3 

.9364321 

.9240824 

.9118487 

.8997287 

.8877205 

.8758219 

3 

4 

.9152428 

.8987765 

.8824649 

.8663050 

.8502940 

.8344293 

4 

5 

1.8940535 

T.  8734707 

1.8530811 

T.  8328812 

1.8128675 

T.  7930366 

5 

6 

.8728642 

.8481648 

.8236973 

.7994575 

.7754410 

.7516439 

6 

7 

.8516749 

.8228589 

.7943136 

.7660337 

.7380145 

.7102512 

7 

8 

.8304856 

.7975531 

.7649298 

.7326100 

.  7005880 

.6688585 

8 

9 

.8092963 

.7722472 

.7355460 

.6991862 

.6631615 

,6274658 

9 

10 

1.7881070 

1.7469413 

T.  7061622 

1.6657624 

T.  6257350 

1.5860731 

10 

11 

.7669177 

.7216355 

.6767784 

.6323387 

.5883085 

.5446805 

11 

12 

.7457284 

.6963296 

.6473947 

.5989149 

.5508820 

.5032878 

12 

13 

.7245391 

.6710238 

.6180109 

.5654912 

.5134555 

.4618951 

13 

14 

.7033498 

.6457179 

.5886271 

.5320674 

.4760290 

.4205024 

14 

15 

1.6821605 

1.6204120 

1.5592433 

1.4986437 

T.  4386025 

1.3791097 

15 

16 

.6609712 

.5951062 

.6298596 

.4652199 

.4011760 

.3377170 

16 

17 

.6397819 

.5698003 

.5004758 

.4317962 

.3637495 

.2963244 

17 

18 

.6185926 

.5444944 

.4710920 

.3983724 

.3263230 

.2549317 

18 

19 

.5974033 

.5191886 

.4417082 

.3649486 

.2888965 

.2135390 

19 

20 

1.5762140 

1.4938827 

T.4123244 

1.3315249 

1.2514700 

T.  1721463 

20 

21 

.5550247 

.4685768 

.3829407 

.2981011 

.2140435 

.1307536 

21 

22 

.5338354 

.4432710 

.3535569 

.2646774 

.1766170 

.0893609 

22 

23 

.5126461 

.4179651 

.3241731 

.2312536 

.1391905 

.0479682 

23 

24 

.4914568 

.3926592 

.2947893 

'  .1978299 

.1017640 

.0065756 

24 

25 

1.4702675 

1.3673534 

1.2654056 

1.1644061 

T.  0643376 

2.9651829 

25 

26 

.4490782 

.3420475 

.2360218 

.1309824 

.0269111 

.9237902 

26 

27 

.4278889 

.3167416 

.2066380 

.0975586 

2.9894846 

.8823975 

27 

28 

.4066996 

.2914358 

.1772542 

.0641348 

.9520581 

.8410048 

28 

29 

.3855103 

.2661299 

.1478704 

.0307111 

.9146316 

.7996121 

29 

30 

1.3643210 

1.2408240 

1.1184867 

i  2.9972873 

2.8772051 

2.7582194 

30 

31 

.3431317 

.2155182 

.0891029 

i  .9638636 

.8397786 

.7168268 

31 

32 

.3219424 

.1902123 

.0597191 

.9304398 

.8023521 

.6754341 

32 

33 

.3007531 

.1649064 

.0303353 

.8970161 

.7649256 

.6340414 

33 

34 

.2795638 

.1396006 

.0009516 

.8635923 

.7274991 

.5926487 

34 

35 

T.  2583745 

1.1142947 

2.9715678 

2.8301686 

2.6900726 

2.5512560 

35 

36 

.2371852 

.0889889 

.9421840 

.7967448 

.6526461 

.5098633 

36 

37 

.2159959 

.0636830 

.9128002 

.7633210 

.6152196 

.4684706 

37 

38 

.1948066 

.0383771 

.8834164, 

.7298973 

.5777931 

.4270780 

38 

39 

.1736173 

.0130713 

.8540327 

;  .6964735 

.5403666 

.3856853 

39 

40 

1.1524280 

2.9877654 

2.8246489 

2.6630498 

2.5029401 

2.3442926 

40 

41 

.1312387 

.9624595 

.7952651 

.6296260 

.4655136 

.3028999 

41 

42 

.1100494 

.9371537 

.7658813 

.5962023 

.4280871 

.2615072 

42 

43 

.0888601 

.9118478 

.7364976 

.5627785 

.3906606 

.2201145 

43 

44 

.0676708 

.8865419 

.7071138 

.5293548 

.3532341 

.1787219 

44 

45 

T.  0464815 

2.8612361 

2.6777300 

2.4959310 

2.3158076 

2.1373292 

45 

46 

.0252922 

.8359302 

.6483462 

.4625072 

.2783811 

.0959365 

46 

47 

.0041029 

.8106243 

.6189624 

.4290835 

.2409546 

.0545438 

47 

48 

2.9829136 

.7853184 

.5895787 

.3956597 

.2035281 

.0131511 

48 

49 

.9617243 

.7600126 

.5601949 

.3622360 

.1661016 

3.9717584 

49 

0-  8 

T.  0464815 

2.8612360 

2.6777300 

2.4959310 

2.3158075 

2.1373291 

0-  9 

10-19 

4.9275515 

4.3306496 

5.7393522 

5.1535554 

6.5731575 

7.9980607 

10-19 

20-28 

6.8086215 

7.8000630 

8.8009744 

i  9.8111799 

10.8305080 

11.8587921 

20-29 

30-38 

1  8.6896915 

9.2694765 

11.8625967 

1 12. 4688043 

13.0878585 

15.7195236 

30-39 

40-48 

1,10.5707615 

12.7388899 

14.9242189 

115.1264288 

17.3452085 

19.5802551 

40-49 

230 


TABLE    XXY. 


LOGARITHM  OF  THE  PRESENT  VALUE  OF  $1,  DUE  AT  THE  END  OF  ANY  NUMBER 

OF  YEARS. 


Tears 

.  3  Per  Cent. 

2i  Per  Cent. 

3  Per  Cent. 

3i  Per  Cent. 

4  Per  Cent. 

4^  Per  Cent. 

Years. 

50 

T.5699914 

1.4638067 

1.3581388 

\  1.2529825 

1.1483330 

1.0441855 

50 

51 

.5613912 

.4530829 

.3453015 

.2380422 

.1312997 

.0250692 

51 

52 

.5527911 

.4423590 

.3324643 

I  .2231018 

.1142664 

.0059529 

53 

.5441909 

.4316351 

.3196271 

.2081615 

.0972330 

2.9868366 

53 

54 

.5355907 

.4209113 

.3067899 

.1932211 

.0801997 

.9677203 

54 

55 

T.5269906 

L 4101874 

T.2939526 

L 1782808 

1.0631663 

2.9486040 

55 

56 

.5183904 

.3994635 

.2811154 

.1633404 

.0461330 

.9294877 

56 

57 

.5097902 

.3887397 

.2682782 

.1484001 

.0290997 

.9103714 

57 

58 

.5011900 

.3780158 

.2554410 

.1334597 

.0120663 

..8912552 

58 

59 

.4925899  ]    .3672919 

.2426037 

.1185194 

2.9950330 

.8721389 

59 

60 

T.4839897  T.3565681 

1.2297665 

T.  1035790 

2.9779996 

2.8530226 

60 

61 

.4753895 

.3458442 

.2169293 

.0886387 

.9609663 

.8339063 

61 

62 

.4667894 

.3351203 

.2040921 

.0736983 

.9439330 

.8147900 

62 

63 

.4581892  i  .3243965 

.1912548 

.0587580 

.9268996 

.7956737 

63 

64 

.4495890 

.3136726 

.1784176 

1  .0438176 

.9098663 

.7765574 

64 

65 

1.4409888 

T.  3029487 

T.  1655804 

T.  0288773 

2.8928329 

2.7574411 

65 

66 

.4323887 

.2922249 

.1527432 

.0139369 

.8757996 

.7383248 

66 

67 

.4237885 

.2815010 

.1399059 

2.9989966 

.8587663 

.7192085 

67 

68 

.4151883 

.2707772 

.1270687 

.9840562 

.8417329 

.7000922 

68 

69 

.4065881  1  .2600533 

.1142315 

.9691159 

.8246996 

.6809760 

69 

70 

T.  3979880  1.2493294 

T.1013943 

2.9541755 

2.8076662 

2.6618597 

70 

71 

.3893878 

.2386056 

.0885570 

.9392352 

.7906329 

.6427434 

71 

72 

.3807876 

.2278817 

.0757198 

.9242948 

.7735996 

.6236271 

72 

73 

.3721875   .2171578 

.0628826 

.9093545 

.7565662 

.6045108 

73 

74 

.3635873   .2064340 

.0500454  '' 

.8944141 

.7395.329 

.5853945 

74 

75 

T.  3549871  1.1957101 

T.0372081  ' 

2.8794738 

2.7224996 

3.5662782 

75 

76 

.3463869 

.1849862 

.0243709 

.8645334 

.7054662 

.5471619 

76 

77 

.3377868 

.1742624 

.0115337 

.8495931 

.6884329 

.5280456 

77 

78 

.3291866 

.1635385 

2.9986965 

.8346527 

.6713995 

.5089293 

78 

79 

.3205864 

.1528146 

.9858592 

.8197124 

.6543662 

.4898131 

79 

80 

1.3119863 

T.  1420908 

2.9730220 

2".  8047720 

2.6373329 

3.4706968 

80 

81 

.3033861 

.1313669 

.9601848  1 

.7898317 

.6202995 

.4515805 

81 

82 

.2947859 

.1206430 

.9473476 

.7748913 

.6032662 

.4324642 

82 

83 

.2861857 

.1099192 

.9345103 

.7599510 

.5862328 

.4133479 

83 

84 

.2775856 

.0991953 

.9216731 

.7450106 

.5691995 

.3942316 

84 

85 

'T.2689854 

1.0884714 

2.9088359 

2.7300703 

2.5521662 

2.3751153 

85 

86 

.2603852 

.0777476 

.8959987 

.7151299 

.5351328 

.3559990 

86 

87 

.2517851 

.0670237 

.8831615 

.7001896 

.5180995 

.3368827 

87 

88 

.2431849 

.0562998 

.8703242 

.6852492 

.5010661 

.3177664 

88 

89 

.2345847 

.0455760 

.8574870 

.6703089 

.4840328 

.2986502 

89 

90 

T.  2259845 

T.0348521 

2.8446498 

3.6553685 

2.4669995 

2.2795339 

90 

91 

.2173844 

.0241282 

.8318126 

.6404282 

.4499661 

.2604176 

91 

92 

.2087842 

.0134044 

.8189753 

.6254878 

.4329328 

.2413013 

92 

93 

.2001840 

.0026805 

..8061381 

.6105475 

.4158994 

.2221850 

93 

94 

.1915839 

2.9919567 

.7933009 

.5956071 

.3988661 

.2030687 

94 

95 

T.  1829837 

2.9812328 

2.7804637 

2.5806668 

2.3818328 

2.1839524 

95 

96 

.1743835 

.9705089 

.7676264 

.5657264 

.3647994 

.1648361 

96 

97 

.1657833 

.9597851 

.7547892 

.5507861 

.3477661 

.1457198 

97 

98 

.1571832 

.9490612 

.7419520  i 

.5358457 

.3307327 

.1266035 

98 

99 

.1485830 

.9383373 

.7291148  ' 

.5209054 

.3136994 

.1074872 

99 

100 
50-59 

.1399828 

.92761.35 

.7162775 

.5059650 

.2966661 

.0883710 

LOO 

5.3129064 

6.1554933 

7.0037125 

9.8575095 

10.7168301 

11.5816217  !. 

50-59 

60-69 

6.4528892 

7.0831068 

9.7199900 

10.3634745 

11.0134961 

13.6699926  ( 

50-69 

70-79 

7.5928720 

8.0107203 

10.4362675 

12.8694395 

13.3101622 

15.7583636  ' 

ro-79 

80-89 

8.7328549 

10.9383337 

11.1525451 

13.3754045 

15.6068283 

17.8467346  1 

JO-89 

90-99 

9.8728377 

11.8659472 

13.8688228 

15.8813695 

L7. 9034943  ' 

19.9351055  |{ 

)0-99 

TABLE     XXY. 


231 
232 


LOGARITHM  OP  THE  PRESENT  VALUE  OP  $1,  DUE  AT  THE  END  OF  ANY  NUMBER 

OF  YEARS. 


Tears. 

5  Per  Cent. 

6  Per  Cent. 

7  Per  Cent. 

8  Per  Cent. 

9  Per  Cent. 

10  Per  Cent. 

If  ears.' 

50 

2.9405350 

2.7347067 

2.5308111 

2.328812^ 

2.1286751 

3.9303657 

50 

51 

.9193457 

.7094009 

.5014273 

.2953885 

.0912486 

.8889731 

51 

52 

.8981564 

.6840950 

.4720436 

.2619647 

.0538221 

.8475804 

52 

53 

.8769671 

.6587891 

.4426598 

.2285410 

.0163956 

.8061877 

53 

54 

.8557779 

.6334833 

.4132760 

.1951172 

3.9789691 

.7647950 

54 

55 

2.8345886 

2.6081774 

3.3838922 

2.1616934 

3.9415426 

3.7234023 

55 

56 

.8133993 

.5828715 

.3545084 

.1282697 

.9041161 

.6820096 

56 

57 

.7922100 

.5575657 

.3251247 

.0948459 

.8666896 

.6406169 

57 

58 

.7710207 

.5322598 

.2957409 

.0614222 

.8292631 

.5992243 

58 

59 

.7498314 

.5069539 

.2663571 

.0279984 

.7918366 

.5578316 

59 

60 

2.7286421 

2.4816481 

2.2369733 

3.9945747 

3.7544101 

3.5164389 

60 

61 

.7074528 

.4563422 

.2075896 

.9611509 

.7169836 

.4750462 

61 

62 

.6862635 

.4310364 

.1782058 

.9277272 

.6795571 

.4336535 

62 

63 

.6650742 

.4057305 

.1488220 

.8943034 

.6421306 

.3922608 

63 

64 

.6438849 

.3804246 

.1194382 

.8608796 

.6047041 

.3508681 

64 

65 

2.6226956 

2.3551188 

2.D900545 

3.8274559 

3.5672776 

3.3094755 

65 

66 

.6015063 

.3298129 

.0606707 

.7940321 

.5298511 

.2680828 

'66 

67 

.5803170 

.3045070 

.0312869 

.7606084 

.4924246 

.2266901 

67 

68 

.5591277 

.2792012 

.0019031 

.7271846 

.4549981 

.1852974 

68 

69 

.5379384 

.2538953 

3.9725193 

.6937609 

.4175716 

.1439047 

69 

70 

2.5167491 

2.2285894 

3.9431356 

3.6603371 

3.3801451 

3.1025120 

70 

71 

.4955598 

.2032836 

.9137518 

.6269134 

.3427186 

.0611194 

71 

72 

.4743705 

.1779777 

.8843680 

.5934896 

.3052921 

.0197267 

72 

73 

.4531812 

.1526718 

.8549842 

.5600658 

.2678657 

4.9783340 

73 

74 

.4319919 

.1273660 

.8256005 

.5266421 

.2304392 

.9369413 

74 

75 

2.4108026 

2.1020601 

3.7962167 

3.4932183 

3.1930127 

4.8955486 

75 

76 

.3896133 

.0767542 

.7668329 

,4597946 

.1555862 

.8541559 

76 

77 

.3684240 

.0514484 

.7374491 

.4263708 

.1181597 

.8127632 

77 

78 

.3472347 

.0261425 

.7080653 

.3929471 

.0807332 

.7713706 

78 

79 

.3260454 

.0008366 

.6786816 

.3595233 

.0433067 

.7299779 

79 

80 

2.3048561 

3.9755308 

3.6492978 

3.3260996 

3.0058802 

4.6885852 

80 

81 

.2836668 

.9502249 

.6199140 

.2926758 

4.9684537 

.6471925 

81 

82 

.2624775 

.9249190 

.5905302 

.2592521 

.9310272 

.6057998 

82 

83 

.2412882 

.8996132 

.5611465 

.2258283 

.8936007 

.5644071 

83 

84 

.2200989 

.8743073 

.5317627 

.1924045 

.8561742 

.5230144 

84 

85 

^.1989096 

3.8490015 

3.5023789 

3M  589808 

4.8187477 

4.4816218 

85 

86 

.1777203 

.8236956 

.4729951 

.1255570 

.7813212 

.4402291 

86 

87 

.1565310 

.7983897 

.4436113 

.0921333 

.7438947 

.3988364 

87 

88 

.1353417 

.7730839 

.4142276 

.0587095 

.7064682 

.3574437 

88 

89 

.1141524 

.7477780 

.3848438 

.0252858 

.6690417 

.3160510 

89 

90 

2.0929631 

3.7224721 

3.3554600 

4.9918620 

4.6316152 

4.2746583 

90 

91 

.0717738 

.6971663 

.3260762 

.9584383 

.5941887 

.2332657 

91 

92 

.0505845 

.6718604 

•2966925 

.9250145 

.5567622 

.1918730 

92 

93 

.0293952 

.6465545 

.2673087 

.8915907 

.5193357 

.1504803 

93 

94 

.0082059 

.6212487 

.2379249 

.8581670 

.4819092 

.1090876 

94 

95 

3.9870166 

3.5959428 

3.2085411 

4.8247432 

4.4444827 

4.0676949 

95 

96 

.9658273 

.5706369 

.1791573 

.7913195 

.4070562 

.0263022 

96 

97 

.9446380 

.5453311 

.1497736 

.7578957 

.3696297 

5.9849095 

97 

98 

.9234487 

.5200252 

.1203898 

.7244720 

.3322032 

.9435169 

98 

99 

.9022594 

.4947193 

.0910060 

.6910482 

.2947767 

.9021242 

99 

100 

.8810701 

.4694135 

.0616222 

.6576245 

.2573502 

.8607315 

100 

50-59 

12.4518321 

14.2083033 

T7. 9858411 

T9. 7840532 

21.6025585 

23.4409866 

50-59 

60-69 

14.3329025 

17.6777170 

19.0474634 

22.4416777 

25.8599085 

27.3017180 

60-69 

70-79 

16.2139725 

19.1471303 

22.1090857 

25.0993021 

28.1172592 

31.1624496 

70-79 

80-89 

18.0950425 

22.6165439 

25.1707079 

29.7569267 

32.3746095 

35.0231810 

80-89 

90-99 

21.9761125 

24.0859573 

28.2323301 

32.4145511 

36.6319595 

40.8839126 

90-9& 

PART    SECOND. 
LIFE   ANNUITIES  AND   INSURANCES, 


The  science  of  Life  Annuities  and  Insurances  is  founded  upon  the  system  of 
Probabilities,  or  chiefly  that  portion  of  the  system,  which  treats  of  "  mathematical 
expectation."  Numerous  plans  and  projects  from  other  sources,  have  generally  ended 
in  failure.  And  while  "mathematical  expectation"  is  admitted  to  govern  the  deter- 
mination of  premiums  and  reserves,  the  same  principles,  confirmed  by  long  experience 
in  connection  with  "  moral  expectation,"  are  essentially  recognized  in  the  management 
of  current  risks  and  investments. 


SECTION    I. 
First  Principles  of  Probability  for  Reference. 

For  future  reference,  let  us  briefly  state  some  of  the  axioms  or  first  principles  of 
the  system  of  Probabilities.  These  have  been  variously  developed  in  the  able  treatises 
of  Professor  De  Morgan,  especially  the  Essay  on  Probabilities  in  Lardner's  Cabinet 
Cyclopaedia,  Galloway's  article,  Probability  in  the  Encyclopaedia  Britannica,  also  pub- 
lished separately,  Demoivre  in  1756,  Lubbock,  Lacroix,  Laplace,  Poisson  and  others. 
A  simple  apparatus  will  serve  for  the  experimental  trials  and  comparisons.  And  a 
record  of  the  results  will  illustrate  the  irregularities  of  small  numbers  and  the 
increasing  regularity  of  large  numbers  of  trials,  as  well  as  the  probable  limits  of 
fluctuation  from  a  mean  result. 

1.  Definitio7i.  According  to  the  usual  definition,  the  mathematical  probability  of  a 
contingent  event  is  fneasured  by  a  fraction,  whose  numerator  is  the  number  of  equal  ways 
in  luhich  it  can  happen,  and  whose  denominator  is  the  number  of  all  the  equal  ways 
in  which  it  can  either  happen  or  fail. 

The  difierent  chances  or  ways  of  happening  are  supposed  to  be  perfectly  equal. 
Otherwise  they  must  be  multiplied  by  numbers  proportional  to  their  respective  facilities 
or  likelihoods.  If  one  chance  is  twice  as  likely  as  another,  it  must  be  regarded  as  two 
chances ;  and  so  generally. 

An  urn  contains,  for  example,  nine  white  balls,  and  one  black  ball.  The  chance 
of  drawing  a  white  ball  by  a  person  blindfold,  is  consequently  -^ ;  and  that  of  the 
black  ball  ^. 

Thus  the  chance  of  throwing  heads  in  the  toss  of  a  symmetrical  coin,  is  ^  or  0.5, 
called  the  "even  chance."     And  the  probability  of  throwing  the  ace  point  with  an 


234  LIFE   ANNUITIES   AND    INSURANCES. 

ivory  die,  having  six  equal  faces,  is  ^.     Generally,  if  the  chances  of  occurrence  are  to 
those  of  failure,  as  a  to  h,  the  probabilities  of  happening  and  of  failing  in  the  next  trial 

will  be,  respectively, 

a  T     h 

7,   and  7. 

a  +  b'  a  +  b 

2.  Certainty.  The  sum  of  the  last  two  fractions  is  evidently  1,  the  symbol  of 
certainty;  since  one  event  or  the  other  must  take  place.  The  practical  applications 
of  this  principle  are  sometimes  called  "hedging,"  or  "compassing  the  main  chance." 
Thus  a  person  having  effected  a  temporary  insurance  on  his  life  for  ten  years  for  15,000, 
next  buys  a  pure  endowment  of  $5,000  for  the  same  period.  Or  what  is  equivalent,  he 
effects  an  Endowment  Insurance  for  $5,000  for  ten  years.  The  opposite  chances  of 
living  and  dying  evidently  make  up  a  certainty,  and  are  both  secured  ;  so  that  he  must 
receive  $5,000  at  the  end  of  ten  years,  or  sooner  in  the  event  of  death. 

3.  The  Opposite  Probability.  If  p  denote  the  probability  of  happening,  and  q 
that  of  failing  in  the  next  trial ;  then  as  just  stated,  p-\-g  z=l,  and  g  =  1  —  p.  That 
is,  the  probability  p  subtracted  from  unity,  gives  the  probability  of  the  opposite  event. 

Thus  the  probability  of  throwing  the  ace  point  being  ^ ;  the  probability  of  not 
throwing  the  ace,  but  some  other  face  of  the  die,  is  1 — \,  or  f. 

In  the  life  table,  let  I  denote  the  number  of  persons  living  at  any  given  age ;  d  the 
number  dying  in  the  ensuing  twelve  months;  jo  the  probability  of  surviving ;  and  g' 
that  of  dying,  in  the  same  year.     As  before  described, 

d  ,  l-d 

4.  Joint  Occurrence.  The  probability  of  an  event  compounded  of  any  number  of 
simjjle  and  independent  events  is  equal  to  the  product  of  their  separate  probabilities. 

It  will  be  useful  to  observe  that  this  product  will  be  the  same,  whether  the  simple 
events  are  simultaneous  or  successive,  or  to  occur  in  any  one  order.  For  example,  if  p, 
p',  p"  denote  the  tabular  probabilities  of  surviving  from  the  age  of  35  to  36,  36  to  37, 
37  to  38;  the  probabiHty  of  surviving  from  35  to  38  wijl  be  equal  to  the  product 
p  p'  p".  In  like  manner,  the  chance  of  surviving  from  35  to  37,  and  dying  in  the 
next  year,  will  be  p  y  {l—p"). 

Since  the  product  of  two  or  more  proper  fractions  is  always  less  than  either  factor, 
the  uncertainty  of  a  compound  event  increases  with  every  new  contingency,  on  which 
it  is  made  to  depend.  For  a  common  illustration,  the  evidence  of  eye-witnesses  is 
preferred  to  hearsay  reports  successively  transmitted. 

5.  Addition  of  Probabilities.  When  a  simple  evetit  may  happen  in  several  ways 
independently,  the  probability  of  the  event  is  the  sum  of  its  separate  probabilities. 
Thus,  the  chance  of  throwing  the  ace  point  in  one  toss  of  an  ivory  die,  being  ^, 
the  chance  of  throwing  just  one  ace  when  two  dice  are  thrown,  is  the  sum  of 
fxi  +  ixf  or -J^.  In  the  same  case,  for  contrast,  the  chance  of  two  aces  by  Prin- 
ciple 4,  is  equal  to  ^  x  |  or  -^^.  The  wide  difference  between  these  two  classes  of 
results,  was  strikingly  illustrated  in  the  military  concentrations  and  combinations  of 
Napoleon  Bonaparte.  "  Military  science,"  said  he,  "  consists  in  calculating  all  the 
chances  accurately  in  the  first  place,  and  then  in  giving  accident  its  place  in  one's 
calculations." 

6.  Repetition  of  Trials.  An  urn  contains  3  white  and  3  black  balls  or  5  in  all. 
A  ball  is  drawn  successively  and  replaced  in  the  urn  after  each  drawing.     The  result 


■       ' /   ^— ^ 

((    UNiVERC;  .  . 
LIFE   ANNUITIES   AND    INSUR^^^Cl^^^  235 

of  two  trials, — if  W,  B,  denote  the  issue  of  a  white  or  black  ball  respectively, — will  be 
represented  thus : 

Possible  Events.        WW,  WB,  BW,  BB. 

Probabilities.  |x|,  |x|,  fx|,  fx|. 

{p  +  qf  =        p'       +       pq       -\-       qp       -\-       q'- 

And  so  generally,  if  p  denote  the  probability  of  any  contingent  event  E,  and  q 
that  of  its  opposite,  so  that  jo  +  g  =  1 ;  the  possible  combinations  in  m  trials,  will  be 
represented  by  the  terms  of  the  development  of  the  binomial, 

{p  +  q)"^  =  p'^  +  7np'^-^q  +  — ^^ '-pm-^q^  + 

w(/w— 1)  (w— 2) (m—n  +  l)  _  „  „  .  ,    ^ 

+ ~^ — ris — ^::t7^ — -^-^p'^'^r  +....+?"». 

The  first  term  expresses  the  probability  that  E  will  happen  in  every  one  of  the  m 
trials.  The  whole  second  term  expresses  the  probability  that  E  will  happen  m—1 
times  and  fail  once,  in  any  order  or  witliout  regard  to  order.  Or  omitting  its  coefficient 
m,  tlie  remaining  product  by  Principle  4,  expresses  the  probability  that  E  will  occur 
m — 1  times  and  fail  once  in  any  particular  or  assigned  order.  And  so  on  for  the  third 
term,  to  the  last. 

In  like  manner,  instead  of  two  simple  events,  had  there  been  three,  whose  proba- 
bilities axe  p,  q,  r,  so  that  p  +  g  +  r  =  1 ;  the  probabilities  in  m  trials  would  be  shown 
in  the  development  of  {p-\-q  +  r)^.    And  so,  for  any  greater  number  of  events. 

The  terms  of  the  development  of  {p  +  q)"^  can  be  represented  by  the  ordinates  of  a 
curve,  termed  the  probability  curve.  And  the  maximum  term  is  proved  to  be  that 
which  has  7np  and  mq,  or  numbers  nearest  to  these,  for  the  exponents  of  the  factors 
p  and  q  respectively.  So  in  the  case  of  three  or  more  simple  events,  whose  probabilities 
are  p,  q,  r  . . . .  the  most  probable  combination  in  m  trials  is  the  maximum  term  of 
(^j  +  g  +  r-l-....)"*,  or 

1.2.3.4 m  ^„      ^„     ^^ 

1.2 mpxl.2 mq  xl.2. .  .mrx 

The  probability  curve,  here  described,  when  materially  simplified  for  large  numbers, 
has  been  made  the  foundation  of  the  "theory  of  errors  of  observations."  Also  its  mean 
area  has  been  tabulated  for  reference,  by  De  Morgan  and  others. 

7.  Mathematical  Expectation.  The  mathematical  expectation  of  a  contingent  gain, 
is  the  inoduct  of  the  sum  at  issue,  by  the  probability  of  receiving  it.  Or,  the  sum 
of  the  expectabions  of  gain,  diminished  by  the  sum  of  the  expectations  of  loss,  gives  the 
total  expectation.     If  the  chance  of  winning  $90  is  \,  the  expectation  is  90  x  \,  or  i?15. 

In  the  original  application  to  games  of  hazard,  the  conditions  of  equal  play  not  only 
required  the  mathematicat  expectations  to  he  equal,  but  also  required  the  option  of 
continuing  the  game  through  a  given  series  of  trials.  If  p  denotes  the  chance  that  A 
will  win  the  sum  a  from  B,  and  q  denotes  the  chance  that  B  will  win  the  sum  b 
from  A,  at  each  trial,  then  the  first  condition  of  equahty  requires  that  pa  =  qb ;  or 
a  :  b '.:  q '. p.  That  is,  if  the  number  of  trials  is  not  limited,  the  stakes  must  be 
mversely  proportional  to  the  probabilities  of  winning  in  each  single  trial. 

In  the  historic  problem  proposed  to  Pascal :  Two  persons  of  equal  skill  (that  is, 
p  —  q  =  \)  sit  down  to  play  on  condition  that  the  one  who  first  gains  three  games 
shall  win  the  stakes.     The  first  has  gained  two  games,  and  the  second  one  game,  when 


236  LIFE  ANNUITIES   AND    INSURANCES. 

they  agree  to  separate.  What  share  is  each  entitled  to  take  ?  Not  equal  shares  ;  but 
the  stakes  must  be  divided  proportionally  to  the  probabilities  of  winning  the  un- 
finished games. 

By  Principle  4,  the  probability  of  the  second  player's  winning  the  next  two  games 
is  ^.  By  Principle  5,  the  probability  of  the  first  player's  winning  the  next  game  is  \ ; 
that  of  losing  this  game  and  winning  the  second,  \,  total  f .  So  that  the  share  of  the 
second  is  \ ;  and  of  the  first,  J ;  being  proportional  to  their  respective  chances  of  finally 
winning  the  stakes. 

At  the  present  day,  these  early  problems  are  still  valuable  as  miniature  illustrations 
of  the  correct  principles,  which  govern  in  questions  of  Insurance  reserves  and  the  dis- 
tribution of  surplus.  The  danger  in  practice,  generally  lies,  as  was  illustrated  by 
Demoivre,  in  ignoring  just  distinctions  and  liabilities,  such  as  the  effect  of  unexpired 
times  and  conditions. 

8.  Moral  Expectation.  In  the  solution  of  problems  relating  to  games  of  chance, 
it  was  noted  at  an  early  period,  that  in  many  cases,  the  numeric  expectation  was  an 
insufilcient  guide,  and  other  circumstances  must  be  taken  into  account.  Among  these 
various  conditions,  the  amount  of  capital  of  the  party  interested,  was  generally  the 
most  important.  In  the  great  majority  of  cases,  the  relation  between  the  capital  and 
the  risk,  proposed  by  Daniel  Bernoulli,  has  led  to  very  satisfactory  conclusions.  This 
principle  more  plainly  stated,  is,  that  when  the  absolute  value  of  the  capital  increases 
in  geometrical  progression,  its  relative  advantages,  termed  the  moral  value,  increase 
not  so  fast,  but  in  arithmetical  progression.  Or  the  relation  in  the  first  case,  is  that  of 
numbers,  and  in  the  second  case,  that  of  their  logarithms. 

Formula. — Let  a  denote  the  original  capital.     Let  e  denote  the  mathematical,  and  e'  the  moral 

expectation  of  the  contingent  gains  h,k,l, of  which,  the  respective  probabilities  are  p,q,r, 

It  is  assumed  that  p  +  q-\-r-\- =1,  so  that  one  or  other  of  the  events  will  certainly  happen.    By 

Principle  7,  we  have 

e  =:ph  +  qk  +  rl+ 

To  tliis,  adding  the  identical  equation  a  =  {p  +  g  +  r+ )a,  we  obtain  under  another  form,  the 

capital  and  mathematical  expectation 

a.  +  e=p(a  +  h)  +  q{a  +  k)  +  iia  +  r)  + 

Changing  from  absolute  to  moral  values,  or  from  amounts  to  their  logarithms,  as  above  described, 
and  from  e  to  e',  we  thus  define  the  moral  expectation  : 

\og{a  +  e')  =  p]og{a+h)  +  qlo^a  +  k)  +  rlog{a  +  l)+.... 

Or  passing  from  logarithms  to  numbers, 

a  +  e'  =  (a  +  h)p.{a+kyi.{a+iy 

Since  a  +  h  —  all  +  -\,  and  p  +  q  +  r+ =1,  we  find  by  developing  either  of  the  last  equations 

in  series, 

e'  =ph  +  qk  +  rl+ —^ph^+gk^  +  rP  + )+ 

The  sum  of  the  first  powers  in  this  series  is  identical  with  e  as  stated  above ;  so  that  the  moral 
expectation  of  a  gain  is  less  than  the  mathematical ;  while  that  of  a  loss  is  greater. 

When  the  moral  expectation  is  thus  expressed  by  an  Algebraic  formula,  the  chief 
advantage  appears  in  the  facility  with  which  the  parts  can  be  varied  to  bring  up  the 
value  of  the  expectation  to  its  maximum.  Thus  from  the  last  formula  of  the  Note 
above,  it  appears  that  when  the  risks  of  an  Insurance  Office  are  so  numerously  dis- 
tributed, and  each  one  is  so  small  in  comparison  Avith  the  capital,  that  the  higher  powers 

h%  F, may  be  neglected  in  comparison  with  the  first,  the  moral  expectation  attains 

its  maximum,  and  the  most  favorable  disposition  of  the  chances  is  so  far  realized. 


LIFE   ANNUITIES   AND    INSURANCES.  237 

The  general  precept  known  in  commerce  under  the  name  of  Distribution  of  Risk, 
immediately  follows,  in  connection  with  that  of  the  selection  or  rejection  of  risks. 

From  the  problems  relating  to  games  of  chance,  the  moral  expectation  appears  to 
be  always  less  than  the  mathematical.  Hence  the  obvious  consequence  that  betting, 
gambling  and  lotteries  are  attended  with  moral  disadvantage,  even  when  the  chances 
of  gain  or  loss  are  perfectly  equal.  As  Prof.  De  Morgan  has  remarked,  "it  does  not 
follow,  that  equal  play  means  prudent  play." 

Among  other  illustrative  problems  of  this  theory,  is  one  for  determining  the 
amount  of  capital  which  an  individual  should  possess  in  order  to  be  morally  indifferent 
whether  he  insures  or  not.  When  the  amount  of  capital  is  below  this  limit,  its  moral 
value  may  be  advanced  by  insurance,  even  when  the  premium  exceeds  the  mathematical 
value  of  the  risk. 


SECTION     II. 
The  Life  Table  and  Law  of  Mortality. 

An  important  application  of  the  system  of  Probability  to  give  increased  accuracy  to 
the  ratios  of  mortality  or  loss,  by  final  series,  has  already  been  described  on  pages  35-38. 
By  this  method,  the  annual  ratios  by  Lives  and  by  Amounts,  for  Male  and  for  Female 
Life  were  severally  computed  from  the  experience  of  the  Thirty  Offices.  According  to 
Principle  3  of  Probability,  the  ratios  of  loss  or  of  mortality,  denoted  by  q,  when  sub- 
tracted from  unity  give  1 — q  or  p,  the  annual  probability  of  surviving  one  year.  Let 
p,  p',  p" .  . . .  denote  the  tabular  probabilities,  thus  found  from  the  Amounts,  of  sur- 
viving from  the  age  of  10  to  11,  11  to  12,  12  to  13,  and  so  on.  Then  assuming 
100,000  to  enter  at  the  precise  age  of  ten  years,  by  Principle  4  of  the  last  Section,  the 

numbers  surviving  at  the  ages  10,  11,  12,  13, will  be  100,000,  100,000  p,  100,000 

pp',  100,000  pp'  p",  and  so  on  to  the  oldest  age,  near  100  years.  The  results  are  based 
on  the  fourth  columns,  pp.  159, 164.  The  standard  Tables  XXVI  and  LXXVII  were 
thus  constructed  from  the  ratios  of  Amounts  with  slight  adjustment  in  a  few  instances 
toward  the  extremes,  from  the  ratios  of  Lives.  The  graduation  of  the  table  for  Female 
Life,  on  account  of  small  numbers  above  the  age  of  seventy,  was  aided  by  comparison 
with  other  larger  collections,  and  then  adjusted  by  the  method  of  Woolhouse  as 
described  in  the  Journal  of  the  Institute  of  Actuaries,  Vol.  21,  p.  45. 

In  the  Table  XXVI  for  Male  Life,  the  values  from  age  ten  to  ninety  years,  were 
calculated  by  the  well-known  law  of  Makeham,  taking  the  ungraduated  values  of 
^2«j  Im  hi,  Aoj  as  data.  The  unknown  q  is  found  first,  by  taking  the  differences  of  the 
four  equations  once  and  again  ;  and  then  dividing  the  last  two  equations,  one  by  the 
other.     The  formulas  and  constants  are  as  follows: 

Ix  =  k.  s^.g^,        Xlx  =  •^^*  +  xXs  +  q^.  Xg. 

A^  =  Xpx  =  Xs-\-q^{q  —  1)A(/.  Xh  —  5.028244,       >\  —  Xg)  =  4.475241. 

5  =  0.9936957,        5^  =  0.9993122,        ^  =  1.099713375. 

As  =  L99725340,        a(7  = —0.000298773,        A^  =  0.041279507. 

Nap.  log.  s  =  —0.00632429,        Nap.  log.  g  =  —0.0006879505 
Nap.  log.  ^  =  0.095050036. 


338  LIFE  ANNUITIES   AND    INSURANCES. 

The  integer  results  computed  from  this  formula,  terminated  with  only  2  persons 
living  at  the  age  of  101  years ;  and  their  close  agreement  with  the  uugraduated  values 
secured  their  entire  adoption,  with  a  slight  change  above  the  age  90,  so  that  the  Table 
ends  at  the  age  of  99  years. 

Here  the  inquiry  arises,  why  should  this  Table  of  Male  Life  from  the  experience 
of  Thirty  Offices,  spontaneously  conform  to  Makeham's  law  of  mortality,  while  previous 
Tables  showed  very  considerable  dcA-iations?  In  explanation,  the  following  circum- 
stances may  be  noted ;  first,  that  the  observations  were  far  more  numerous  than  any 
previous  collection  of  life  insurance  statistics,  and  comprised  nearly  a  million  of 
entrants.  Second,  that  the  observations  were  nearly  homogeneous,  in  respect  to  the 
agencies,  medical  examinations,  climate,  nationality,  education,  and  habits  of  living. 
Third,  that  the  observations  were  reduced  with  the  greatest  care  by  select  clerks,  and 
the  results  always  verified  by  two  independent  operations.  Fourth,  that  they  contain 
the  first  application  of  the  improvement  in  construction  by  final  series,  already  men- 
tioned.    Fifth,  that  the  observations  are  essentially  free  from  the  mis-statement  of 

ages  adjacent  to  30,  35,  40,  45,  50, years,  a  common  source  of  error  in  population 

returns. 

The  present  collection  also  determines  the  fluctuating  nature  of  climacterics,  or 
periods  of  health  and  sickness,  at  the  different  ages  of  life.  Physicians  assert  the 
existence  of  periodic  alternations,  more  or  less  regular,  of  health  and  disease,  observed 
in  their  own  persons,  and  in  their  professional  practice.  It  is  like  the  surface  of  a 
body  of  water,  disturbed  by  the  wind  or  other  causes,  and  taking  the  form  of  waves, 
having  like  periods  of  oscillation.  And  as  the  force  of  gravitation  by  insensible 
degrees,  causes  the  waves  gradually  to  subside,  so  does  the  innate  vital  force  tend,  from 
conditions  of  disease,  to  the  original  conditions  of  health.  Detached  portions  of  the 
present  statistics,  will  show  these  fluctuations ;  an  increase  of  mortality  at  one  age, 
being  followed  by  a  decrease  at  a  future  age,  and  conversely.  The  manifestations  prove 
to  be  so  different  in  particular  individuals,  that  in  the  average  of  several  hundred 
thousands,  the  opposite  fluctuations  compensate  each  other,  leaving  in  adult  life,  only 
the  mathematical  law  before  stated. 

Down  to  the  present  time,  the  statistics  of  life  tables  have  been  regarded  in  practice 
merely  as  observations,  with  irregularities  to  be  smoothed  down  and  graduated  like  any 
other  set  of  observations. 

For  a  particular  account  of  the  earlier  life  tables,  reference  can  be  made  to  the 
original  publications,  or  to  Walforcls  Cyclopcedia,  or  to  the  Journal  of  the  Institute  of 
Actuaries.  In  respect  to  the  mathematical  law  of  mortality,  the  celebrated  Demoivre 
first  observed  that  the  portion  of  the  life  table  between  the  ages  of  22  and  86  years, 
was  approximately  represented  by  the  simple  formula,  I  =  86— a:;  where  I  denotes  the 
number  living  at  the  age  x.  This  appeared  in  the  year  1727.  Different  formulas  were 
subsequently  prepared  or  published  by  Lambert  in  1776;  by  Babbage  in  1823;  by 
Thomas  Young  in  1826;  by  Littrow  in  1832;  by  Moser  in  1839;  and  by  Orchard 
before  1856.  But  the  chief  interest  centers,  upon  the  formula  of  Gompertz,  published 
in  the  Philosophical  Transactions  of  1825 ;  and  upon  Makeham's  modification  of  it, 
which  appeared  in  1859  in  the  Assurance  Magazine  or  Journal,  Vol.  8,  p.  301. 

Gompertz's  formula  is  Ix  =  h-gi^'',  Makeham's,  Ix  =  k.g^.S^. 

Here  I  denotes  the  number  living  at  the  age  x,  and  k,  g,  q,  s  are  constants  to  be 
derived  from  the  observations.     Now  with  reference  to  the  usual  expression  of  force 


LIFE  ANNUITIES   AND   INSURANCES.  239 

in  the  science  of  Mechanics,  taking  the  Napierian  logarithms  of  either  formula,  and 
diflferentiating  twice,  we  find  the  relative  Force  of  Mortality 

That  is,  in  the  average  of  a  great  number  of  adult  males,  the  relative  force  of 
mortality,  increases  regularly  with  advancing  age,  in  geometrical  progression. 

But  the  chief  value  of  this  law,  like  that  of  the  law  of  gravitation,  is  found  in  its 
relations  to  analysis.  Integrating  the  last  formula,  we  obtain  by  adding  the  usual 
constant,  the  Instantaneous  Rate  of  Mortality,  computed  in  Table  XLIII : 

^"^  ~ ^^  ~  -log.S-log.^r.log.gr.^a'. 

^a.=  — ^  =  1.187753  X  A— +1.114833x^1. 

IxdX  J)3^1  px 

f^x  =  Hk=l-A-Az^^^:=J^^  nearly. 

When  the  quantities  are  determined  from  four  fixed  ages,  as  25,  40,  55,  70  years, 
the  common  Log.  q  is  found  to  have  almost  the  same  value  0.04  in  all  collections.  But 
the  constant  s  changes  from  one  table  or  latitude  to  another,  and  representing  the 
uniform  influence  of  exterior  causes,  may  be  named  the  climatic  constant.  Also  in 
certain  cases,  s  may  be  used  to  represent  an  auxiliary  or  relative  rate  of  interest. 

Having  found  the  law,  par  excelletice,  of  adult  mortality,  above  the  age  of  22  years, 
we  have  extended  the  same  law,  in  Table  XXVI,  down  to  the  age  of  ten,  to  represent 
the  very  few  and  exceptional  insurances  contracted  at  the  youthful  ages.  With  more 
complete  statistics,  like  the  results  of  the  census,  we  might  extend  the  same  law  down 
to  the  birthday,  and  compare  with  the  ungraduated  values,  to  indicate  the  residual 
series  or  law  in  infancy  and  youth. 

A  numerical  example  of  this  kind  was  given  by  the  writer  in  the  thirteenth  Report 
of  the  Insurance  Commissioner  of  Massachusetts,  for  the  year  1868,  page  106.  Aided 
by  this  and  some  further  data,  Mr.  Makeham  happily  completed  his  formula  down  to 
the  birthday,  as  described  in  the  Journal  of  the  Institute  for  1871,  Vol.  16,  page  344. 
Thus,  for  the  entire  period  of  Male  Life,  the  number  living  I  in  the  life  table,  at  any 
age  X  is 

lx  =  k.  g<f.  s^—kx.  gx'f.  si^  +  la .  gz^.  s^. 

Since  the  middle  term  vanishes  about  the  age  of  20,  and  the  last  term  vanishes  at 
the  age  of  7  or  8 ;  the  first  term,  or  rather  the  constants  k,  g,  q,  s  are  computed  from  ages 
above  20,  as  previously  described  on  page  237.  The  value  of  q  remaining  the  same,  the 
maximum  residual  at  age  6  or  7,  and  the  residuals  at  3  and  6  years  older,  define  k\,  g\,  s\. 
And  the  final  or  second  residuals,  at  ages  0,  1,  2,  determine  k^,  g-2,  sg- 

In  seeking  for  the  physical  cause  or  causes,  the  analogy  of  "latent  and  sensible 
heat "  is  first  suggested,  in  a  general  way.  For  in  children,  the  sensible  part  of  the 
bodily  temperature  is  stated  to  slowly  decline  from  birth  until  about  the  sixth  year  of 
age.  After  this,  it  gradually  increases  until  maturity,  and  then  slightly  declines  again, 
as  old  age  advances. 

Let  us  further  observe  that  when  complete  life  tables  have  been  referred  to  three 
or  four  exponentials,  as  computed  by  the  writer,  one  of  the  exponentials  always  cor- 
responds with  that  of  Makeham's  formula  in  adult  life,  while  the  rest  take  the  fonn  of 


240  LIFE   ANNUITIES   AND    INSURANCES. 

exponential  waves,  such  as  hc^ .cos>.{ax-\-a').  But  in  adult  life,  considered  separ/itelv, 
these  waves  are  so  discordant,  dissimilar  and  evanescent  in  different  Tables,  that  they 
must  disappear  in  the  average  of  a  very  great  number,  as  already  shown  numerically 
by  the  present  statistics. 


SECTION     III. 
Present  Value  of  Life  Annuities. 

The  early  history  of  Annuities  on  Lives  is  given  in  the  various  memoirs  of  the 
Assurance  Magazine,  and  in  Walford's  Insurance  CyclopcBdia,  art.  Annuities  on  Lives. 
Like  some  occasional  applications  in  modern  times,  the  earliest  dealings  rested  on  mere 
conjectural  estimates.  The  growth  of  a  correct  system  is  associated  with  the  early 
Table  of  the  Prefect  Ulpian,  the  unpublished  State  papers  of  Johan  de  Wit  in  1671, 
the  papers  of  Dr.  Halley  in  the  Philosophical  Transactions  of  1693,  and  with  the  noted 
formula  of  derivation, 

ax  =  vpx{l  +  ax+TL), 

published  by  Demoivre  in  1725,  and  independently  by  Euler  in  1760.  The  system  of 
Commutation  Columns  was  next  perfected;  and  in  1849  Mr.  Peter  Gray  in  his  admirable 
Tables  and  Formulce,  gave  new  derivative  formulas,  and  improved  the  form  of  Gauss's 
Tables  for  finding  Log.(l  +  a,)  and  Log.(l— a;)  from  the  argument  Log.  x.  The  com- 
putation of  Tables  of  temporary  annuities  in  the  present  work,  for  example,  was 
especially  facilitated  by  Gray's  Tables.  For  the  calculation  of  a  large  class  of  applied 
results,  tl'ie  process  by  temporary  annuities  or  their  logarithms,  is  found  to  be  consid- 
erably shorter  than  by  commutation  columns. 

Further  improvements  relative  to  Annuities  on  Joint  Lives  and  Survivorships  have 
been  successively  derived  from  the  formulas  of  Gompertz  and  Makeham.  Also  "  the 
theory  of  continuous  annuities "  has  been  successfully  introduced  by  Mr.  Woolhouse 
in  connection  with  Euler's  formula  of  summation  or  quadrature,  as  described  hereafter. 
A  parallel  method  by  Mr.  Makeham,  for  determining  all  values  of  Life  Annuities  by 
integration,  has  been  given  under  an  improved  form  by  Mr.  Emory  McClintock. 
The  equivalent  formula  or  series  will  be  found  on  page  293. 

In  order  to  explain  how  Life  Annuity  Tables  are  calculated,  let  us  compare  the 
Present  Values  year  by  year,  as  follows : 

Years,  1  2  3  n 

Annuity  Certain,  Value  =     v        -\-     v^        +    v^ -\-       +     V^  +  . . . 

Life  Annuity,  Ux  =  -^—  •  v  +  -j-  •  v^  +  -j-  •  v^  +  ...  +  -^—  -tf^  +  ... 

Ix  ix  ix  'x 

Here  r,  r*,  v^,  etc.  represent  the  present  value  of  $1  due  at  the  end  of  the  Ist  year, 
of  II  due  at  the  end  of  the  2d  year,  of  $1  due  at  the  end  of  the  3d  year ;  and  so  on  to 

the  last.     If  i  denotes  the  rate  of  interest,  v  =  - — -:. 

1  +  1 

In  the  lower  formula,  -^  is  the  proportion  by  the  life  table,  or  probability  of 

Ix 

surviving  the  1st  year  to  receive  II  whose  present  value  is  v ;  hence  by  Principle  7, 
Sect  I,  the  product  -^  •  v  is  the  mathematical  Expectation  relative  to  the  Ist  year. 


LIFE  ANNUITIES   AND    INSURANCES.  241 

Again,  -—  is  the  probability  of  surviving  the  first  two  years  to  receive  the  next 

Ix 

payment  of  $1,  whose  present  value  is  vK    Hence  the  product  -^  •  v^  is  the  mathemat- 

Ix 
ical  Expectation   relative  to   the   2d  year;    and  so   on.      The   sum  of  these  yearly 
Expectations  is  the  present  Value  of  the  Life  Annuity,  Table  XXVIII. 

When  the  series  extends  over  but  5,  7, 10  or  n  years,  the  sum  is  called  a  Temimrary 
Life  Annuity^  or  Temporary  Annuity,  denoted  by  a^^S^,  to  continue  n  years  if  the 
annuitant  shall  so  long  live.  When  the  series  extends  to  the  end  of  the  life  table,  near 
100  years,  the  sum  is  termed  a  Life  Annuity,  denoted  by  ax.  "  With  present  pay- 
ment," the  expression  is  \-\-ax,  given  by  logarithms  in  Tables  XLIV-XLVII. 

From  another  point  of  view,  let  us  suppose  l^  persons  of  the  common  age  30  to 
buy  each  a  Life  Annuity  of  $1.  By  the  life  table  Z31  survive  to  the  age  31  to  receive 
each  the  first  payment  of  $1,  of  which  the  present  value  is  v,  and  total  present  value, 
/31  •  V.  In  like  manner  l^  will,  on  the  average,  survive  to  the  end  of  the  second  year, 
when  the  present  value  of  the  second  disbursements  will  be  l^-v^ ',  and  so  on. 
Dividing  the  sum  of  all  the  present  values  by  the  original  number  of  persons  /30,  to 
find  the  average,  ax,  we  obtain  the  same  formula  as  before, 

«30  = 


^30 

Recurring  to  the  general  formula,  let  us  observe  that  on  multiplying  and  dividing 
by  /a;+i,  which  does  not  alter  the  value, 

fa;-*-2        *a;  +  l    ^a;+2  ta;+3        fx+1    ^x+2    ^+3 

^—  =  -7— -7 =i?a;-i>a;+i;  'T~  —  ~i~  '  1 T —  =  Px-Px+l-Px+i'y  ••• 

ix  tx      I'X+l  IX  ix      <'x+l    tx+2 

Hence  when  the  annuity  is  expressed  in  annual  probabilities, 

ax  =  V.px  +  v'^.px.px+l-\-1^'Px'Px+l'Px^2+ 

Deferred  Annuity.  Let  the  present  value  of  $1  annuity  deferred  m  years  on  a 
life  now  aged  x,  be  denoted  by  "^Ux.  At  the  advanced  age  x  +  m,  the  value  of  a  life 
annuity  will  be  ax+m.     Multiplying  this  by  v"^  to  reduce  it  to  present  value,  and  by 

-^^,  the  probability  of  attaining  it,  we  have  the  value  of  the  deferred  annuity, 

„  'x+m      ^ 

""(ix  =  -J—  .  V"' .  ax^m. 
Ix 

By  examination,  it  will  be  seen  that  the  sum  of  the  temporary  and  the  deferred 
annuity  is  equal  to  the  whole  life  annuity;  that  is, 

a^  +  "*ffx  =  ttx ;        ax"*  =  ax— '^ax- 
Joint  Lives'.    The  probability  that  two  lives  aged  x  and  y,  shall  both  survive  one 
year,  is  ^^^~—,  being  the  product  of  their  separate  probabilities.    Hence  by  the  same 

reasoning  as  for  single  lives,  the  present  value  of  $1  annuity  payable  at  the  end  of  tach 
year,  during  the  joint  continuance  of  both  lives,  is  as  follows: 

„      _  Ix+l'^y  +  i  .V-\-lx+2.ly-i.2.v'^  \-lx^^'  ^y+S-V^  f 

axy  — j — J 

tx'  iy 

For  three  or  more  joint  lives,  the  formula  depends  on  the  same  simple  principle. 


242  LIFE   ANNUITIES   AND   INSURANCES. 

Annuity  on  Three  Lives  hy  Simpson's  Rule.  From  Tables  for  one  and  two  lives, 
the  annuity  for  three  lives  was  approximately  determined  by  the  author  T.  Simpson  in 
1701,  as  follows :  "  Take  the  value  of  an  annuity  on  the  joint  lives  of  the  two  oldest, 
and  find  the  age  of  a  single  life  of  the  same  value.  Then  find  the  annuity  on  the  joint 
lives  of  the  one  just  found,  and  the  remaining  life  of  the  three,  and  the  result,  (which 
Francis  Baily  diminished  by  .05),  will  be  very  nearly  the  true  value."    Table, page  260. 

Professor  De  Morgan  proved  that  Simpson's  method  would  be  strictly  true,  if  the 
Table  followed  the  law  of  mortality  of  Gompertz.     {Journal,  Vol.  10,  p.  27.) 

Half-yearly  and  Quarterly  Aiinuities.  When  the  annuity  is  changed  from  annual 
to  half-yearly  installments,  add  .25  ;  and  when  to  quarterly  installments,  add  .375  to 

fifi \ 

the  tabular  value  of  the  annuity.     Or,  generally  add  ~ ,  when   the  installment  is 

payable  m  times  a  year,  as  demonstrated  on  page  70.  Thus  the  value  $14. 662  of  II 
annual  payment  is  changed  to  14.912  for  half-yearly  installments  of  $0.50,  and  to 
51.037  for  quarterly  installments  of  $0.25.  The  more  exact  formula  by  Woolhouse  for 
the  value  of  an  annuity  payable  m  times  a  year  is  {Journal,  Vol.  11,  p.  327), 

m — 1      m^ — \,        .. 
«-+-2^-l2^('^  +  ^)- 

And  Mr.  Spra^Tie's  formula  for  the  value  of  a  complete  annuity,  payable  by  m 
equal  installments  in  each  year,  with  a  proportionate  part  to  the  day  of  death  is 
{Journal,  Vol.  13,  pp.  377-380), 

.  i.'iiiUi-— U-- 

"^^       12  /  ^       2m/"^12m2* 

Here  ii-=  —  -r-  log.  Ix  ■=  {lx—\—lx+\)-^'^lx  nearly  ;   6  =  Nap.  log.  (1-f  0'  ^"^  *  = 

rate  of  interest.    The  values  of  /*,  d  are  given  in  Table  XLIII. 

From  the  present  value  for  1,  the  value  for  any  other  sum  is  found  by  multiplying 
the  value  for  1,  by  the  actual  annuity  or  yearly  income.  The  further  consideration  of 
Life  Annuities  is  deferred  till  after  the  system  of  Commutation  Columns  described  in 
Section  V. 


SECTION     IV. 
Expectation  of  Life  and  Probable  Life. 

The  phrase  Expectation  of  Life  has  long  been  used  to  denote  the  after-life- time,  or 
average  number  of  years  and  the  decimal  part,  lived  after  a  given  age. 

Let  Ix  denote  the  number  living  shown  in  the  life  table  at  the  age  x.  Assuming 
the  deaths  of  each  separate  year  to  occur  uniformly,  the  number  of  years  lived  in  the 
first  year,  second  year,  third  year, will  be 

Ix-^lx+l  .  lx+l-\-lx+i  .  lx+2-\- Ix+S  , 
'2       "^  2         "^  2'     +•••■ 

Taking  the.  sum  of  the  contiguous  terms  continued  to  the  oldest  age  or  end  of 
the  life  table,  and  then  dividing  by  Ix  to  give  the  average,  we  obtain  the  common 
formula  for  the  expectation  of  life,  denoted  by  e : 

1  ,  ix+i-\-lx+si-\-lx+3-\- '  •  •  • 


l. 


LIFE   ANNUITIES   AND    INSURANCES.  243 

Hence  the  Rule :  Divide  the  sum  of  the  tabular  numbers  living  above  the  given 
age,  by  the  number  living  at  the  age,  and  to  the  quotient  add  ^  year. 

For  example,  the  expectation  of  life  at  the  age  95  by  Table  XXVI  is  found  to  be 

eyn  =  IH j^ =  1.338  or  1^  years,  nearly. 

To  demonstrate  the  derivative  formula,  let  a:  +  l  be  substituted  in  place  of  re  in  the 
formula  above;  then  clearing  of  fractions,  and  subtracting  one  equation  from  the 
other,  we  find 


ex+i  =  o  + 


1   ,   'a;  +  8+^a!+3  +  ^a;+4  + 


2  lx+1 

In  the  formulas  of  Section  III  for  Life  Annuities,  if  we  make  v  =  1,  that  is, 
1  =  0;  we  obtain  what  is  termed  "the  curtate  expectation  of  life."  In  the  case  of 
single  lives,  it  is  the  quantity  here  denoted  by  ex—^,  and  expresses  thei  average  number 
of  complete  years  to  be  lived,  or  of  annuities  received,  or  of  annual  premiums  to  be 
finally  paid. 

Again  making  v  =  1  in  the  formula  for  Joint  Life  Annuities,  we  obtain  the  curtate 
expectation  of  the  jomt  life,  denoted  by  exy—\  ;  where  the  complete  expectation  is 
denoted  by  exy.  According  to  "  the  continuous  theory,"  the  tabular  expectations  usually 
given,  slightly  exceed  the  true  values,  by  one-twelfth  of  p^x- 

For  comparing  the  longevity  of  different  Life  Tables,  let  the  particular  expectation 
of  life  which  is  just  equal  to  the  age  past,  be  termed  the  even  expectation.  By  the 
Thirty  Offices  Table  XXVI,  at  the  age  33.37  years,  for  example,  the  even  expectation 
or  mean  duration  of  future  life  is  also  33.37  years.  In  like  manner,  the  even  expecta- 
tion of  the  Carlisle  Table  is  32.62  years ;  of  the  table  of  Des  Parcieux  32.49 ;  of  the 
Equitable  Society  by  Davies  32.38 ;  of  the  British  government  Male  Annuitants  32.00; 
of  the  Female  Annuitants  34.58 ;  and  of  the  Northampton  Table  by  Dr.  Price  28.86  years. 
The  shorter  the  even  expectation  or  half-interval,  the  shorter  will  be  the  whuie  and  other 
connected  intervals  of  life  in  the  same  Table,  as  shown  in  Tables  XXVI  and  LXXX. 

A  prevalent  error  on  the  part  of  persons  imperfectly  versed  in  these  matters,  con- 
sists in  calculating  life  annuities  and  other  similar  results,  from  the  expectation  of  life. 
At  the  age  of  29  years,  for  example,  the  true  present  value  of  a  life  annuity  by  the 
Carlisle  Table  at  4  per  cent,  is  16.997 ;  as  found  empirically  from  the  expectation  of 
hfe,  it  is  18.665,  which  is  too  great  by  one-tenth  part.  The  nature  of  this  erroneous 
practice  may  be  further  explained  by  comparison  of  the  preceding  formulas  for  life 
annuities  and  for  expectations,  which  are  evidently  designed  for  separate  objects. 

Probable  Life.  At  any  given  age,  "  the  probable  life  "  or  "  vie  probable  "  denotes 
the  future  period,  which  there  is  the  chance  ^  of  surviving,  and  the  chance  ^  of  not 
surviving  ;  these  chances  being  equal.  Let  x  and  x-{-  7" denote  any  two  ages  of  the  life 
table,  connected  by  the  relation,  \lx  =  Ix-^t',  then  will  the  difference  of  ages  T  denote 
the  probable  life  at  the  age  x.  The  column  of  Probable  Life  in  Table  XXVI  was 
computed  by  the  preceding  formula.  In  this  Table  at  the  age  of  thirty,  for  example, 
the  probable  life  is  38.48  years,  which  is  2.63  years  more  than  the  expectation  of  life  at 
that  age.  But  at  the  age  of  57|,  the  expectation  and  the  probable  life  become  equal  to 
each  other  in  the  common  period  of  16.61  years;  and  at  older  ages,  the  expectation 
exceeds  the  probable  life. 


244 


LIFE  ANNUITIES   AND    INSURANCES. 


A  remarkable  agreement  of  the  probable  life  of  males  and  females  combined,  was 
observed  by  the  distinguished  Professor  Quetelet,  in  comparing  the  tables  for  England 
by  Farr,  Sweden  by  Berg,  Belgium  by  Quetelet,  Netherlands  by  Baumhauer,  and 
Bavaria  by  Hermann.  All  Europe,  he  observes,  as  will  be  seen  by  the  following 
columns,  follows  a  law  of  mortality  nearly  the  same  ;  and  the  slight  differences 
between  the  results  above  five  years  of  age,  appear  due  to  particular  advantages 
arising  from  opulence,  and  a  more  regular  mode  of  life.  {Physique  Sociale,  1869, 
Vol.  1,  page  307.) 

YEARS    OF    PROBABLE    LIFE    IN    EUROPE. 


Ages. 

Sweden. 

England. 

Belgium. 

Netherlands. 

Bavarla. 

Ate RAGE. 

0 

51 

45 

42 

34 

27 

40 

5 

56 

55 

53 

53 

53 

54 

10 

53 

51 

50 

50 

50 

51 

15 

48 

47 

46 

46 

45 

46 

20 

43 

43 

43 

42 

41 

42 

30 

35 

35 

35 

34 

34 

35 

40 

27 

27 

27 

26 

26 

27 

60 

19 

20 

20 

19 

18 

19 

60 

18 

13 

13 

12 

13 

13 

70 

7 

8 

7 

7 

7 

7 

80 

4 

4 

4 

3 

4 

4 

SECTION     V. 
Comimitation  Tables. 

Statistics  are  ancient,  but  their  scientific  forms  are  modem,  as  Professor  Quetelet 
has  observed.  The  origin  of  commutation  columns,  or  preparatory  researches  from 
which  the  system  was  at  length  perfected,  were  published  by  William  Dale  in  1772, 
William  Morgan  in  1779,  .John  Nicholas  Tetens  in  1785,  George  Barrett  in  1812,  and 
Griffith  Davies  (who  added  the  M  and  R  columns),  in  1825.  The  work  of  David  Jones 
in  1844  was  the  first  to  give  an  extended  series  of  commutation  tables ;  and  his  notation 
is  still  followed  in  the  Journal  of  the  Institute  of  Actuaries.  Indeed  all  subsequent 
writers  retain  the  D,  0,  M,  R  columns  on  the  same  plan.  But  it  is  very  needful  to  bear 
in  mind,  that  in  the  Tables  of  Dr.  Farr,  Chisholm,  Henry  and  most  American  actu- 
aries, the  N  and  S  columns  only  are  shifted  down  one  space ;  so  that  Na;  and  Sx  denote 
the  same  quantities,  which  David  Jones  had  designated  by  N»i_i  and  S^-i-  However, 
by  simply  adding  1  to  the  suffix  of  N^^-i  and  S^-i,  the  formulas  of  Jones  and  of  the 
Journal  will  evidently  coincide  with  the  change  of  Dr.  Farr,  which  under  present 
circumstances,  is  adopted  in  this  collection. 

The  name  of  Commutation  Tables  was  proposed  by  Professor  De  Morgan  in  1840, 
He  had  noticed  the  singular  property,  that  on  transposing  or  commuting  any  two  ages, 
say  30  and  34,  whatever  may  be  the  present  age,  if  less  than  30,  the  person  might  now 
give  up  IDm  due  at  the  age  of  30,  to  receive  IDao  if  he  lives  to  be  34.  Similar  prop- 
erties belong  to  the  N  and  other  columns.    Journal,  Vol.  12,  p.  332. 


COMMUTATION   TABLES.  245 

Proceeding  now  to  explain  the  D  and  N  commutation  columns,  let  us  refer  to 
Sect.  Ill,  and  multiply  both  numerator  and  denominator  of  the  expression  for  the  Life 
Annuity  by  the  same  factor  v^,  which  does  not  alter  the  value, 

Ox  = 


Ox 


Ix.V^ 


Dx  ~    D«,  • 


Thus  the  formula  is  entirely  resolved  into  similar  elements,  of  the  type  'Dx=^lx-if^. 
And  Na5+i  denotes  the  sum  of  the  terms  of  the  numerator  continued  to  age  99,  or  to 
the  end  of  the  life  table.  The  letters  N,  D,  appear  to  be  chosen  from  the  words 
Numerator  and  Denominator.  A  Temporary  Life  Annuity  for  3,  or  more  generally  n 
years,  will  evidently  have  the  expression,  where  the  exponents  3,  n  are  used,  (not  in  the 
Algebraic  sense  of  powers),  but  simply  to  denote  so  many  years  after  entry, 


<    = 


Da;  +  l  +  Dx+2  +  Da;+3  _  Na;+1  — Na!+4  ^  _  Na;+i  — ]S"a;+n+l 

D;.  -  Da,        '         ''«'-  D^  • 


Again,  referring  to  Section  III,  and  multiplying  both  numerator  and  denominator 
by  If',  the  Deferred  Life  Annuity  takes  the  surprisingly  simple  form, 

n/»    —  ^«+»  •  ■^''""     «        _  ^x+n   Nar+n+l  _  '^x+n+1 
lx-1^  yJx       Dar+n  Dx 

The  results  already  described,  will  exemplify  the  superior  advantage  of  commuta- 
tion columns,  for  determining  the  value  of  Life  Annuities,  whether  immediate  or 
deferred,  for  the  whole  life,  or  a  portion  of  it.  So  manifest  have  these  advantages 
appeared,  that  all  the  standard  formulas  of  Life  Annuities  and  Assurances  have  been 
resolved  into  similar  elements.  In  all,  six  columns  are  required ;  whereof  D,  N,  S  are 
termed  annuity  columns,  and  0,  ,M,  E  are  termed  insurance  columns.  These  columns 
are  connected  with  each  other,  by  the  following  simple  relations : 

Let  V  = r,  where  i  denotes  the  rate  of  interest ; 

1+* 

dx  =  Ix — ^^+1,  where  x  denotes  the  age,  d  the  deaths,  /  the  living  in  the  -life 

table ;   then, 

'Dx  =  Ix.v^;  Cx  =  dx.  v^+i  ={lx-  Ix+i)  v»+^. 

.Na,  =  D«,  +  D«,+i  +  Da,+2+ Ma,=   Ca,+  Ca,+1+  0«,j.2+ •  • 

Sir  =  N'«,  +  N"a,+i  +  N«,+2+  ....  Ra,  =  Ma,  +  Ma,+i  +  Ma,+2  +  .... 

Each  series  is  to  be  continued  to  the  end  of  the  life  table.  By  writing  x+1  ia 
place  of  X,  and  then  eliminating,  we  find, 

Nfl,  =  Da,  +  N«,+i ;  Ma,  =  Co,  +  Ma,+1. 

Sa,  =  Na5+  Sa,+1  ;  Ea,  =  M«,  +  Ea,+1. 

In  the  former  equations  for  S  and  R,  substituting  in  place  of  N  and  M  the  series 
of  D  or  C  which  they  represent,  and  adding,  we  have 

Sa,  =  Da,-l-2Da,+i  +  3Da,+2+  .  .  .  .  ;  £«,  =  Ca,  +  20«,+i  +  3Ca,+8+  .... 


246  LIFE   ANNUITIES  AND    INSURANCES. 

Note. — By  differentiating  the  life  annuity  in  Section  III,  etc.  with  respect  to  v,  we  also  have 

^     ^Sx+i,  d/Nx\     Sx.  dm^\      Rr 

dv         «Dx  '  dv\v^^}     vx'  dv\vx/~'cf+^' 

Again,  for  temporary  periods, 

Na,  —  Na,+„  =  Da,  +  Da,+l  + +  Dx+t^h 

Mflj — Mx+n  =  Cas  +  Ca;+i  +  .  .  .  .  +  Caj+n—l. 

=  Da,  +  2Da,+i+ +n.  Da,+n-l+W.  Na^Hi. 

Ee— Ea>+n=  Ma,+  Ma.+1  +  •  •    •  +M«,+„_i 

=  Cfl,  +  2Ca!+l+ +Jl.Cx+n-l  +  n.'M.g>+n. 

When  C,  M,  R  are  not  tabulated,  their  values  can  be  derived  from  v,  D,  N,  or  S, 
by  the  following  relations : 

Making  x  to  represent  in  separate  equations,  x,  x-{-l,x-{-2,  ....  and  taking  the 
sum  of  results, 

M«,  =  f.  No,-Na,+i  =  Da,-(l-i;)Na> 

Again  making  x  to  represent  x,x-\-l,x  +  2, and  taking  the  sum  as  before, 

Ea)  =  'y  .  S<B— S(B+1  =  Na,— (1  — y)Saj. 

Construction  of  Commutation  Tables.  Among  various  methods,  the  ^rs^  proceeds 
by  independent  computation  of  Cx  or  Dj  by  six  or  rather  seven  place  logarithms,  in 
columns,  according  to  the  formulas. 

For  this  object,  the  common  logarithms  of  the  factors  V,  h,  dx  are  already  given 
in  Tables  XXV  and  XXVII.  The  process  of  adding  these  logarithms,  may  be  proved 
by  comparing  the  sum  of  every  ten  results,  with  the  corresponding  sum  obtained 
directly  from  the  Tables.  To  facilitate  this  mode  of  Proof,  the  sum  of  each  ten 
logarithms  is  added  in  Table  XXV.  The  numbers  answering  to  the  logarithmic 
results,  have  been  usually  found  from  Filipowski's  seven  place  Table  of  Anti- 
logarithms. 

A  second  method  devised  by  Gray,  takes  advantage  of  the  simple  factor  (1+*)  or 
1-T-i'  for  determining  D^,  after  the  column  Cx  has  been  previously  constructed ;  thus, 

Dx  =  (H-0(Dx+i  +  Cx). 

For  example,  by  the  Thirty  Offices  Table,  with  4  per  cent,  interest,  Dioo  =0; 
and  Cioo  =  0 ;  then, 

i399  =  1.04  C99  =  .082368  ;  C99  =  .079200 

D98=1.04(D99  +  C98)  =  .256988;  etc.  x.04=       3168 

1. 04099  =  .  082368 


COMMUTATION   TABLES.  247 

The  operation  is  easily  applied  with  eight  decimal  places,  and  is  continuous,  so 
that  the  separate  computation  of  Da,  at  every  tenth  or  fifteenth  value  will  verify  the 
whole  series. 

A  third  method  proceeds  entirely  by  continuous  operations  with  logarithms  and 
Gray's  Table  of  Log.(l+a:),  according  to  the  formulas, 

Da,+1  =  VpJ)„.  Ca,+i  =  V^^Ca,. 

(Ix 

N«,=  Da,  +  N-a,+i,  ANa,  =  ADa,  +  ;i(l  +  ^*). 

Ma,+l 


Ma,=  Ca,  +  Ma;+i,  AM^  =  ;iCa, +  /-(!+ -Q—y 

In  all  cases,  when  the  elementary  columns  D  and  C  have  been  fully  constructed, 
the  N  and  M  columns  can  be  formed  from  them,  by  successive  additions;  or  by  the 
previous  logarithmic  formulas,  in  connection  with  Gray's  Table ;  and  so  with  the  S 
and  R  columns.  The  logarithm  of  vpx  is  already  given  in  Table  XXXIII;  and  a 
column  for  Mx+i — ^dx  will  be  simply  the  differences  of  Xdx  in  Table  XXVII,  to  which 
Xv  can  be  added  from  a  separate  slip. 

Commutation  Tables  for  Joint  Lives.  In  the  older  Tables  of  David  Jones  and 
of  David  Chisholm,  D^y  =  v^Wy  =  Da;/^ ;  where  x  denotes  the  older  life.  This  dis- 
tinction of  the  older  age  is  not  needed  in  De  Morgan's  arrangement,  nor  in  the  case 
of  equal  ages.  Prof.  De  Morgan  suggested  the  symmetrical  form,  adopted  in  the 
English  Life  Table : 

x+y  x+y+i 

J)ggyZ=lxlyV  ^  .  Cxy  =^  {Uy  —  lx+lly  +  i)^      2       =  vT>xy—T>x+l.y+l' 

Na^y  =  Da:y  +  Da;+l.y+l+  .  .  .  .  M^y  =    Cxy+Ca;+l.y+l+  . 

Sajy  =  Na:y  +  Na;+i.y+i4- .  . . .  Eary  =  Ma:y  +  Ma;+i.y+i+ .  .  . . 

•  For  two  Equal  Ages,     Dxx  =  IxlxV^  =  Ix^x,       ''^xx  =  ^xx 4- Da;+i.a;+i  + 

Two  joint  lives  of  unequal  ages  x,  y  have  the  same  life  annuity  as  two  equal  lives, 
w,  u,  defined  in  one  way  by  the  equation  axy  =  auu,  and  in  other  ways  under  Make- 
ham's  law  of  mortality,  'by  the  relations, 


PxPy=PuPu,      Pu=-  VpxPy',  (f-^qy  —  %q^,      w  =  2;  +  Cor.        Table  LXV. 

Since  any  two  joint  lives  are  thus  reducible  to  the  case  of  two  equal  ages,  the 
corresponding  D  and  N  columns,  annuities  and  premiums  may  be  found  in  Tables 
LXVI-LXXIV.  The  radix  of  these  Tables  was  taken  as  100,000  at  the  age  of  ten; 
or  the  usual  D  and  N  values  were  divided  by  the  constant  factor  Dio- 

All  the  preceding  Commutation  formulas,  for  single  life,  become  applicable  to 
joint  lives,  by  merely  extending  the  suffixes  to  every  life.  For  illustration,  multiplying 
numera.tor  and  denominator  of  the  formula  in  Section  III  for  joint  lives,  by  v*,  or  by 

x+y 

V  8  ,  we  obtain  in  either  way, 


ttxy 


Da;+i.y-|.l-|-Dx+2.y+2-f-  •  •  '  •   N^+l^y+1 


iJxy  Djcy 


248  LIFE   ANNUITIES   AND    INSURANCES. 

The  law  is  perfectly  regular  for  two,  three,  or  any  number  of  joint  lives ;  thus, 

l^g+l.y+l.z+l  4'Da;+2.y+2.z+2+  •  •  •  •         ^x+\.y+l.z+l 

O^CyZ  —  =R  ■ —  TT . 

y  ^xyz  ^xyz 

Ma^  =  Darys— (1— r)Na;y2  =  ■yNxys— Na;+l.y+1.3+l. 

Note  1. — It  will  be  proper  to  observe,  that  formulas  on  the  plan  of  De  Morgan,  when  applied 
to  the  order  of  survivorship  will  involve  the  square  root  of  c.  Thus  the  single  premium  for  an 
insurance  of  $1  "  on  x  against  y,"  that  is,  payable  on  the  death  of  x  provided  y  be  then  living,  is 

The  annual  premium  will  be  found  by  simply  changing  Dxy  to  N^y.  In  each  term  of  the 
numerator,  the  sum  of  the  suffixes  added  to  the  exponent  of  i  o  counted  as  1,  gives  the  homogeneous 
sum  x  +  y  +  2. 

Note  2. — Repeated  additions  of  At).  There  are  two  methods  of  correcting  the  final  decimal. 
For  example,  at  4  per  cent,  /.n  is  1.982,966,6607,  which  falls  between  the  six-decimal  values  1.982,967 
and  1.982,966.  Firstly  then,  if  no  more  than  ten  or  fifteen  results  are  to  be  computed  so  as  to  be  exact 
to  six  decimal  places,  the  computation  can  be  made  with  four  extra  decimals,  that  is,  with  ten  places, 
retaining  only  six  at  the  end  of  the  process.  But  if  /»  is  to  be  implicitly  added  a  hundred  times  in 
computing  so  many  results  exact  to  six  places,  the  computation  can  be  made  with  five  extra  decimals, 
in  order  that  the  first  six  places  may  be  accurate  in  all  the  results. 

Secondly,  the  computations  can  be  correctly  made  with  six  decimals  by  suitable  changes  of  the 
sixth  decimal.  In  using  1.982,967  for  7.v,  we  commit  an  error  of  .338  in  the  sixth  place,  in  excess  ; 
and  in  using  1.982,966,  we  commit  an  error  of  ,661  in  deficiency.  A  compensation  will  ensue  by 
using  the  endings  7  and  6  in  frequency,  inversely  as  those  errors ;  that  is,  as  661  :  338,  or  2  :  1  nearly. 

Hence  the  sixth  decimal  of  ~Av  at  4  per  cent,  should  be  taken  as  7,  7,  6,  7,  7,  6 in  order.     At  5  per 

cent,  the  ratio  is  7 :  3,  so  that  the  sixth  decimal  of  Ic  should  be  9,  9,  8,  9,  9, 8,  9, 9,  8,9,  when  the  series 
recommences.  An  adjustment  can  be  made  at  every  tenth  value.  These  corrections  have  already 
been  applied  to  the  sixth  decimal  place  in  Table  XXXIII,  and  in  all  the  other  regular  Tables. 


SECTION    VI. 
Single  and  Annual  Premiums  of  Insurance. 

By  general  custom,  the  sum  insured  is  assumed  in  theory,  to  be  payable  at  the  end 
of  the  year  of  decease.  The  age  at  which  the  insurance  is  eflfected  is  often  termed  the 
age  of  issue,  or  the  age  of  entry.  The  contract  between  the  insuring  party,  and  the 
insured  is  named  the  policy.  The  first  premium  thereon  is  paid  at  the  time  when  the 
contract  is  made ;  and  the  subsequent  payments  of  premium  are  due  at  the  commence- 
ment of  each  policy  year.  The  premiums,  however,  may  be  single,  annual,  half-yearly 
or  quarterly.  The  single  premium  pays  for  the  insurance  in  full  at  the  beginning, 
in  one  payment. 

"By '^ deferred  premium"  is  meant,  the  remaining  semi-annual  or  quarterly  pre- 
miums to  be  paid  during  the  current  policy  year.  In  the  estimate  of  liabilities,  these 
deferred  premiums,  with  some  reduction  for  the  expense  of  collection,  and  for  discon- 
tinuances, are  accounted  as^  Assets ;  and  in  case  of  death,  the  Company  usually  deducts 
them  from  the  policy.  To  provide  for  expenses,  fluctuations  of  mortality  and  other 
contingencies,  the  net  premium  of  theory  is  augmented  in  practice,  by  a  margin  or 
loading,  such  as  one-fifth,  one-fourth  or  one-third,  and  is  then  termed  the  gross  or 
Office  premium. 


SINGLE   AND    ANNUAL    PREMIUMS,  249 

In  order  to  explain  the  computation  of  net  premiums,  let  Ix  denote  the  number 
living  at  the  age  x  in  the  life  table,  and  let  i  and  v  represent  the  given  rate  of  interest. 

1.   SINGLE   PREMIUMS. 

Let  Aa,  denote  the  single  premium  at  the  age  of  entry  x,  to  insure  $1  payable  at 
the  end  of  the  year  of  death.     Then  by  the  principles  of  the  system  of  Probabilities, 

.     _  {lx—1x+l)f>^-{lx^rl  —  lx+^V^  +  lx+i—h+^^-\- 

Ax  —  ;  J  -. 

ix 

Here  the  tabular  probability  of  the  life  failing  in  the  1st  year  is  — -, or  y-  ; 

Ix  l-x 

and  this  multiplied  by  the  sum  at  risk  $1,  and  again  by  v,  to  reduce  to  present  value, 
gives  the  first  term.  In  like  manner  the  remaining  terms  express  the  present  value  of 
the  mathematical  expectation  for  the  2d  year,  the  3d  year,  and  so  on  to  the  end  of  the 
life  table.     This  sum  is  therefore  the  present  value  of  the  life  insurance. 

Writing  c4  for  its  equal  Ix—lx+i,  and  similarly  for  other  ages,  then  multiplying 
both  numerator  and  denominator  by  if,  which  does  not  alter  the  value,  the  fraction  is 
changed  to  the  commutation  terms : 

A-x  — 


Ixlf 

Ma, 

A,  =  l_(l-^& 

In  the  first  formula,  the  positive  and  the  negative  terms  are  easily  identified  with 
the  series  for  the  life  annuity,  so  that  we  have  also 

A^  —  v—ax+vax  =  l  —  {l—v){l  +  ax)  =  —-^^. 

1  -ft 

To  facilitate  practical  applications,  the  single  premium  for  life  is  already  computed 
in  the  four  different  forms  of  Tables  XXX  and  XXXI,  L  and  LI. 

2.    ANNUAL   PREMIUMS. 

Instead  of  a  single  premium,  the  payment  for  insurance  is  more  usually  made  by 
equal  annual  premiums  at  the  beginning  of  each  policy  year.  Let  Px  denote  such 
annual  payments  on  $1  insured.  The  present  value  of  all  these  premiums  being 
equal  to  the  single  premium,  we  have  for  common  life  policies,  on  $1, 

Px(l +«a:)  =  Ax,  whence  Px  =  :f—^-. 


250 


LIFE  ANNUITIES   AND    INSURANCES. 


For  common  life  policies,  the  annual  premium  P  or  rr  is  already  computed  in 
Table  XXIX,  for  each  11000  insured. 


3.   INSURANCE  BY  A  LIMITED  NUMBER  (»)  OP  ANNUAL  PREMIUMS. 

The  rule  proceeds  on  the  same  general  principle  as  before.  That  is,  "  divide  the 
single  premium  by  unity  added  to  the  present  value  of  a  temporary  annuity  for  one 
year  less  than  {n)  the  number  of  premiums  which  are  to  be  paid": 


P.= 


Aa; 


M« 


l+Oa,"-!         Na,  — Na,+„' 


Example.  A  person  at  the  age  of  39  years  insures  his  life  for  $7000  by  ten  equal 
premiums,  to  be  paid  annually  at  the  beginning  of  the  first  ten  years  ;  required  this 
premium  when  interest  is  4  per  cent. : 


Table  LI,     -    -    -    -    AA39  =  1.552218 

Table  XXXVI,     - 

-     aM39  =  3.796864 

«      XLIV,    -    A(l+a^i)  =  0.908205 

^39=  293,818.6) 
^49=  151,634.5) 

X  =  5.152851 

...2.644013 

...2.644013 

«      LXXXII,    -    -    Pa,    -    0.0440568 

142,184.1  . 

Pa,     -   '0.0440568 

X7000 

x7000 

Annual  Premium  -    -    -    -  =  1308.3976 

Annual  Premium  - 

-    -    -  =$308.3976 

For  five,  ten,  fifteen  or  twenty  payments,  the  premiums  are  already  computed  in 
Table  LXI,  for  each  $1000  insured. 

Note. — If  a  special  payment  is  made  at  the  beginning,  in  order  to  reduce  the  future  annual 
premiums,  it  can  be  regarded  as  a  single  premium,  for  one  part  of  the  sum  insured  ;  and  the  annual 
premium  will  be  computed  on  the  remaining  part. 

4.   TEMPORARY   INSURANCES. 

Eequired  the  single  premium  to  insure  $1  for  7  or  w  years.  By  reference  to  the 
explanation  of  the  first  three  formulas  of  this  Section,  it  will  be  seen  that  the  single 
premium  will  be  the  sum  of  the  first  m  terms  of  the  series  there  described ;  thus, 


JXnf.     


Cx4-C!ar+1+ .  .  • +Ca;+wi— 1        ^x  —  ^x+t 


Dx 


Da 


The  equivalent  annual  premium  is  obtained  by  dividing  the  single  premium  by  1 
plus  the  temporary  annuity  for  one  year  less : 


ie  = 


l+«: 


m— 1 


N-E+i— Nar+m+1 
^x — ^x+m 


n 

ttx 


l+«! 


n— 1' 


pw» Ma; — Ma;+ffi Da; — JJx+m      /-,         \ 

^x  —  '-i^        ^ij-       —  -vr  _-»T       -  —  \^      '^r 
ISx  —  ^x^m        ^x  —  -lNx+»» 


SINGLE  AND    ANNUAL   PREMIUMS.  251 

The  Premium  for  Temporary  Insurance  on  each  $1  for  One  Year  only,  is 

Car  /^  N  Da;+1 


PI             ^X                 /^                  N                                               ^x+1 
X  =  p-  =  v{l—px)  =  vqx  =  V ^. 


For  example,  by  Tables  LII  and  LIII,  at  the  age  of  35  years,  on  $1000  insured  for 
7  years,  the  single  premium  is  $51.70,  or  the  annual  premium  is  $8,486. 

5.   PURE   ENDOWMENTS. 

The  single  premium  or  present  value  of  $1  to  be  received  at  the  end  of  m  years,  it 
the  party  now  aged  x  be  then  living,  is 


Ix  i^x 


The  annual  premium  for  the  same,  payable  at  the  beginning  of  each  year,  unless 
the  risk  is  voided  by  death,  is  found  on  the  principle  before  described : 

Ptn  Aflj  ^x+m  *-, 

l+a»i-i      Na,— N«,+«' 

Table  LXIII,  APS'  =  0.-ABSV  on  $1  Pure  Endowment. 

For  example,  at  the  age  16,  the  annual  premium  is  $173.88  on  $1000,  payable  at 
the  age  of  21  if  the  person  be  then  living.  The  same  result  is  also  found  by  sub- 
tracting the  premium  of  term  insurance.  Tables  LII  and  LIII,  from  the  premium  of 
endowment  insurance,  next  to  be  described. 

6.   ENDOWMENT   INSURANCES. 

The  sum  insured  is  payable  on  attaining  a  specified  age,  or  sooner  in  the  event  of 
death.  By  simply  adding  the  single  premiums  of  temporary  insurance  and  of  pure 
endowment  for  the  term  of  m  years,  after  the  age  of  entry  x,  we  have  at  once  the 
single  premium  of  Endowment  Insurance  on  $1  : 

*  (w»)        Mju  —  Mas+^-j-l^as+m         -.        /-.  \/i    ,      m— 1\ 

Aaj     = =;r =  \  —  {l—v){l-\-ax       ). 

To  find  the  equivalent  annual  premium,  we  divide  by  1  plus  the  annuity: 

For  a  limited  number  {n)  of  equal  annual  premiums  to  be  paid  at  the  beginning 
of  the  first  {n)  years  of  the  whole  period  m,  the  divisor  is  changed  as  below : 

Pn         Mas  —  Ma!+w»  +  Da5+f»     „^    *-, 
a,  =  — n~:zn '  °°  ^^' 

^»  —  -i-ia!+n 

The  various  species  of  Endowment  Premiums  are  already  computed  in  the  seven 
Tables  LIV  to  LX. 


m  LIFE  ANNUITIES  AND   INSURANCES. 

Computation  of  Tables. — By  taking  the  difference  of  single  premiums,  and  observing  that 
Mxfm+i— Mj+TO  =  — Cj+m  =  — i'I>j+OT  +  I*x+in-ri,  we  obtain  the  simplified  annual  difference  : 

■  (m)       .  On+1)  _  {l  —  v)'Dx+m 
•»«     — -O^c  —  =r . 

This  difference  can  be  easily  computed  by  the  aid  of  two  moveable  slips  of  paper,  the  one  con- 
taining /.D,  and  the  other  'a{\—v)  +  AD.  When  the  period  of  insurance  is  only  1  year,  the  premium  is  v, 
as  shown  in  Table  LIV.  From  v,  we  subtract  the  difference  (1 — v)T>x+i-^^x  to  give  the  single  pre- 
mium for  the  term  of  3  years.  From  this,  we  subtract  (1— cjDa;-r2-i-Ds  to  give  the  single  premium  for 
the  term  of  3  years ;  and  so  on. 

But  in  single  Examples,  the  shortest  method  will  be  to  find  the  logarithm  of  1  plus  the  tem- 
porary annuity  for  one  year  less,  in  Table  XLIV-XLVII.  This  will  guide  to  the  required  premium, 
by  mere  inspection,  in  the  next  or  Conversion  Tables. 


7.   DEFERRED   INSURANCES. 

On  the  principle  of  deferred  Annuities  in  Sections  III  and  V,  and  by  Section  VI, 

,the  present  values  of  the  temporary  and  of  the  complementary  deferred  insurance, 

added  together,  equal  the  present  Value  for  the  whole  life.     Hence  by  subtraction,  the 

present  value  or  single  premium  to  insure  a  person  now  aged  x,  for  the  period  of  life 

which  may  remain  after  the  age  x-\-m,  will  be  on  each  $1  insured, 

P,»     -M^g+wi ^x+m — (1 — v)^x+m 

The  equivalent  annual  premium  payable  m  years,  will  be 

m^^  =  ^^^-^    ,  on  each  $1. 
The  annual  premium  payable  during  the  whole  life,  on  $1  insured,  is 

^X    


x+m  -^x 


Na;  1+ffa; 

For  a  Deferred  Temporary  Insurance,  or  to  be  deferred  m  years,  then  to  continue 
in  force  during  r  years ;  if  the  annual  premiums  are  payable  during  m  -^  r  years,  we 
have  on  each  II  insured. 

Single  Premium    =  ^x^m-^x^m^r^ 


Annual  Premium  = 


-Na; — ^x+m+r 


8.   RETURN   PREMIUMS. 

Required  the  net  annual  premium  P  to  secure  a  Pure  Endowment  of  $1  at  the  end 
of  m  years,  if  the  life  now  aged  x  should  live  so  long,  or  the  Return  of  all  Premiums 
paid,  at  the  end  of  the  year  of  death,  if  it  occur  before  that  time. 

This  plan  may  be  regarded  as  an  endowment  of  II,  added  to  a  series  of  m  deferred 
temporary  insurances  of  P.  By  making  the  collective  annual  premiums  equal  to  P, 
then  substituting  R,  and  reducing  the  equation,  we  find 


SINGLE  AND  ANNUAL  PREMIUMS.  253 


=P., 


T>:c^m  +  I'xO^x+'M.jc  +  l  + +  Mjc  +  m-J—rnMjc  +  m)  _ 

'-^x  +  m . 

Also  by  changing  T):c^m  to  ^x+m+\  we  determine  the  annual  premium,  pay- 
able from  age  x  to  age  x  +  m — 1,  to  provide  a  Deferred  Life  Annuity  of  $1  per 
annum,  first  payment  at  age  x  +  m+l.  The  premiums  paid  are  to  be  returned 
without  interest,  six  months  after  death,  in  the  event  of  death  before  the  age 
x+m.  Or  if  the  premiums  are  not  to  be  returned,  cancel  R  and  M  in  the 
above  formula. 

By  the  same  mode  of  solution,  the  Single  Premium  of  a  Pure  Endoiument  of 
$1,  with  return  of  the  premium  six  months  after  death,  if  it  occur  before  the 
age  X  i-m,  will  be 


D^— (M;,— M^+;„) 

Required  the  gross  premium  to  insure  $1  for  the  Whole  Life,  and  the  return 
of  gross  premiums  equal  to  g  times  the  net,  without  interest,  six  months  after 
death. 

Let  fifP  denote  the  gross  annual  premium  to  provide  for  the  ordinary  insurance 
of  $1,  together  with  the  series  of  deferred  insurances  of  grP,  all  for  the  whole  life. 
Then,  as  before  described: 

p   _gM:^+  gT':c  {M:c+'M.^+i+  ■  •  •  )__gM.:^  +  g'Px^x.  ^j. 

g'^x    . 

Annual  Premium  gPx  =  ^^    p> 

Single  Premium  gA^  =      '^    1,  >  by  similar  solution. 

i-/x         -'•"-jr 

By  making  (/  to  be  1,  the  solutions  will  apply  to  the  case  of  net  return 
premiums,  without  interest. 

Again,  if  the  insurance  of  $1  for  the  whole  life  is  to  be  secured  by  m 
Limited  Annual  Payments  of  P^,  with  return  of  the  gross  premiums,  six  months 
after  death,  or  at  the  end  of  the  year  of  death : 

g'^x 


9^^ 


(N^— R^)— (N;^+„— R^+^) 


9  INCREASING  AND  DECREASING  SCALES  OF  PREMIUMS. 

Suppose  the  annual  premium  to  increase  b}'^  a  certain  fraction  of  the  first 
premium  every  n  years,  and  after  r  such  additions,  the  premium  to  continue 
constant  during  the  remainder  of  life.  Required  the  annual  premium  during 
the  first  n  years. 

On  each  $1  insured  let  P  denote  the  first  annual  premium,  and  q  its  pro- 
portional increase,  added  at  the  end  of  every  n  years. 

The  present  value  of  all  the  premiums  P,  continued  for  the  whole  life,  is 
F{l+ax).  And  the  present  value  of  all  the  increments  P^isthat  of  so  many  deferred 


254  LIFE   ANNUITIES   AND   INSURANCES. 

life  annuities.     By  equating  the  expression  of  the  single  premium  to  the  sum  of  these 
present  values,  and  then  reducing  the  equation : 

A      _  M?  —  P     ^^a'  +  g(Na,-t-raH-Na.  +  2n+ +Na,  +  r») 

p   _  M«  ■■    \ 


Instead  of  a  proportional  increase  q  of  the  premium,  let  there  be  an  absolute 
increase  h  in  every  n  years,  the  premium  to  remain  constant  after  rn  years,  to  find  the 
first  premium  Pa;.  We  have  only  to  substitute  h  in  place  of  its  equal  Yq  in  the  primary 
formula,  then  reducing,  we  find  again  on  $1  insured : 

^     _  Ma,  — ^(Na,.,.n  +  Na,+2w4- +N^+m) 

When  the  scale  of  premiums  is  to  be  decreasing,  let  the  sign  of  q  and  of  h  be 
reversed  in  the  given  formulas. 

The  above  method  is  evidently  applicable  to  premiums  reduced  or  increased 
arbitrarily.  But  as  David  Jones  has  observed,  the  value  of  q  or  h  should  be  chosen  so 
as  to  make  the  premium  for  the  first  interval  more  than  the  premium  for  a  risk  to  be 
determined  at  the  expiration  of  that  term,  as  the  party  assured,  has  the  option  of 
continuing  or  discontinuing  the  risk. 

In  the  case  of  annual  premiums  diminished  at  the  end  of  every  successive  year,  by 
the  mih.  part  of  the  first  premium,  so  that  after  m  payments,  the  policy  is  paid  up,  the 

first  solution  will  apply  by  making  w  =  1,  g  = ,  and  substituting  S  for  its  equal. 

Thus  the  first  premium  on  $1  insured,  will  be 

M. 


P„  = 


10.    INCREASING    AND    DECREASING    INSURANCES. 

The  single  premium  for  a  temporary  Insurance  for  m  years,  commencing  at  la  and 
increasing  %h  each  year,  will  be 

a(Ma,  — M^-,.m)+^(Ma,  +  i  — Ma,  +  ;ra)  +  6(Ma,+2  — Ma,+m)+  •  »     •  +hQS.x+m-l  —  '^xArm) 

Da, 

This  aggregate  is  evidently  made  up  of  the  present  insurance  of  $«  together  with 
the  series  of  deferred  temporary  insurances  of  %b.  By  substituting  R  for  its  well 
known  equal,  we  have  the  required  formula : 

Single  Premium  ^«(M.-M..^)  +  3[R..i-R..^-(m-l)M..^] 

By  merely  reversing  the  sign  of  5,  we  obtain  the  single  premium  for  a  similar 
insurance,  commencing  with  %a  and  decreasing  %h  annually. 


SINGLE   AND    ANNUAL    PREMIUMS,  255 

lu  either  case,  the  divisor  to  give  the  annual  premium  will  be       ' 


1.  7/*— 1 

+  ax     ,        or 


D. 


By  extending  x-\-m  to  the  end  of  the  life  table,  we  evidently  have  for  an  insur- 
ance commencing  at  %a  and  increasing  $b  each  year. 

Single  Premium    ^  ^M^^lkll. 

Dx 

Annual  Premium  =  ^M£+*_^i. 

Nx 

When  the  similar  insurance  is  to  decrease  $b  each  year,  we  have  only  to  make  b 
negative. 

Finally,  making  a  =  b  =  1,   we  obtain   the  more  simple  formulas   for   a   life 
insurance  commencing  with  $1,  and  increasing  $1  annually : 

Single  Premium  =  ^r  •  Annual  Premium  =  ^' 

Ux  -Na; 


11.    PRICE    OF    ANNUITIES    SECURED    BY    LIFE    INSURANCE. 

An  ordinary  life  annuity  of  $a  per  annum  is  to  be  sold.  Required  the  price  $s 
which  will  allow  the  purchaser  a  given  rate  i  of  interest,  besides  p&,ying  the  premium 
of  life  insurance  to  secure  the  return  of  his  outlay  after  the  death  of  the  annuitant. 

Solution. — The  purchaser  must  insure  the  price  s,  and  a  final  annuity  a,  both  payable  at  the 
end  of  the  year  of  death  of  the  annuitant.  An  annuity  a  will  then  be  receivable  at  the  end  of  each 
year,  for  which,  the  premium  will  be  payable  at  the  beginning  of  the  year.  But  each  premium  may 
be  transferred  from  the  beginning,  to  its  equivalent  at  the  end  of  the  year,  by  adding  the  year's 
interest.  When  this  equivalent  is  subtracted  from  the  annuity  a,  the  remainder  must  be  sufficient  to 
pay  «i  the  current  year's  interest  on  the  price. 

Accordingly,  if  p  denote  the  office  annual  premium  to  insure  $1  for  life,  then  the  premium 
payable  will  be  p{8  +  a).    Adding  the  year's  interest,  and  subtracting  from  a,  we  have 

a—p{8  +  a)  (1  +  i)  =  si. 

l-p{l  +  i) 


Hence,  the  Price  s  =  a. 


i+p{l+i) 


The  Rate  of  Interest    j  =  ^^1±^J  . 
s+p{8  +  a) 

In  case  the  Problem  is  changed  in  any  of  its  conditions,  a  corresponding  change  will  be  made  in 
the  solution.  Thus,  if  the  annuity  a  is  to  be  continued  to  the  end  of  the  year  of  death,  the  purchaser 
need  only  insure  the  price  s,  and  the  solution  will  be 

%+p{l  +  i)  8(1+P) 

Or  if  the  annuity  a  is  to  be  paid  at  the  beginning  of  the  first,  and  each  subsequent  year  <  of  life, 
the  price  «  alone  need  be  insured,  and  the  equations  will  evidently  be 

/          \/-<  .  %        •                       cUl  +  t)    .                      a—p8 
(a--^«)(l+j)  =  M;  8=  .^  ,.  .\;  =  :jr-r^ 


256  LIFE  ANNUITIES   AND    INSURANCES, 


12.    INSURANCE    ON    FEMALE    LIFE. 

From  the  Observations  on  Female  Life  in  Table  II,  a  Life  Table  has  been  con- 
structed and  graduated  on  the  plan  mentioned  at  page  237.  The  usual  columns  are 
given  in  Table  LXXVII,  in  which  the  column  of  annual  mortality  q  exhibits  the  very 
singular  feature  of  the  almost  unifonn  value  0.011  from  the  age  of  20  to  50  years. 
The  principal  cause  is  indicated  on  page  34.  On  account  of  this  and  other  peculiarities, 
a  simple  correction  of  the  age  has  appeared  sufficient  for  entering  and  employing  the 
general  Tables  for  male  life,  to  give  the  values  for  female  life. 

Preparatory  to  this  object,  the  4  per  cent,  commutation  and  annuity  columns  were 
computed  in  Table  LXXVIII.  The  simple  Formula  for  determining  the  correction 
or  column  c,  and  an  illustrative  Example  are  given  on  the  first  page  of  this  Table. 
The  sum  of  the  actual  Age  and  Correction  may  be  termed  the  Equivalent  or  Relative 
Age.  And  the  Tables  of  Male  Life  entered  with  this  Relative  Age,  give  the  true 
Annuity  and  Premium  for  Female  Life. 

On  account  of  the  smallness  and  fluctuating  nature  of  the  corrections  above  the 
age  of  39,  and  the  irregularities  of  the  data  at  the  oldest  ages,  it  appears  that  above  the 
ar/e  of  39,  the  "rating  up,"  or  correction  of  the  age  can  safely  he  omitted.  That  is,  the 
actual  age  when  above  39,  may  be  taken  as  the  Relative  Age  of  Female  Life. 

In  relation  to  Months,  and  under  the  age  39,  the  actual  age,  from  the  birth-day 
to  the  (^ate  of  entry,  is  to  be  expressed  in  years  and  months,  as  well  as  the  correction, 
and  their  sum,  taken  to  the  nearest  integral  year,  will  be  the  Relative  Age.  Thus  if  a 
female  life  at  entry  has  the  age  25  Y.  8  M.,  and  from  Table  LXXVIII,  or  page  *226,  the 
correction  is  4  Y.  3  M.,  the  nearest  Relative  Age  will  be  30  years. 

13.    INSimkNCE    ON    JOINT    LIVES. 

Required  the  single  premium  to  insure  $1  during  the  joint  existence  of  two  lives, 
X  and  y,  the  insurance  to  be  paid  at  the  end  of  the  year  of  the  first  death. 

The  mathematical  expectation  (pages  235,  234)  for  each  year,  as  the  third  for 
example,  will  be  the  product  of  the  present  value  of  the  insurance  i^,  by  the  compound 

probability  ~-  -^j— ,  that  both  persons  will  be  alive  at  the  beginning  of  the  third  year, 

Ix  ty 

multiplied  by  the  probability  (l — ^^  ^^    that  both  will  not  live  through  that  year, 

or  that  one  or  both  will  die  in  the  third  year:  The  sum  of  the  series  of  similar 
expectations  for  each  and  every  year,  to  the  end  of  life,  gives  the  total  present  value, 
or  Single  Premium  k^y ;  thus, 

A        _  ^a-^y/i       lx  +  lly  +  l\         l^c+^y+\l.       /ar+2  ?y+2\   o 

Axy  —  ry|i 7       7~/^H T/      \^~~7 —  7 — r  +  •  •  •• 

Performing  the  multiplications  indicated,  we  have 

1        (?x?y  —  ^x-t-l^y  +  l)^'-f-(^x+l^y+l — ^x+ily+2)v^ -h  {ix+jly+i  —  ^x43?y+3)^^+ » 

Axy  —  j-j 

x+y 

Again,  multiplying  and  dividing  by  w  2  ,  in  order  to  substitute  0,  according  to  the 
notation  of  page  247 : 

A         C'xy  +  Ca.  +  l.y+l-|-Ca;+2.y+2-|-  •  •  •  .  Mxy 

Aary  —  ^^ =  jy 


SINGLE   AND    ANNUAL    PREMIUM3,  257 

A,^  =  1-^^^  =  l-(l-.)(l  +  «a^). 

\ 

Annual  Premium,  Pj^  =  =~  =  =^— (1— v). 

A                1 
Annual  Premium,  Pxy  =  .  ^    =  :j— (1— ^)« 

For  a  joint  insurance  of  $1  on  three  lives,  x,  y,  and  z,  we  have  only  to  substitute 
xyz  in  place  of  the  suffix  xy  in  the  last  formulas ;  and  so  for  four  or  more  lives.  The 
insurance  on  joint  lives  continues  only  while  they  are  all  living.  Also,  the  Premiums 
may  be  found  from  Conversion  Tables  XLVIII  and  XLIX. 

For  a  Temporary  hisurance  of  $1  to  be  paid  at  the  end  of  the  year  of  the  first 
death  of  the  two  lives  a;  or  y,  if  it  occurs  within  n  years : 

Single  Premium, 

in    -M-xy  —  -M-x+n.y  +  ra  V\^xy  —  ^x  +  w.y  +  «)  —  (JNar+i.y+i  —  -INx+w  +  l.y  +  n  +  l) 

^xy  —  -  Y)  ~  ~  T) 

^  -L'ary  iJxy 

Annual  Premium,   P^y  = ^r-r  =  v =~ -^ • 

'^+Cixy  ^ — ^x+n.y+n 

For  a  Deferred  Insurance  of  $1  payable  on  the  first  death  of  x  or  y,  if  it  occur  , 
after  the  expiration  of  n  years : 

Single  Premium,  ^A^y  =  ^"J^  =  Dx^..y.n-(l-^^)Nx^n.y^n^ 
Single  Premium,  ^Kxy  —  -^^^— .Ax+n.^+n- 

iJxy 

■M-x+n.y+n. 


Annual  Premium  for  n  payments,    "P^y  = 


-Nary — ^x+n.y+n 


Annual  Premium  during  joint  life,  "P^y  =  — '^■^"-— • 

For  an  Insurance  of  $1  on  the  Longest  of  Two  Lives,  x  and  y : 
Single  Premium,    A^y  =  Ax  +  Ay— Axy  =  1  —  (1  —  v)  (1  +  «« + ay—a^y). 
Annual  Premium,  Pxy  =  ^^+^y-^^j  ^  — _J /|_^n 

l+«a;  +  «y  — «a!y        l  +  «a;  +  flfy — «xy 

For  a  Temporary  Insurance  of  $1  for  n  years  on  the  Longest  or  Survivor  of  Two 
Lives,  X  and  y : 


Single  Premium,    A^y  =  Ax+Aj— A^. 

Annual  Premium,  Pj,  =  —A^+Av^I^S'       , 

±-\-ux     "vay     — uxy 


258 


LIFE  ANNUITIES   AND    INSURANCES. 


Tables  foe  Two  Joint  Lives,  Equal  Ages. — The  agreement  of  the  Thirty 
Offices  Experience  with  Makeham's  law  of  mortality,  offers  a  great  advantage,  in  super- 
seding the  old  and  cumbrous  system  of  joint  life  tables,  by  the  new  method  of  equal 
lives  or  ages,  shown  in  Tables  LXV-LXXVII.  For,  under  Makeham's  law,  if  the 
joint  probability  pxPy  is  equal  to  puPu,  that  of  two  equal  lives,  at  the  ages  of  entry,  the 
relation  of  equality  will  always  continue  during  their  joint  existence. 

Example.  When  interest  is  4  per  cent.,  required  the  annual  and  the  single 
premium  to  insure  $1000,  payable  at  the  end  of  the  year  of  the  first  death  of  two  lives, 
X  aged  30  and  y  aged  40  years.  Entering  Table  LXV,  with  the  difference  of  ages 
y — X,  or  10  years,  we  find  the  correction  6  Y.  1.8  M.,  which  being  added  to  the  younger 
age  30,  gives  the  nearest  Equal  Age  36.  That  is,  36,  36  may  be  substituted  for  the 
given  ages  30  and  40.  Entering  Table  LXXITI  with  36  years,  we  find  the  annual 
premium  $29.74;  and  in  the  next  Table,  the  single  premium  $436.06. 

Method  foe  Three  Joint  Lives. — By  Table  LXV,  change  the  given  Ages  x,  y, 
z,  to  the  two  equal  Ages  u,  u,  which  increase  equally  in  equal  times,  like  the  actual 
ages,  from  the  date  of  entry.  The  current  value  of  u,  in  any  year,  increased  by  the 
Annual  Correction  below,  under  the  proper  rate  of  interest,  will  be  the  argument  for 
entering  Tables  LXV-LXXVII,  for  premiums,  reserves,  etc.  The  correction  can  be 
adjusted  to  other  rates  of  interest  by  the  Difference  column. 


THREE    LIVES.- 

-ANNUAL    CORRECTION    (c)    TO 

THE    EQUAL 

AGE 

u. 

Equal 

3 

4 

5 

&4 

1  Equal 

3 

4 

5 

Ut 

Equal 

3 

4 

5 

Ages. 

Pbr 

Pbk 

Per 

1 

Ages. 

Feb 

Feb 

Feb 

eI! 

Ages. 

Feb 

Feb 

Feb 

U. 

Cent. 

Cent. 

Cent. 

ft 

U. 

Cent. 

Cent. 

Cent. 

Q 

u. 

Cent. 

Cent. 

Cent. 

Yr. 

Y. 

M. 

Y. 

M. 

Y. 

M.    M. 

Yr. 

Y.    M. 

Y.    M.Y.    M. 

,'M. 

Yr. 

Y.    M. 

Y.    M 

Y.    M. 

10 

13 

8.7 

14 

11.7 

16 

1.6  13.9 

40 

3     3.2 

3     4.93     6.61.7 

70 

0     5.5 

0     5.5 

0     5.5 

11 

13 

2.2,14 

4.5 

15 

5.813.3 

41 

3     0.9 

3     2.53     4.1,1.6 

71 

5.1 

5.1 

5.1 

J2 

12 

8.1 

13 

9.7 

14 

10.412.7 

42 

2  10.8 

3     0.33     1.7il.4 

72 

4.7 

4.7 

4.7 

13 

12 

2.2 

13 

3.0 

14 

3.1112.1 

43 

2     8.9 

2  10.2;2  11.51.3 

73 

4.3 

4.3 

4.3 

14 

11 

8.4 

12 

8.5 

13 

8.011.5 

44 

2     7.0 

2     8.2|2     9.31.1 

74 

4.0 

4.0 

4.0 

15 

11 

2.7 

12 

2.1 

13 

l.llll.O 

45 

2     5.2 

2     6.32     7.31.0 

75 

0    3.7 

0     3.7 

0     3.7 

16 

10 

9.1 

11 

7.9 

12 

6.410.5 

46 

2    '3.4 

2     4.42     5.3i   .9 

76 

3.4 

3.4 

3.4 

17 

10 

3.7 

11 

1.9 

11 

11. 8|  9.9 

47 

2     1.8 

2     2.712     3.51   .8 

77 

3.2 

3.2 

3.2 

18 

9 

10.5 

10 

8.1 

11 

5.5 

9.4 

48 

2     0.3 

2     1.1 

2     1.9 

.8 

78 

2.9 

2.9 

2.9 

19 

9 

5.4 

10 

2.4 

10 

11.2 

8.8j 

49 

1  10.9 

1  11.6 

2     0.3 

.7 

79 

2.7 

2.7 

2.7 

20 

9 

0.5 

9 

8.9  10 

5.2 

8.3 

50 

1     9.5 

1  lO.lll  10.7 

.6 

80 

0     2.5 

0     2.5 

0     2.5 

21 

8 

7.7 

9 

3.6 

9 

11.4 

7.8 

51 

1     8.1 

1     8.7 

1     9.2 

.5 

81 

2.3 

2.3 

2.3 

22 

8 

3.0 

8 

10.5 

9 

5.9 

7.4! 

52 

1     6.9 

1     7.4 

1     7.9 

.5 

82 

2.1 

2.1 

2.1 

23 

7 

10.5 

8 

5,5 

9 

0.4 

6.9 

53 

1     5.6 

1     6.1 

1     6.5 

.4 

83 

1.9 

1.9 

1.9 

24 

7 

6.2 

8 

0.8 

8 

7.3 

6.5! 

54 

1     4.6 

1     5.0 

1     5.4 

.4 

84 

1.8 

1.8 

1.8 

25 

7 

2.0 

7 

8.1 

8 

2.1 

6.0 

55 

1     3.5 

1     3.9 

1     4.2 

.3 

85 

0     1.6 

0     1.6 

0     1.6 

26 

6 

9.9 

7 

3.6 

7 

9.2 

5.6 

56 

1     2.4 

1     2.8 

1     3.1 

.3 

86 

1.4 

1.4 

1.4 

27 

6 

5.9 

6 

11.3 

7 

4.4 

5.1 

57 

1     1.6 

1     1.9 

1     2.1 

.2 

87 

1.2 

1.2 

1.2 

28 

6 

2.1 

6 

7.1 

6 

11.8 

4.7 

58 

1     0.6 

1     0.9 

1     1.1 

.2 

88 

.9 

.9 

.9 

29 

5 

10.5 

6 

3.2 

6 

7.4 

4.2j 

59 

0  11.9 

1     0.1 

I     0.2 

.1 

89 

.8 

.8 

.8 

30 

o 

7.1 

5 

11.4    6 

3.2 

3.8| 

60 

0  11.1 

0  11.3  0  11.4 

.1 

90 

0       .8 

0       .8 

0       .8 

31 

5 

3.7 

5 

7.7 

5 

11.3 

3.6 

61 

0  10.3 

0  10.5i0  10.6 

.1 

91 

.8 

.8 

.8 

32 

5 

0.4 

5 

4.1 

5 

7.5 

3.4 

62 

0     9.7 

0     9.80     9.9 

.1 

92 

.7 

.7 

.7 

33 

4 

9.5 

5 

0.8 

5 

3.9 

3.1 

63 

0     9.0 

0     9.1I0     9.2 

.1 

93 

.6 

.6 

.6 

34 

4 

6.5 

4 

9.5 

5 

0.4 

2.9 

64 

0     8.5 

0     8.5  0     8.7 

.2 

94 

.5 

.5 

.5 

35 

4 

3.7 

4 

6.4 

•4 

9.1 

2.7 

*65 

0     7.8 

0     7.8  0     8.0 

.2 

95 

0       .4 

0       .4 

0      .4 

36 

4 

1.0 

4 

3.5 

4 

6.0 

2.5 

66 

0     7.3 

0     7.30     7.5 

.2 

96 

.4 

.4 

.4 

37 

3 

10.3 

4 

0.6 

4 

2.9 

2.3 

67 

0     6.8 

0     6.80     7.0 

.2 

97 

.2 

.2 

.2 

38 

3 

7.8 

3 

9.9 

4 

0.0 

2.1 

68 

0    6.3 

0     6.30     6.4 

.1 

98 

.1 

.1 

.1 

39 

3 

5.4 

3 

7.3 

3 

9.2 

1.9 

69 

0     5.9 

0     5.90     6.0 

1 

.1 

Formula,  for  3.654,  4.660,  5.666,  or  the  rate  of  vs,  Uuu  =  au+c.u+c  for  3,  4,  5  per 
cent,  interest  respectively,  or  the  rate  of  v. 


SINGLE  AND    ANNUAL   PREMIUMS. 


259 


Method  fob  Foqb  Join^t  Lives, — By  Table  LXV,  change  the  three  youngest 
Ages  to  two  equal  Ages,  u,  u.  With  w,  u,  and  the  fourth  or  oldest  age,  re-enter 
Table  LXV,  and  find  the  equal  ages,  u',  ic,  for  record,  at  the  date  of  entry.  In  any 
year,  the  current  value  of  u'  augmented  by  the  Annual  Correction  below,  will  be  the 
argument  for  entering  Tables  LXV-LXXVII,  for  the  life  annuity  or  other  monetary 
value. 


FOUR 

LIVES 

—ANNUAL 

CORRECTION    (c) 

TO    THE 

EQUAL     AGE    ti 

• 

E<)UAL 

3 

4 

5 

fn 

Equai 

3         4 

5 

^ 

Equal 

3 

4 

5 

Aess. 

Per 

Peb 

Peb 

Pu 

Ageb. 

Peb        Peb 

Per 

^ 

Ages. 

Pee 

Peb 

Per 

^l'. 

Cent. 

Cent. 

Cent. 

fi 

u'. 

Cent.     Cbkt. 

Cent. 

5   ! 

u\ 

Ce»t. 

Cent. 

Cent. 

Yr. 

T. 

M. 

Y. 

M. 

Y. 

M. 

M. 

Yr. 

Y.    M.|Y.    M. 

Y. 

M. 

M. 

Yr. 

Y.    M. 

Y.    M. 

Y.    M. 

10 

21 

10.4 

23 

1.6 

24 

4.2 

14.6 

40 

6       .56     3.2 

6 

5.9 

2.7 

70 

0  10.6 

0  10.7 

0  10.7 

11 

21 

1.8 

22 

4.5 

23 

6.7 

14.2 

41 

5     9.15  11.6 

6 

2.12.5 

71 

9.8 

9.9 

9.9 

12 

20 

5.4 

21 

7.6 

22 

9.3 

13.7 

42 

5     4.95     7.2 

5 

9.5|2.3 

72 

9.0 

9.1 

9.1 

13 

19 

9.1 

20 

10.7 

23 

0.0 

13.3 

43 

5     1.5  5     3.6 

5 

5.712.1 

73 

8.6 

8.6 

8.6 

14 

19 

0.9 

20 

2.0 

21 

2.8 

12.8 

44 

4  10.15     0.0 

5 

1.91.9 

•74 

7.8 

7.8 

7.8 

15 

18 

4.8 

19 

5.4 

20 

5.8 

12.4 

45 

4     7.04     8.7 

4  10.4|l.7! 

75 

0     7.3 

0     7.3 

0     7.3 

16 

17 

9.0 

18 

9.1 

19 

9.0 

11.9 

46 

4     3.94     5.5 

4 

7.11.61 

76 

6.8 

6.8 

6.8 

17 

17 

1.2 

18 

0.8 

19 

0.3 

11.5 

47 

4     1.0  4     2.4 

4 

3.8jl.4i 

77 

6.2 

6.2 

6.2 

18 

16 

5.6 

17 

4.7 

18 

3.7 

11.0 

48 

3  10.2  3  11.5 

4 

0.8 

1.3 

78 

5.8 

5.8 

5.8 

19 

15 

10.1 

16 

8.7 

17 

7.3 

10.6 

49 

3     7.5i3     8.6  3 

9.7 

1.1 

79 

5.3 

5.8 

5.3 

20 

15 

2.9 

16 

1.0 

16 

11.1 

10.1 

50 

3     5.0  3     6.0  3 

7.0 

1.0 

80 

0     4.9 

0    4.90     5.0    1 

21 

14 

7.8 

15 

5.4 

16 

3.0 

9.6 

51 

3     2.5  3     3.4  3 

4.3 

.9 

81 

4.4 

4.4 

4.4 

22 

14 

1.0 

14 

10.1 

15 

7.2 

9.1 

52 

3     0.33     1.1 

3 

1.9 

.8 

82 

4.0 

4.0 

4.0 

23 

13 

6.0 

14 

2.7 

14 

11.3 

8.6 

53 

2  10.0  2  10.8 

2 

11.6 

.8 

83 

3.7 

3.7 

3.7 

24    13 

11.5 

13 

7.7 

14 

3.8 

8.1 

54 

3     8.02     8.7 

2 

9.4 

.7 

84 

3.3 

3.3 

3.3 

1  25    12 

5.1 

13 

0.8 

13 

8.4 

7.6 

55 

2     6.0:2     6.6 

2 

7.2 

.6 

85 

0     3.1 

0     3.1 

0     3.0 

26  ill 

10.8 

12 

6.1 

13 

1.4 

7.3 

56 

2     4.12     4.6 

2 

5.1 

.5 

86 

2.7 

2.7 

2.7 

27 

11 

4.6 

11 

11.5 

12 

6.4 

6.9 

57 

2     2.3  2     2.8 

2 

3.2 

.4 

87 

2.4 

2.4 

2.4 

28 

10 

10.8 

11 

5.2 

11 

11.8 

6.6 

58 

3     0.72     1.1 

2 

1.5 

.4 

88 

2.1 

2.1 

2.1 

29 

10 

5.0 

10 

11.0 

11 

5.2 

6.2 

59 

1  11.1:1   11.5 

1 

11.8 

.3 

89 

1.8 

1.8 

1.8 

30 

9 

11.4 

10 

5.0 

10 

10.9 

5.9 

60 

1     9.6'l     9.9 

1 

lO.li   .2 

90 

0     1.6 

0     1.6 

0     1.8 

31 

9 

6.0 

9 

11.3 

10 

48 

5.5 

61 

1     8.2il     8.5)1 

8.7 

.2 

91 

1.4 

1.4 

1.4 

32 

9 

0.6 

9 

5.5 

9 

10.7 

5.2 

62 

1     6.81     7.1 

1 

7.3 

.2 

92 

1.3 

1.3 

1.3 

33 

8 

7.6 

9 

0.2 

9 

5.0 

4.8 

63 

1     5.7il     5.9 

i 

6.0 

93 

1.2 

1.2 

1.2 

34 

8 

2.6 

8 

6.8 

8 

11.3 

4.5 

1   64 

1     4.41     4.6!l 

4.7 

94 

1.1 

1.1 

1.1 

35 

7 

9.9 

8 

1.8 

8 

5.9 

4.1 

65 

1     3.31     3.51 

3.6 

95 

0     1.0 

0     1.0 

0     1.2 

36 

7 

5.2 

7 

8.9 

8 

0.7 

3.8 

i   66 

1     2.21     2.4 

1 

2.5 

96 

.8 

.8 

.8 

37 

7 

0.8 

7 

4.2 

7 

7.7 

3.5 

1   67 

1     1.21     1.4 

1 

1.5 

97 

.7 

.7 

.7 

38 

6 

8.4 

6 

11.6 

7 

2.9 

3.3 

68 

1     0.31     0.4 

1 

0.4 

!o 

98 

.3 

.3 

.3 

39 

6 

4.4 

6 

7.3 

6 

10.3 

3.0 

69 

0  11.4|0  11.5 

0 

11.5 

.0 

Formula,  for  4.311,  5.324,  6.337,  or  the  rate  of  vs\  au'u' 
cent,  interest  respectively,  or  the  rate  of  v. 


ciu'+c.u'+c,  for  3,  4,  5  per 


Equalization  of  Annuity  Elements. — In  explanation  of  the  preceding  Tables, 
the  single  life  annuity  a^,  on  page  240,  is  or  may  be  resolved  into  the  sum  of  products 
of  elementary  factors  of  the  form  vpat .  In  like  manner,  the  annuity  aan/  on  two  lives, 
may  be  resolved  into  elementary  factors  of  the  form  vp^Py ;  on  three  lives,  into  vpxpypz ; 
and  so  on.  In  the  logarithmic  form  of  Makeham's  law  of  mortality,  from  page  237,  we 
find  these  Annuity  Elements: 

X  (vp.,./)  =  A  {vs)+q'''(q—'i)  Xg. 
A  {vp^py)  =  A  (vs^)  +  {q^+  qy)  {q-\)  Xg. 
l{vpuPu)  =  X{vs^)  +  {q''  +  q^){q-l)Xg. 
A  {v'p^pypz)  =  A  (v's^)  +  (r  +  qv  +  q'){q-l)  ^g,  etc. 
o2  _  y'^.  ajj(j  qu-[.qu  z=  2q'"  =  q^-^-q^  +  q^,  the  annuity 


For  a  Single  Life, 
For  Two  Joint  Lives, 
For  Two  Equal  Lives, 
For  Three  Joint  Lives, 
Now  if  V  =  v's,  that  is 


US'' 


element  of  three  lives,  z,  y,  z,  with  the  rate  v',  evidently  becomes  equal  to  that  of  two 
equal  lives,  u,  u,  with  the  rate  vs.    Also  the  same  element  with  the  rate  v'  equals  that 


260 


LIFE   ANNUITIES   AND    INSURANCES. 


of  the  single  age  x  (defined  by  g*'  =  q'^  +  qy  ^-q'^)  with  the  rate  vs^.  By  the  last  two 
Tables  giving  the  correction  c,  the  true  annuities  first  computed  for  the  ages  u,  u,  and 
rate  vs,  or  vs^,  are  more  conveniently  found  through  the  ages  u  +  c,  w  +  c,  and  the  rate  of  v. 
Method  for  Simpson's  Eule  on  Page  242. — For  greater  convenience,  two 
Tables  are  here  brought  together;  the  first,  from  Table  LXV,  gives  the  Correction 
to  change  two  joint  lives  to  two  equal  ages,  which  does  not  involve  the  rate  of  interest. 
The  second,  computed  from  auu  =  ctu+c",  gives  the  correction  c"  to  change  from  two 
equal  ages,  u,  u,  to  the  equivalent  single  age,  u  +  c",  which  last  depends  on  the  rate  of 
interest 

CORRECTION    TO    BE    ADDED    TO    THE    YOUNGER    AGE    FOR    REDUCING    TWO 
JOINT    LIVES    TO    THE    CASE    OF    TWO    EQUAL    AGES. 


DUT. 

AaiES. 

0 

1 

2 

UNITS. 

3 

4 

5 

6 

7 

8 

1 
9 

Yrs. 

Y.    M. 

Y.    M. 

J.    M. 

Y.     H. 

Y.     M. 

Y.     M. 

Y.     M. 

Y. 

M. 

Y.    M. 

Y.     M. 

0    0.0 

0    6.1 

1     0.6 

1    7.3 

2    2.3 

2    9.5 

3    5.0 

4 

0.8 

4    8.9 

5    5.2 

1 

6    1.8 

6  10.6      7    7.6 

8    4.7 

9    2.0 

9  11.6 

10    9.5 

11 

7.3 

12    5.5 

13    3.7 

2 

14    2.0 

15    0.6  i  15  11.2 

16  10.0 

17    8.8 

18    7.7 

19    6.7 

20 

5.9 

21    5.0 

22    4.3 

?;3 

23    3.6 

24    3.0  !  25    2.4 

26    1.9 

27    1.4 

28    1.0 

29    0.6 

30 

0.2 

30  11.9 

31  11.5 

^4 

32  11.3 

33  11.0  ;  34  10.8 

35  10.6 

36  10.4 

37  10.2 

38  10.1 

39 

9.9 

40    9.8 

41    9.7 

5 

42    9.6 

43    9.5  !  44    9.4 

45    9.3 

46    9.2 

47    9.2 

48    9.1 

49 

9.0 

50    9.0 

51    9.0 

6 

52    8.9 

53    8.9    54    8.8 

55    8.8 

56    8.8 

57    8.7 

58    8.7 

59 

8.7 

60    8.7 

61    8.7 

7 

62    8.7 

63    8.6 

64    8.6 

65    8.6 

66    8.6 

67    8.6 

68    8.6 

69 

8.6 

70    8.6 

71    8.6 

CORRECTION    (c")    TO 

REDUCE 
AGE 

.    TWO    EQUAL 
.—INTEREST    4 

AGES   TO    THE 
PER    CENT. 

EQUIVALENT 

SINGLE 

Equal 
Agbs. 

0 

1 

2 

UNITS. 

3 

4 

5 

6 

7 

8 

•  9 

Yrs. 

Y. 

M. 

Y.     M. 

Y.     M. 

Y.     M. 

Y.     M. 

Y.    M. 

Y.    M. 

Y.     M. 

Y. 

M. 

Y.    M. 

1 

2 

3 

c«4 
2 

21 
16 
13 

10 

5.2 

6.8 
.1 

7.2 

20  10.7 
16    1.8 
12    8.6 
10    4.9 

20    4.3 
15    9.0 
12    5.2 

10    2.8 

19  10.0 
15    4.3 
12    2.1 
10    ■  .8 

19    3.9 

14  11.9 

11  11.0 

9  10.9 

18  10.0 

14    7.5 

11    8.1 

9    9.0 

18    4.2 
14    3.3 
11     5.2 

9    7.2 

17  10.6 

13  11.3 

11    2.5 

9    5.6 

17 

13 

11 

9 

5.2 

7.4 

.0 

40 

16  1L9 

13    3.6 

10    9.5 

9    2.5 

H  6 

6 

7 
8 
9 

9 

8 
7 
7 
5 

1.1 
2.5 
8.4 
.5 
7.6 

8  11.8 
8    1.8 
7    8.0 
6  10.4 
5    3.8 

8  10.5 
8     1.0 
7    7.5 
6    7.6 
4  11.6 

8    9.3 
8      .3 
7    7.0 
6    4.8 
4    6.1 

8    8.1 
7  11.7 
7    6.4 
6    2.5 
3    9.5 

8    7.1 
7  11.1 
7    5.8 
6    0.9 
3    1.0 

8    6.0 
7  10.5 
7    5.2 
5  11.4 
2    3.8 

8    5.1 
7  10.0 
7    4.4 
5  10.1 

8 

7 
7 
5 

4.2      8    3.3 
9.4      7    8.9 
3.4      7    2.2 
9.2      5    8.2 



i                1 

Thus  for  two  Equal  Ages  of  38  years  each,  the  4  per  cent,  annual  correction  addi- 
tive, is  11  Y.,  giving  the  equivalent  single  Age  49  Years.  Ten  years  after  this,  the 
equivalent  single  age  for  finding  the  life  annuity  will  be  48  Y.  +  9  Y.  4  M.,  or  57  Y.  4  M. 

For. a  rate  (i)  of  Interest  other  than  Jf  per  cent. — First  find  the  4  per  cent,  correc- 
tion c",  and  re-enter  the  Table  with  the  corrected  argument  m-|-10(.04 — i)c",  which  will 
guide  to  the  correction  sought.  Here  10  (.04 — t)c"isfor  3  per  cent,  ^-^ig^"  ;  3^  per 
cent. -1-^V^"  ;  4|  per  cent  — ^V '  j  ^  P^^  cent— ^c'' ;  6  per  cent— ^". 

14.    SURVIVORSHIP    INSURANCES. 

Required  the  single  premium  to  insure  $1,  to  be  received  at  the  end  of  the  year  in 
which  X  dies,  provided  another  life  y  be  then  living.  This  is  sometimes  termed  the 
insurance  of  "  x  against  y." 

The  probability  of  receiving  the  $1  at  the  end  of  any  specified  year,  as  the  second, 

depends  on  the  probability  -~  •  -y-  that  both  are  alive  at  the  beginning  of  the  year, 
multiplied  into  the  sum  of  the  two  probabilities,  (1)  that  x  may  die  in  said  second  year 


SINGLE   AND    ANNUAL    PREMIUMS.  261 

and  y  survive  through  it,  or  {l—px+i)py+\-  (3)  that  both  may  die  in  the  second  year, 
X  dying  first,  or  i(l— J^ar+i)  (1— JOy+i).  This  last  expression  is  multiplied  by  ^,  since  it 
is  considered  an  even  chance  for  so  short  a  period  as  one  year,  whether  x  or  y  will  die 
first,  whatever  be  the  difference  of  their  ages. 

The  sum  of  (1)  and  (2)  is  ^{\-p^^-^)  {l+py^i),  or  \  (l-^)  (l  +  ^^--).  And  the 

product  of  this  sum  by  the  previous  factor  and  by  v^  gives  the  second  term  of  the  series 
or  formula  for  the  single  premium  : 

A?_  ix — 'x+1    Iy-\-iy+l         .    ix+l — 'x+2    'y  +  l-\-iy+2    .gi 

Ix  '^'y  ^x  '^'y 


In  this  notation  for  A,  the  1  written  over  the  x,  expresses  the  condition  that  x  is 
to  die  before  y:  otherwise  the  insurance  is  void.  Performing  the  multiplications 
indicated,  we  have 

Aa^  =  „,   ,    l\tx'y — lx  +  l'y  +  l-{-lx'>/  +  l — 'yix+l)V 
4)1  xly 

+  (Jx+liy+X  —  ix+fliy+2  +  Ix+liy+fi  —  iy+l^x+yf^ 
+ ]. 

This  expression  can  be  resolved  into  three  simpler  series,  as  shown  on  page  184  of 
Milne's  treatise.  Thus,  the  sum  of  the-  terms  characterized  by  the  first  factor 
ixiy — ^x+i^y+i  is  identical  with  the  half  joint  life  premium  ^Aa^.  The  factor  Ix^y+i  is  a 
type  of  the  next  series,  which  being  multiplied  and  divided  by  lx-\ly,  takes  the  form  of 
\ax-i.y-^Px-i  •     And  the  remaining  series  is  like  it ;  so  that 


L  _  1  /  A       1  ^x-l.y     ax.y—\\ 

'  2  \  Px-\  py-l  / 


Px-1        Py- 
Aa;y  -f"  -^xy  =^  Aa^  ',  A.xx  ^^^  i-^xx' 

When  x  and  y  are  both  of  the  same  age,  the  expression  is  thus  simplified  by  the 
evident  cancelling  of  the  last  two  terms.  Also,  by  changing  each  term  into  the  Com- 
rmUation  notation,  and  observing  that  Vvpx-iT)x—\.y  =  ^tey,  we  verify  the  formula 
already  given  on  page  248,  Note  1,  for  the  single  and  the  annual  premium. 

Another  formula  can  be  obtained  by  substituting  the  middle  value  /y+|  in  place  of 
i(^y  +  ^y+i)j  3,nd  so  forth,  in  the  primary  formula,  which  will  be  sufiiciently  exact.  The 
coefiicient  of  v  divided  by  Ixly,  thus  becomes  {Ix—iee+ijly+i ,  or  ljy+i—lm+iiy+^ ,  the 
result  for  the  first  year.     And  the  sum  of  the  series  for  the  first  and  following  years, 

will  be,  if  ~^  is  replaced  by  \  / : 

ly  ^  \  Py-i 

A^  =  . /X.  («^-^i_«,.^_A 
V  Py-l   ^   Px-i  / 

Example. — Let  ar  =  «/  ==  35  years,  with  interest  4  per  cent.  The  equal  ages  to 
give  the  two  annuities,  are  found  by  Table  LXV  to  be  34^  and  34|-  years,  for  entering 
Table  LXXII.  And  the  logarithm  of  the  radical  factor  is  \  of  0.003500  found  in 
Table  XXVII.  Completing  the  calculation,  we  find  the  single  premium  0.21416  on 
each  $1  insured.  Verification  is  obtained  by  the  previous  formula,  which  gives 
iA35.35  =  .21408 ;  and  this  appears  a  trifle  more  exact  than  the  result  above,  which 
depends  substantially  on  the  difference  of  annuities  tabulated  to  three  or  four 
decimals.  Dividing  the  single  premium  by  1+aa-y,  that  is,  by  l  +  ass.ss  or  by  14.8678, 
gives  the  annual  premium  0.014399  on  each  $1  insured. 

Changing  now  the  last  formula,  or  rather  its  previous  series,  into  the  notation  of 
De  Morgan  and  of  Chisholm,  we  may  find  the  values  of  D,  N,  in  the  Tables  for  Two 


262  LIFE   ANNUITIES   AND    INSURANCES. 

Joint  Lives,  or  the  values  of  D,  N,  S,  in  the  Tables  of  Single  Life,  entered  with  the 
equivalent  single  age  from  page  259,  and  thence  the  value  of  M^  or  E^  below : 

1  M —  1  ^.tiLti  x+y+A 

A^  =  Yr^;       '^s^-={lx—lx+\){ly^\)v     2       +{lx+l  —  lx+^){ly+\\)v     2"  + 

SJxy 

E^  =  M^  +  Ma;  +  l.y+l+  Ma;+2.j,+2+  •  '  •• 

Mi^  =  vlNa-.y+i  — ■y^Na;+i.y+4  ;      Ei^  =  vi^x.y+\—V^^x+\.y+\. 

Insurance  of  $1  on  the  life  of  x,  if  y  be  the  survivor : 

Single  Premium,     N^  =  ~  ;  Annual  Premium  =  =--^- 

'^xy  -Nary 

Insurance  of  11  on  the  life  x,  if  y  be  the  survivor,  with  return  of  net  premium 
or  premiums  paid,  if  y  die  first : 

Single  Premium, ^—  ;  Annual  Premium  = ^ 

-L'a^ — -iVlxy  ^xy  —  -tncy 

Insurance  of  $1  on  the  life  of  x,  provided  he  die  last  of  the  two  lives  x,  y : 

1  ^  j^ 

Single  Premium  =  Aas— A^  ;  Ani;iual  Premium  =  -- — ^^- 


l+a. 


xy 


Insurance  of  $1  upon  the  life  x,  deferred  n  years,  and  contingent  upon  v  surviving 
that  term  : 

Mx+n    ly+n^  A„„„„i  T>„„^:: ^x  +  iJy  +  n 


Single  Premium    =  -^:c — .  ^ — ;  Annual  Premium  =  -p^       , 


'^x   '   ly   '  ^xly{l  +  a^) 

Deferred  and  Temporary  Survivorship  Insurances. — For  the  single  pre- 
mium of  the  contingent  insurance  deferred  n  years,  and  of  the  temporary  insurance 
during  n  years,  we  have  respectively, 

„  A  L  _  Dx  +  n.y+n    j^A 

iJxy 


An-  —  A-      «A-  —  A-         ^x+n.y+n    .— !^ 

■"•ay  —  -ti-ary —   -^scy  —  ^^xy  —        j^ '-i^x+n.y+n' 

■L'a 


^x+n.y+n 
'xy 


The  divisor  to  give  the  annual  premium  will  be  1  plus  the  temporary  annuity  on 
the  joint  lives  for  one  year  less  than  the  whole  period  of  payment. 

Attention  has  been  called  to  this  advantageous  method  of  determining  the  single  premium  of 
deferred  or  of  temporary  insurances,  by  Mr.  Peter  Gray,  who  states  that  it  applies  to  all  insurances, 
depending  on  the  first  death  from  among  any  assigned  number  of  lives.  The  commutation  formula  for 
temporary  annuities  will  furnish  another  illustration.  An  equation  between  two  or  more  benefits  is 
first  presupposed.  Then  by  transposition,  or  solution,  each  benefit  may  be  expressed  in  terms  of 
the  others. 


SINGLE   AND    ANNUAL    PREMIUMS. 


263 


General  Solution. — For  the  more  general  case  of  an  insurance  of  $1,  payable  at  the  end  of 
the  year  of  first  death  among  the  {m)  lives  x,  x",  x'",  ....  provided  all  the  other  (n)  lives  y',  y",  y'" , 
....  are  then  surviving,  Mr.  Makeham  has  given  a  strikingly  original  formula  in  the  Journal,  vol.  9, 
page  363,  reproduced  by  Mr.  Woolhouse  in  vol.  15,  page  403.  First,  two  auxiliary  single  ages  x,  y, 
are  to  be  found  such  that, 


gx  —  q<tfj^qx"^qx"'^ 


—  qv'^qy"j^qy"'^ 


The  logarithms  of  q  and  s  are  given  on  page  237 ;  and  that  of  8  or  —log  v,  at  the  end  of  Table 
XLIII.  As  usual,  Ax',  y'..  will  denote  the  ordinary  single  premium  of  insurance  on  all  the  joint  lives. 
Multiplying  by  ^v  in  order  to  change  from  "  continuous  "  to  ordinary  premiums,  we  find  the  formula 
equivalent  to 

mqv—nq^  j  \/v 


^{x'x" . .  )y'y" . .  — 


(    VV     ,  1  /        1  1     ,  1\    .  \        ,  m  K 

I    <5        ^s     Xtn  +  n     d      ^  si      "     |       m  +  w 


as',  .y' .. 


For  the  simplest  case,  that  of  an  insurance  payable  after  the  death  of  x,  provided  y  survives  him, 
we  have  w  =  w  =  1.    And  first,  if  x  be  the  younger  life,  with  interest  4  per  cent. 

a|,  =  -y^^  (0.158117-0.661249A„^)  +  iAa^. 


a'  -\-V  Kxy 


Alog-  =  3.801012; 


X^fo  =  1.991483. 


Here  a!  denotes  the  first  term,  and  V  the  whole  coefficient  of  kxy.  To  facilitate  calculation,  their 
values  are  sketched  in  the  following  Table.  The  Italic  n  is  annexed  to  the  logarithm,  when  the 
number  6'  is  negative.  When  x  is  greater  than  y,  q^  will  exceed  qy  in  the  general  formula  ;  hence  if 
X  be  the  older  of  the  two  lives,  and  if  the  difference  of  ages  is  accounted  positive. 


A^=:  -a'  +  {l-b')A 


<ey 


Also  page  294. 


VALUE   OF   a'    AND    Xb'   ACCORDING    TO    THE    DIFFERENCE    OF    AGES. 
INTEREST    4    i'ER    CENT. 


TUFF. 

A  ass. 

a'. 

Ab'. 

DiFF. 

Ages. 

a'. 

Xb'. 

DiFF. 

Aqes, 

a'. 

Xb'. 

DiFP. 

Ages. 

a'. 

Xb'. 

1 

0.00751 

1.67080 

13 

0.08690 

i.13536. 

25 

0.13124 

2.6887l7i 

37 

0.14900 

1.09030?i 

2 

.01499 

.64079 

14 

.09201 

.06150 

26 

.13348 

.76515/i 

38 

.14980 

.10202n 

3 

.02239 

.60891 

15 

.09684 

2.97774 

27 

.13556 

.82546?i 

39 

.15054 

.11246ft 

4 

.02970 

.57494 

16 

.10140 

.88044 

28 

.13747 

.87449?i 

40 

.15121 

.12178ft 

5 

.03688 

.53878 

17 

.10569 

.76339 

29 

.13923 

.91520/1 

41 

.15182 

.13012ft 

6 

.04390 

.50023 

18 

.10972 

.61445 

30 

.14085 

.94956^1 

42 

.15238 

.13760» 

7 

0.05074 

1.45908 

19 

0.11349 

2.40475 

31 

0.14234 

2.97889/i 

43 

0.15290 

1.14431ft 

8 

.05738 

.41505 

20 

.11701 

.02821 

32 

.14370 

1.00418« 

44 

.15336 

.15034ft 

9 

.06379 

.36781 

21 

.12029 

3.48477» 

33 

.14496 

.02615?* 

45 

.15379 

.15577ft 

10 

.06996 

.31690 

22 

.12334 

2.l9920tt 

34 

.14610 

.04535ft 

46 

.15418 

.16066ft 

11 

.07587 

.26176 

23 

.12618 

.44206/1 

35 

.14715 

.06222/i 

47 

.15453 

.16507ft 

12 

.07974 

.22151 

24 

.12880 

.58729» 

36 

.14812 

.07711» 

48 

.15485 

.16905ft 

Example. — Required  the  single  premium  on  each  $1  of  insurance  payable  after  the 
death  of  a;  aged  17,  if  y,  now  aged  57,  shall  then  be  living.     Interest  4  per  cent. 


Ai7.57 


0.15121- [1.12178]  An.57  =  0.07574.. 


Here  the  difference  of  ages,  40  years,  gives  the  Equal  Ages  49  Y.  11.3  M. ;  whence 
by  Table  LXXIV,  Aiy.s?  is  .57016  on  $1,  for  the  remaining  operation,  with  a'  and  Xb'  at 
(x—y)  40  years.     The  former  approximation  by  annuities  verifies  the  answer  0.07575. 


864 


LIFE  ANNUITIES   AND   INSURANCES, 


15.     INSURANCES    PAYABLE    AT    THE    INSTANT    OF    DEATH. 

The  received  system  of  premiums  assumes  the  sum  insured  to  be  paid  at  the  end 
of  the  year  of  death  ;  that  is,  on  the  average,  six  months  after  death.  Hence,  if  the 
sum  insured  (s)  were  paid  at  the  instant  of  death,  it  would  be  increased  at  the  year's 

end  by  six  months'  interest,  that  is,  by  the  factor  11 4--),  or  the  divisor  *<Jv  according 

to  some  writers,  where  i  denotes  the  yearly  rate  of  interest.     If  the  common  insurance 

sis  to  be  thus  increased  to  s(l  +  -j,  the  premiums  should  be  increased  in  the  same 

ratio,  that  is,  by  adding  6  months'  interest,  or  by  the  factor  1  +  ^  •     By  similar  reason- 

ing,  if  the  insurance  is  to  be  paid  three  months  after  death,  that  is,  on  the  average, 
three  months  before  the  expiration  of  the  year  of  death,  then  3  months  interest  should 
be  added  to  the  premium,  whether  the  premium  be  single,  annual,  or  by  other  install- 
ments. The  factor  (i  +  t)  will  make  this  last  addition,  which  illustrates  the  process 
for  other  cases. 

It  will  be  proper  to  add,  that  a  three  months  increase  is  more  commonly  included 
in  the  "loading"  of  the  office  premiums.  The  subject  is  more  fully  analyzed  in  the 
"continuoiis  method,"  which  assumes  all  insurances  to  be  payable  at  the  instant 
of  death. 


16.    SEMI-ANNUAL    AND    QUARTERLY    PREMIUMS. 

According  to  Mr.  Woolhouse  in  the  Assurance  Magazine,  Vol.  XI,  page  327 ;  in 
official  practice,  it  is  a  safe  and  convenient  rule  to  take  the  yearly  premium  a  year 
higher  when  one-fourth  of  it  is  to  be  paid  quarterly,  and  half  a  year  higher  when  one- 
half  of  it  is  to  be  paid  half-yearly.  This  will  rather  more  than  cover  the  true  calcula- 
tion, as  it  should  do  to  provide  for  the  additional  cost.  Rigorously,  if  tt  denote  the 
annual  premium  on  II  insured  for  life,  and  tt'  the  increased  value  when  payable  in  m 
instalments,  it  is  there  proved  that 

Table  XLIII. 


i_(:_„+.)['±^V"^  (,+.)] 


SECTION    VII. 
Keserve   or    Valuation    of  Policies. 

The  annual  changes  of  Reserve  or  Net  Value  are  exemplified  in  the  common  life 
policy.  By  Table  LXIII,  at  the  age  of  entry  4G  years,  the  net  Annual  Premium  is  $28 
on  11000  insured  ;  and  the  Reserve  for  different  Durations,  or  Policy  Years,  as  the 
annual  premiums  are  paid,  will  be  as  follows : 


Policy  Years .... 
Duration  Years .... 

1st. 

2nd. 

3rd. 

Etc. 

0 

01 

1 

1 

u 

3 

2 

2h 

3 

Premiums  paid .... 

28.00 

28.00 

28.00 

— 

Net  Value 

28.00 

22.82 

17.64 

45.64 

40.66 

35.68 

63.68 

58.89 

54.10 

.... 

VALUATION   OF  POLICIES.  265 

At  the  beginning  of  the  insurance,  the  Net  Value  is  equal  to  the  Premium  paid : 
the  risk  of  death  incurred  during  the  following  twelve  months,  continually  decreases 
this  value  till  the  close  of  the  first  year.  Then  the  premium  paid  at  the  beginning  of 
the  second  year,  carries  up  the  Reserve  joer  saltum  to  a  much  higher  point;  when  the 
twelve  months  decrease  again  commences ;  and  so  on. 

In  the  case  of  paid-up  Pohcies,  the  Net  Reserve  changes  continuously;  either  hy 
increase,  as  in  Table  XXXI,  for-  whole  life  policies;  or  by  decrease,  as  in  Table  LII, 
where  the  Single  Premium  at  the  age  of  24  is  $36.86,  and  at  the  age  of  25  it  is  $31.58, 
on  an  Insurance  of  $1000  terminating  at  the  age  of  30. 

MONTHS    AND    DATS. 

The  decrease  of  Net  Value  from  the  beginning  to  the  end  of  each  policy  year,  is 
conventionally  assumed  to  be  uniform.  For  example,  when  a  policy  has  been  in  force 
5  years  and  4  months,  the  decrease  in  the  4  months  is  one-third  of  the  whole  decrease 
between  the  beginning  and  the  end  of  the  6th  policy  year.  Or  multiply  the  tabular 
difference  for  the  mean  half-month  {\m.  d.)  by  double  the  number  of  months.  And 
for  odd  days,  take  proportional  parts  of  {^m.  d.)  representing  15  days.  That  is, 
account  1  day  as  ^j  or  -^,  and  2  days  as  -^j  also  3  days  as  ^  or  ■^,  and  6  days  as  ^, 
also  9  days  as  ^j^,  and  12  days  as  ^^ ;  also  5  days  as  ^,  and  10  days  as  f.  The  correction 
will  be  added  or  subtracted  according  to  increase  or  decrease  of  the  tabular  Reserve. 
Other  modes  of  proportional  correction  will  be  indicated  in  Tables  LXIII  and 
LXXIV. 

VALUATION    TABLES    FOR    PAID-UP    POLICIES. 

At  every  age,  the  Net  Value  evidently  coincides  with  the  Single  Premium,  for  the 
unexpired  term  of  the  same  species  of  insurance.  Single  Premiums  will  be  found 
already  computed  in  Tables  XXX,  XXXI ;  by  Months  in  Tables  L,  LI ;  for  Terra  and 
Endowment  Insurances,  Tables  LII,  LIV ;  and  for  Joint  Lives  in  Table  LXXIV. 

ANNUAL    PREMIUM    POLICIES. 

^     ■ 

Prospective  Forms  of  Net  Valuation. — The  general  principle  is  simply, 
from  the  net  single  premium,  of  the  given  species,  at  the  age  of  valuation,  to  deduct 
the  present  value  of  the  future  net  annual  premiums  receivable. 

Let  s  denote  the  sum  insured,  and  Px  the  annual  premium  thereon,  at  the  age  of 
entry  x.  At  the  end  of  the  nth  policy  year,  or  at  the  age  x-\-n,  when  the  next  annual 
premium  is  just  due  but  unpaid,  the  Net  Value  of  a  common  life  policy  will  be,  if 
Ax+n  denote  the  net  single  premium  ou  each  $1  insured, 

yx  +  n^=S.Ax+n — Pa'(l +^x+7i)> 

If  the  premium  has  just  been  paid,  by  adding  it,  and  accenting  V, 

y  x+n '=  S .Ax+n — i^x-(^x+n- 

When  the  valuation  is  made  by  the  same  table  of  mortality  and  rate  of  interest 
with  the  premium,  the  former  expression  will  be  simplified  by  substituting,  for  A,  P, 
their  equivalents  in  terms  of  v,  a;  the  result  is,  on  each  $1  insured, 

V'l       ^-\-ttx  +  n        ttx  —  flx^n  \ri  .        (h;+n 

x+n  =  J- -.    ,  ^       —  -^TT  7. —  '  V  ar+n  =  V—z.         -  , 

l  +  «a:  l+««  l  +  Oflj 


266  LIFE  ANNUITIES   AND    INSURANCES, 

^j         _  -,       1— Aa.+n_  Vx+l—V 

Va:+re  —  -L ^        i        —  J-- 


In  the  case  of  two  joint  lives, 


x+n.y 

And  on  the  survivor  of  two  lives, 


-(       1  -{-(Ix+n.y+n 

x+n.y+n  —  J- -.    ,    "  * 

1-t-ttary 


1       1  -T-Q'X+n~\~((y-¥n  —  flx+n.y+n 

x+n.y+n  —  J- ^    r~~     j  * 


-\-ttx-\-tty  —  ttxy 

By  another  mode  of  reasoning,  if  Fx+n  denote  the  annual  premium  at  the 
advanced  age  x-{-n,  then  the  difference  Fx+n — Paj  measures  the  annual  saving  in 
premium  of  the  former  policy  over  an  assumed  new  policy.  The  present  value  of  these 
sa"sdngs  will  of  course  be  the  present  value  of  the  former  policy ;  that  is,  if  the  premium 
is  just  due,  but  not  paid, 

Va;+«  =  {"x+n  —  ^x)  (l+Cfx+n)- 

EuLE. — Take  the  difference  between  the  net  annual  premium,  which  would  be 
required  at  the  advanced  age,  and  the  net  annual  premium  charged  in  the  pohcy, 
multiply  it  by  unity  added  to  the  value  of  the  annuity  at  the  advanced  age  of  the  life 
insured ;  the  product  will  be  the  Reserve. 

The  last  formula  is  equal  to  the  first  one,  since  Ax+n  =  Pa!+n  (l  +  «ar+»).  Again, 
since  Ax+n  =  1  —  (1 — v)  (1  +«x+w)>  we  have  from  the  first  formula  on  page  265  : 

Var+«  =  1  — (1— v  +  Par)  (l+ctx+n),  ou  each  $1  insured. 

By  proper  change  of  the  annuity,  as  noted  above,  this  formula  will  likewise  apply  to 
two  joint  lives,  or  to  the  survivor  of  them. 

On  all  Temporary  and  on  Endowment  Insurances  of  $1  insured  for  the  term  of  m 
years,  after  the  age  of  entry  x,  the  Reserve  at  the  intermediate  age  x-\-n,  when  the  next 
premium  is  just  due  but  unpaid,  will  be 

V       —  A'""'*       P  n  4-^"*""'"^^ 

^x  +  n  —  ^x  +  n   —  J:x\^n^"x  +  n       )• 

Here  A  denotes  the  single  premium  of  the  given  species  of  policy,  and  a  the 
temporary  annuity  at  the  age  x-{-n  for  the  remaining  m—n  years.  The  same  Reserve 
with  the  annuity  expressed  in  commutation  terms,  will  be 


m—n      T»     ^x  +  n  —  ^x+m 


y  x+n  —  -i^x+n — ^x-  -r\ 

iJx+n 

) 

The  value  of  an   Endowment  Insurance   for  m  years,  with   premiums  payable 
annually,  may  be  simplified  like  that  of  the  common  life  policy,  as  follows : 

-,       1  -{-dx+n        1       ^x+n  —  ^x  +  m      ■L'a; 


1+af'-^  ^x-^x+m    "Ox  +  n 

Valuation  by  Gross  Premiums. — Let  Pa;  denote  the  net  annual  premium  on 
any  policy,  and  P'a;  the  loaded,  gross,  or  office  premium.  Then  will  the  difference 
between  the  gross  and  the  net  valuation  be  expressed  by 

{P'x-Fx){li-a^+r'),  or  (P',_P,)^^=-_%.-- 


VALUATION   OF  POLICIES.  267 

This  is  the  present  value  of  the  loading  receivable  in  the  future.  Since  many 
policies  will  be  discontinued,  it  belongs  to  the  uncertain  or  "unrealized  assets ;"  which, 
as  they  accrue,  may  be  the  material  of  future  dividends.  In  the  early  years  of  life 
insurance  in  the  United  States,  the  Carlisle  4  per  cent,  mutual  premiums  were  loaded 
35  per  cent. 

RETROSPECTIVE    FORMS    OP    NET    VALUATION. 

In  apparent  contrast  with  "  Prospective  Valuation  "  which  has  just  been  shown  to 
be  based  on  the  present  single  premium,  and  on  future  annual  premiums,  "  Ketrospec- 
tive  Valuation  "  is  based  only  on  past  premiums  already  received.  Yet  by  a  singular 
coincidence,  in  net  valuation,  the  Keserve  found  by  the  first  method,  from  premiums 
future  and  unpaid,  is  precisely  the  same  as  the  Reserve  of  the  second  method  from 
premiums  past  and  paid.  This  will  be  the  more  evident  from  the  direct  transformation 
of  Prospective  formulas  into  Retrospective.  Let  us  take,  for  example,  the  Prospective 
formula,  giving  the  Reserve  at  the  end  of  6,.  or  more  generally,  n  years,  on  a  ten-pre- 
mium life  policy  for  $1  insured : 

Substituting  for  Ma;+w  its  equal,  M^— (Ma;— Ma;+n), 

Ma;— Ma,+« 


„         _     Ma;    /         Na;+ra  — Na;  +  10\ 
^^■^"-Da;.„r         N^-Na:.10   / 


Da:^ 


^^  Pa;(Na;  — Na;  +  n)  — (Ma;  — Maj+n) 

M3. 

Here  the  premium  P^,  =  ^r^: ^ ;  and  the  formula  now  involves  no  future  age, 

-Ma;  — JNa;  +  10 

but  only  the  past  or  retrospective  ages  x  and  x-\-n  ',  hence  the  name  of  Retrospective 
Formula,  proposed  in  the  original  memoir  by  James  Meikle,  Journal,  Vol.  XI,  p.  245. 

If  Tx  denote  the  annual  premium  of  Temporary  Insurance,  and  E^  that  of  Pure 
Endowment,  for  w  years;  then  dividing  both  numerator  and  denominator  of  the 
formula  by  'Nx—l^x+n,  and  substituting  equivalents,  we  have  the  second  form,  on 
each  $1  insured : 


Va+n  — 


X —  J-g; 

En 
3! 


By  substituting  for  Ma;  its  equal  Da;— (1  — y)  Na; ,  and  so  for  Ma;-t.«,  we  obtain  a 
third  form  ;  and  then  by  substituting  773,+ (1—v)  Na,  for  its  equal  D^,,  the  fourth  form 
following,: 

V  _(Pa,  +  l-v)(Na,-N«,  +  n)-(Da,-D.+«) 

VtB+re  — =P^ • 

iJx  +  n 

XT         _  (P«— 7ra,)N"a,— (P„  +  l  — v)N<B+n  ,  1 

yx+n  — T=^ r-»-« 

iJx  +  n 

By  an  obvious  modification,  we  obtain  a  fifth  and  more  general  formula,  which 
includes  the  single  premium  and  others: 

V  _  bx'Dx  +  bx  +  l.'Dx+l-}- — J?  (Ma,  — Mfl,  +  n) 

V«!  +  n  — '~ ~ jC ""■ ~  • 

iJx+n 


268  LIFE  ANNUITIES   AND   INSURANCES. 

Here  each  annual  payment  hx,hx+i, (which  may  be  negative),  is  treated  as  a 

single  premium  of  pure  endowment,  due  at  the  age  of  valuation  x  +  n.  The  sum  of 
these  terms,  less  the  cost  of  temporary  insurance  of  s  from  age  x  to  the  age  x-^-ii^ 
gives  the  required  reserve  or  net  value.  All  the  retrospective  formulas,  coinciding 
entirely  with  the  principle  here  stated,  require  no  further  demonstration. 


ELEMENTARY    FORMULA    OF    VALUATION. 

Let  Sx  denote  the  amount  of  insurance  in  force  during  the  1st  year;  Sx+i  the 
amount  during  the  2d  year :  Sx^^  during  the  3rd  year  ;  etc.  The  years  are  past,  but  at 
the  age  x,  the  series  may  be  resolved  into  deferred  temporary  insurances  of  one  year 

each;     so    that    the    factors    to    give    their    present  values,   would    be   — ~Tr~^^» 

Dx 

— ^i^— — —  , And  the  common  factor  to  change  these  present  values  to  equiva- 

I) 
lent  endowments  or  reserve,  at  the  age  x+7i,  will  be  ^pr—  •    So  that  on  cancelling  Dx, 

iJx+n 

and  writing  Ox ,  C»+i , ,  f or  the  differences  of  M, 

(E)  V«,+„  = 

&a;.Dai  +  5a;+l.Dj+l+  •  •  •  •  +^tg+w-l  •  Djb+w-I — gg-Cg) — ■Sg+i-Cg+l —  .  .  .  •  — gg,4-n-i  ■  C-p+n-l 

Da!+n 

Eeturn  Premiums. — For  application,  let  Pa-  denote  the  net  annual  premium  to 
insure  a  sum  s ;  and  let  V'x  denote  each  of  the  total  premiums,  whether  gross  or  net, 
to  be  returned  without  interest,  at  the  end  of  the  year  of  death,  with  the  sum  insured. 
Then  by  the  last  formula  (E),  and  by  Sect.  V,  the  net  reserve  will  be 


Va!+n  = 


_   PtB  (Na,  — Nx+w)— g  (Ma;  — M3,+n)— P'tB  (Rg  — Bx+ft— ^Mg+w) 

Note. — For  a  Pure  Endowment,  with,  return  of  all  premiums  only  in  the  event  of  death,  let  a 
be  made  0,  in  the  last  formula. 

Increasing  or  Decreasing  Insurances. — If  5  +  P  =  I,  the  sum  insured  dur- 
ing the  first  year;  or  s  =  l  —  V'x,  and  P'ai  the  annual  increase,  the  formula  (E)  will 
give  the  net  value  of  any  increasing  insurance.  Or  by  changing  the  sign  of  P',  it  will 
give  the  value  of  a  decreasing  insurance,  proNided  s — Pa;  =  I,  denote  the  sum  insured 
during  the  first  year  ;  whence  s  =  I  +  P'«;. 

Increasing  or  Decreasing  Premiums. — By  the  general  formula,  if  V  -\-h  denote 
the  first  net  annual  premium,  and  h  its  annual  increment,  so  that  P  +  A,  P  +  2A,  .... 
P  +  nh,  are  the  annual  payments,  by  reference  also  to  Sect,  V, 

^         _  Pte  (^x—^x+n)+h  {^x  —  ^x+n  —  nl^x^r^  —  S  (Ma;  — Ma,+n) 

By  making  h  negative,  and  determining  P  from  the  relation  V—h  =  b,  the  first 
annual  premium,  or  Fx^=  bx  +  h;  this  formula  will  apply  to  decreasing  premiums. 


VALUATION   OF  POLICIES.  369 


VALUATION     TABLES    FOR    ANNUAL    PREMIUM    POLICIES. 

The  Net  Value  or  Reserve  on  Ordinary  Life  Policies  of  $1000  is  given  in  Table 
LXIII,  for  the  middle  and  the  end  of  each  year,  with  half-monthly  differences  for 
interpolation.  The  similar  values  for  Ten  Payment  Life  Policies  are  computed  in 
Table  LXII.  For  other  species,  such  as  Limited  Premium  Life,  Term  and  Endow- 
ment Insurances,  on  the  plan  of  an  average  annual  premium,  the  several  Tables  which 
give  this  premium  P,  give  also  the  auxiliary  A  (P — tt).  And  the  mode  of  applying 
this  auxiliary  to  give  the  Reserve,  is  fully  described  at  the  beginning  of  Table  LXIII, 
on  Page  *154.     The  formula  there  given  for  the  "  End  of  Policy  Year  "  is  thus  found  : 

Let  TTa,  denote  the  Annual  Premium  of  the  Ordinary  Life  Policy  on  $1000,  at  the 
age  X ;  then  by  the  preceding  first  form  of  Retrospective  Valuation : 

y  _  -n-a-  (Na,-ya,+n)-1000  (M^  — Ma;+n)^ 
l^aj+n 

And  let  Pa-  denote  the  Annual  Premium  of  a  different  species  of  Policy  on  $1000 
issued  at  the  same  age  x.  Writing  the  similar  Retrospective  Formula  of  Yx+m  and 
taking  the  difference  of  the  two  equations,  also  transposing  V,  we  obtain  the  formula 
required,  for  the  end  of  the  wth  Policy  Year : 

V.+„  =  V  +  (Pa;-Tr,)?^^^^  =  V+(P«,-^a,)  BS. 
■L'a!+n 

The  Retrospective  Formula  has  peculiar  advantages  :  firstly,  in  that  the  computer 
knowing  the  annual  premium  P,  is  exempt  from  the  trouble  of  inquiring  into  the  year 
of  termination  of  temporary  and  endowment  insurances.  Secondly,  in  showing  that 
the  Reserve  from  premiums  past  and  paid,  is  the  same  as  from 'premiums  future  and 
unpaid.  And  thirdly,  the  use  of  five  place  logarithms  in  computation,  generally  gives 
the  same  degree  of  accuracy  in  the  result,  as  six  place  logarithms  with  the  older 
prospective  formulas. 

Adjustment  for  Months,  Tables  LXIII  and  LXIV.  Let  Yx+n  denote  the 
Reserve  at  the  age  x-\-n  just  before  the  annual  premium  falls  due;  and  let 
V  =  P.r  +  Va;+n-i  denote  the  Reserve  twelve  months  previous,  just  after  the  current 
premium  was  paid.  Then,  as  will  presently  be  shown  in  Section  IX,  for  each 
$1  insured: 

Yx^n  =  l l—iy-Y'). 

Let  h  denote  the  fraction  of  the  year  elapsed  since  the  date  of  V;  and  let  V*+» 
denote  the  Reserve  at  that  time.  Then  by  proportional  decrease  since  the  beginning 
of  the  year : 

Vj.„  =  V'-A(V-V^^„)  =  {\-h)Y' ^-hYx^n. 

Eliminating  V  by  comparison  of  the  two  equations,  we  have,  on  each  $1  insured 

Yx  +  n  —  (1— /O  iy  —  V2)x^n-\)-\-Yx^n  [/i-t-(l— ^)  vpz  +  n-l]- 

Let  /=  7i  +  (l— 7i)  VyOa;+n-i-  Por  Vx+re>  let  its  former  equal  V+(Pa;  — Tr-c)  Bj 
be  here  substituted.    Then  observing  that  the  (1— /i)  (v— t;j9a;+n-i)  +  y/"  denotes  the 


270  LIFE   ANNUITIES   AND    INSURANCES. 

interpolated  value  of  the  ordinary  Life  Policy,  hereafter  denoted  simply  by  V,  we  find, 
for  each  $1000  insured,  as  on  page  *154.  or  Table  LXIII : 

The  last  equation  but  one^  may  be  transformed,  by  substituting  for  Yx+n  its  equal 
(Vx+n  —  1)  + 1 ;  thus  we  obtain  another  formula  when  Yx+n  is  known : 

Yi^n=h  +  {l-h)v-{l-Yxin)f=f'-{l-Yx,n)f. 

f  =  h  +  {l-h)v;  f=h  +  {l-h)vpx+n-i.^ 

The  value  of/'  and  the  common  logarithm  of/,  for  4  per  cent.,  are  given  in 
Table  LXIV,  for  the  beginning  and  middle  of  each  year,  and  the  middle  of  each  month. 
Intermediate  values  can  be  found  from  these  by  proportioning  the  differences.  Like 
the  last  valuation  formula,  /'  is  adapted  to  1  or  unity,  as  the  amount  insured  on  a 
single  life.  By  changing  the  decimal  point  three  places  to  the  right  in  the  final  result 
for  $1,  it  will  be  adapted  to  $1000  insured  or  the  value  of/"  below.  It  may  be  proper 
to  observe  in  the  preceding  expressions,  that  the  exponent  n  or  h  is  merely  an  extension 
of  the  suflSx  under  it;  Yx+n  meaning  the  same  as  Yx+n+h' 

VALUATION    TABLES    FOR    JOINT    LIFE    POLICIES. 

It  will  be  advantageous  to  apply  the  correction  to  give  two  equal  ages,  at  the  time 
of  entry,  by  first  taking  account  of  months,  and  applying  the  correction  from  page  260, 
or  from  Table  LXV,  so  far  as  to  determine  the  nearest  integral  age  for  the  Office 
Equal  Age.  All  future  calculations  on  the  Policy,  can  then  be  made  by  single  entry 
in  the  Tables  LXV-LXXVI,  in  the  same  manner  as  for  a  single  life.  In  the  case  of 
three  or  four  joint  lives,  the  method  of  current  "  equal  ages"  with  an  Annual  Correc- 
tion (c)  for  calculations  only,  has  been  given  on  pages  258,  259. 

Paid-up  Policies  on  Two  Joint  Lives  admit  of  Valuation  by  inspection  or  inter- 
polation in  Table  LXXIV.  On  Annual  Premium  Policies,  the  Eeserve  can  be 
calculated  from  the  single  entry  factors  in  Table  LXXVI,  when  the  net  Premium  has 
been  prepared,  as  illustrated  in  Table  LXXV.  The  formula  of  valuation  having 
precisely  the  same  form  as  for  a  single  life,  is  demonstrated  as  follows: 

Substituting  the  expression  for  Va?+w,  from  the  fourth  form  of  Retrospective 
Valuation,  into  the  preceding  formula  containing/'  and  /  we  obtain  on  $1  insured: 

Vj  n  =/'+-^  [(P^_Tr^)]^^^_(P^  +  l_^;)N^+„]. 

Assuming  P^^,  ttx,  to  be  premiums  on  $1000  insured,  and  adjusting  the  other 
terms  accordingly,  let  /"  hereafter  denote  the  former  1000/'.  Let  the  former 
/-r-Da;+«  =  Jx+n ;  and  let  h'x^n^=hx+n^x+n-  Also  let  the  prepared  premiums 
V'x  =  (Px— ^x)  Nx  ;  P"a;  =  Px  +  1000  il—v).  Then  as  computed  in  Tables  LXXV 
and  LXXVI: 

Yl+n  =f"  +  ^'x.hx^n-^"x-Vx^n,  ou  $1000  insured. 

Example  1. — An  ordinary  Policy  issued  on  the  Joint  Lives  aged  37  and  37  has 
been  in  force  5  years  4^  months.     Required  the  4  per  cent.  Reserve. 

L 84012  =  AP"37,  Table  LXXV. 
-  /"  =  975.962  1.09963  =  AJ'^,    Table  LXXVI. 

-870.46  ....2.93975       Sum,    Table  LXXXIL 

$105.50  =  Reserve  on  $1000  Insured. 


VALUATION   OF  POLICIES,  271 

Example  2. — A  Ten  Payment  Policy  on  two  Joint  Lives  was  issued  at  the  ages  of 
entry  43  and  43.     Kequired  the  4  per  cent.  Reserve  at  the  end  of  8  years  7^  months. 

6.76553  =  AP'43,     2.01450  =  AF'43,  Table  LXXV. 
/"  =  985.577  4.01727  =  uli,       1.01345  =  Xb'ii,    Table  LXXVI. 

+  606. 46      ....  2. 78280  ....  3. 02795       Sums,   Table  LXXXII. 

—  1066.50 

$525.54  =  Reserve  on  $1000  Insured. 

Value  of  a  Sukvivorship  Insurance. — At  the  end  of  n  years,  the  annual 
premium  P  being  just  due  but  unpaid,  the  Reserve  on  a  Policy  of  $1  payable  on  the 
death  of  x,  provided  y  be  then  living,  will  be 

Reserve  =  AiT^:^-P(l+«x+n.,+«)  =  {a' +  h')  (i_i+^±^J^\, 

=  {a'-\-h')  X  Reserve  on  Ordinary  Joint  x,  y,  at  the  end  of  n  years. 

This  expression  is  based  on  the  Single  Premium  a'  -\-h'Kxy  ;  and  a',  V ,  being  con- 
stant during  the  continuance  of  the  same  Policy,  are  tabulated  on  page  263.  The  age 
X  is  presupposed  to  be  younger  than  y.  When  x  is  the  older  age,  a! ,  h',  must  be 
replaced  by  — a'  and  1 — b'  respectively,  in  all  the  expressions.  These  formulas,  first 
investigated  in  the  present  collection,  depend  on  the  comparison  of  different  expres- 
sions for  equal  reserves. 

To  correct  for  Months,  whether  the  insurance  be  for  the  whole  Life,  or  Temporary, 
let  V  denote  the  Reserve  on  1000,  computed  from  Table  LXXVI,  as  if  for  ordinary 
Joint  Lives,  or  for  the  same  term,  if  Temporary ;  then,  on  the  corresponding 
Survivorship  Policy: 

Reserve  =  («'  +  *')  V  +  a'(1000— /"). 

Insurance  of  II  on  the  life  x,  if  y  be  the  survivor,  with  return  of  wP  the  net  annual 
premiums  paid,  if  y  die  first.  At  the  end  of  n  years,  when  the  next  premium  is  just 
due,  but  unpaid : 

Reserve  = ^^^^n.y^n     _ P(l+a^^„.^,„). 

l  —  {l  +  7l?)kx  +  ny^n 

For  other  rare  varieties,  reference  may  be  made  to  the  work  of  Chisholm,  who  has 

tabulated  Da^,  N^-y',  M^,  and  R^^,    for    every    yearly    difference    of    the    Carlisle 
Table. 

Short  Method  of  Determining  the  Equivalent  Amount  Insured  by 
Paid-up  Policy.  —  A  remarkably  simple  formula  was  devised  by  Sprague,  and 
extended  by  Macfadyen,  showing  at  once  the  result  of  the  double  process  of  finding 
the  reserve,  and  thence  the  equivalent  amount  insured  by  a  paid-up  policy.  In  the 
common  formula  of  valuation,  the  term  kx+n  is  the  single  premium  on  $1  of  paid-up 
insurance,  page  266.  Dividing  the  Reserve  Yx+n  or  the  whole  equation  by  this  term, 
will  consequently  give  the  equivalent  sum  insured,  which  is 

■1 -p    l+^x+n        -,  ^x 


k-^f+n 


272  LIFE   ANNUITIES   AND    INSURANCES. 

By  dividing  the  first  numerator  and  denominator  by  the  numerator,  the  denomi- 
nator takes  the  well-known  expression  for  ^xau,  given  in  the  last  fraction.  Let  s 
denote  the  amount  insured  by  the  first  policy.  Multiplying  the  above  result  for  $1 
by  5,  we  have  the  equivalent  Amount 


Insured  by  the  Paid-up  Policy  =  s  (l — :p — I  = 


Vx  +  n 
S  -T • 


Here  P  denotes  the  net  premium,  or  the  oflBce  premium  when  loaded  with  a 
uniform  percentage. 

Example  1. — A  temporary  insurance  of  $5000,  for  ten  years,  is  eflPected  at  the  age 
of  40.  After  four  annual  premiums  have  been  paid,  at  the  end  of  four  years,  the 
equivalent  amount  of  paid-up  policy  for  the  remaining  six  years  will  be,  from 
Table  LIII, 

s  (l-ps)  =  s  (l-n^)  =  5000  (1-.91799)  =  $410.05. 

Example  2. — A  person  at  the  age  of  thirty-five  years  has  an  ordinary  endowment 
insurance  of  $10,000  on  his  life,  payable  at  the  age  sixty-five  or  at  previous  death.  At 
the  end  of  ten  years,  the  sum  insured  by  paid-up  policy,  equivalent  to  the  ten  annual 
premiums  paid,  will  be,  from  Table  LV, 

This  sum  is  payable  at  "  Death  or  65,"  as  under  the  original  policy. 

NoN-FORFEitiNG  Plan. — In  comparison  with  this  correct  result  $4042.28,  "  the 
non-forfeiting  plan,"  so  called,  would  give  a  paid-up  policy  for  ten-thirtieths  or  one- 
third  of  the  original  $10,000,  which  is  only  $3,333.33.  This  is  in  the  ratio  of  the 
total  number  of  premiums  payable,  to  the  number  already  paid.  For  shorter  periods 
of  insurance,  not  much  exceeding  ten  years,  the  results  of  this  empiric  rule  will 
approach  nearer  to  accuracy.  Further  discussion  of  this  subject  may  be  found  in  the 
fifteenth  and  sixteenth  volumes  of  the  Journal,  and  an  able  article  by  Mr.  McClintock 
in  the  seventeenth  volume. 

Surrender  Value. — The  Massachusetts  non-forfeiture  law  provides  that  on 
lapsed  policies,  four-fifths  of  the  net  value  at  the  time  of  lapsing,  less  the  outstanding 
note,  if  any,  shall  be  applied  as  a  single  premium  of  temporary  insurance  to  continue 
the  policy.  And  in  case  of  death  during  such  term  of  extension,  the  unpaid  premiums 
may  be  deducted  from  the  sum  insured.  We  may  observe  that  the  premiums  of  term 
insurance  in  this  collection,  are  given  in  Table  LII ;  from  which,  corresponding  result? 
may  be  found  by  proportion. 

In  ordinary  practice,  a  deduction  is  made  from  the  Net  Value  to  giv6  the  Surren- 
der Value,  depending  on  the  health  of  the  insured,  on  the  cost  of  replacing  the  risk,  or 
other  circumstances.  The  office  system  of  deductions  generally  refers  to  surrenders 
made,  as  they  usually  are,  at  the  end  of  the  policy  year.  Todd's  Tables,  Edinburgh, 
1852,  may  illustrate  this  topic.  If  a  surrender  is  made  earlier  in  the  year,  as  at  the 
middle  of  it,  a  portion  of  the  Premium  last  paid,  will  be  returnable  to  the  insured,  for 
risk  not  incurred  in  the  unexpired  part  of  the  year.  For  illustration,  let  the  tabular 
net  value  during  the  second  year,  be  separated. into  two  parts  thus  described  :  (1)  The 


I    VALUATION   OF  POLICIES.  273 

net  value  117.64  at  the  end  of  the  first  year,  increasing  uniformly  to  $35.68  at  the  end 
of  the  second  year,  as  noted  at  the  beginning  of  this  Section.  (2)  The  net  premium 
of  $28  paid  at  the  beginning  of  the  second  year,  gradually  decreases  to  0  during  the 
ensuing  second  year.  The  full  reserve  at  any  time  in  the  second  year,  is  made  up  of 
these  two  continuous  parts,  (1)  and  (2) ;  and  the  office  percentage  is  deducted  by  Todd 
from  the  former  part  only,  while  the  latter  or  premium  part  is  directly  returnable. 
Thus  at  the  middle  of  a  policy  year,  half  the  net  premium  which  was  paid  six  months 
before,  is  subtracted  from  the  present  tabular  reserve ;  then  the  office  reduction  is 
made  for  surrender  value,  to  which  the  half  premium  is  again  restored. 

Annual  Valuation  of  an  Insurance  Office.  —  The  general  plan  is  thus 
stated  in  De  Morgan's  Essay  on  Probabilities,  page  275 : — "  The  most  simple  theoretical 
way  of  conducting  the  process,  is  to  ascertain  the  value  of  every  policy;  that  is,  to 
ascertain  how  much  should  be  given  to  the  holder  of  each  policy  to  renounce  his 
claim,  the  office  also  abandoning  the  future  premiums.  When  this  is  done,  it  is 
obvious  that  the  office  is  not  solvent,  unless  the  assets  arising  from  the  accumulation 
of  former  years  be  sufficient  to  pay  the  values  of  all  the  policies,  and  thus  to  buy  them 
all  up.  Otherwise,  calculate  the  present  value  of  all  premiums  due  to  the  office,  and 
also  the  present  value  of  all  claims  to  which  it  is  liable.  To  the  former  add  the  sum 
total  of  the  assets  of  the  office,  and  to  the  latter  add  the  present  value  of  a  perpetuity 
equal  to  the  expenses  of  management.    Thus,  let 

P  =  present  value  of  all  premiums. 

0  =  present  value  of  all  claims.  i 

A  =  total  assets  of  the  office. 

M  =  present  value  of  all  expenses  of  management. 

If  then  P  and  A  together  6xceed  C  and  M  together,  the  office  is  solvent.  On  each 
of  these  items  a  few  remarks  may  be  made. 

(P.)  All  the  parties  who  are  of  the  same  office  age,  may  have  their  several  policies 
considered  as  one  collective  policy,  in  respect  of  which  the  sum  of  the  premiums  is  paid 
as  one  premium,  and  the  sum  of  the  possible  claims  is  one  claim.  But  as  these  pre- 
miums are  payable  at  all  periods  of  the  year,  they  may  be  considered^  as,  one  with 
another,  due  at  six  months  after  the  valuation,  at  which  time  the  present  office  age  of 
the  parties  may  be  considered  to  be  their  real  age. 

(C.)  All  bonuses  which  have  actually  been  added  to  the  policies  must  be  included 
in  the  claims ;  and  the  value  of  each  claim  must  be  carefully  found,  with  reference  to 
the  time  after  death  at  which  it  is  paid. 

(A.)  The  principal  of  the  assets  must  be  deduced  entirely  by  means  of  the  income 
it  yields,  and  must  be  ascertained  from  the  income  by  njieans  of  the  rate  of  interest 
assumed. 

(M.)  Against  the  expenses  of  management  may  be  set,  as  far  as  they  go,  the 
incidental  profits,  when-  they  can  be  tolerably  well  ascertained." 

Distribution  of  Surplus.  —  The  methods  employed  in  upwards  of  seventy 
British  Life  Offices,  are  very  plainly  exhibited  by  Hewat  in  the  Assurance  Magazine, 
Vol.  XXII,  page  286.  It  appears  that  nearly  all  the  Companies  allow  the  option  of 
applying  the  dividend  to  reduce  the  current  premium  ;  and  in  the  general  average,  the 
"  loading  "  on  the  premiums  is  practically  refunded. 

The  Thirteenth  Eeport,  1868,  of  the  Insurance  Commissioner  of  Massachusetts, 
contains  a  series  of  communications  on  the  Contribution  plan  of  dividends,  originated 


274 


LIFE  ANNUITIES  AND    INSURANCES. 


by  Messrs  Homans  and  Fackler  in  1863.  A  single  illustration  and  the  formula  below 
are  recalled  and  revised  from  a  former  article  in  the  Insurance  Times  (New  York,  1868), 
Vol.  I,  page  545  : 

A  party  aged  thirty-five  years,  takes  out  an  ordinary  life  policy  of  $10,000,  at  an 
annual  premium  of  $273  (Carlisle  four  per  cent,  net,  with  35  per  cent,  loading). 
Eequired  his  annual  dividends  on  the  contribution  plan,  according  as  the  Reserve  is 
reckoned  at  three,  four,  five,  or  six  per  cent,  interest,  by  the  Carlisle  Table  ;  the  Com- 
pany receiving  six  per  cent  on  investments,  above  expenses. 


RESERVE    AT 

THREE    PER    CENT. 

RESERVE    AT 

FOUR    PER 

CENT. 

End  of 

Resebve 

Contribution 

Premium  less 

End  oi" 

Reserve 

Contribution 

Premium  less 

Ykab. 

V. 

Dividend. 

Dividend. 

Year. 

V. 

Dividend. 

Dividend. 

1 

$128.70 

$63.25 

$209.75        i 

1 

$108.50 

$81.26 

$191.74 

2 

259.90 

67.19 

205.81       ! 

2 

230.00 

83.69 

189.31 

3 

393.20 

71.19 

201.81 

3 

334.60 

85.78 

187.22 

4 

539.10 

76.56 

196.44 

4 

451.20 

88.11 

184.89 

5 

663.80 

79.30 

190.70 

5 

567.40 

90.44 

182.56 

10 

1,322.60 

99  07 

173.93 

10 

1,136.06 

101.89 

117.19 

20 

3,100.50 

152.40 

120.60 

20 

2.782.10 

134.73 

138.27 

30 

4,898.00 

207.83 

65.17 

30 

4,538.40 

169.86 

103.14 

RESERVE    AT 

FIVE    PER 

CENT. 

RESERVE    AT 

SIX    PER 

CENT. 

End  of 

Reserve 

Contribution 

Premixtm  less 

End  of 

Reserve 

Contribution 

Premium  less 

Ykab. 

V. 

Dividend 

Dividend. 

Year. 

V. 

Dividend. 

Dividend. 

1 

$92.20 

$96.16 

$176.84 

1 

$79.20 

$108.33 

$164.67 

2 

188.60 

97.12 

175.88 

2 

161.10 

108.33 

164.67 

3 

285.90 

98.12 

174.88 

3 

245.80 

108.38 

164.67 

4 

386.90 

99.11 

173.89 

4 

333.60 

108.33 

164.67 

5 

486.90 

100.11 

172.88 

5 

420.80 

108.33 

164.67 

10 

977.90 

105.02 

167.98 

!    10 

843.60 

108.33 

164.67 

20 

2,498.90 

120.23 

152.77 

20 

2,246.60 

108.33 

164.67 

30 

4,205.90 

137.30 

136.70 

30 

3,898.90 

108.33 

164.67 

In  general  terms,  let  x  denote  the  age  of  entry.  Let  V  denote  the  Eeserve  or  net 
value  on  each  SI  insured  at  the  end  of  n  policy  years,  when  the  next  premium  is  just 
due  but  not  paid.  Also  let  Vi  denote  the  corresponding  Reserve  twelve  months  after, 
at  the  date  of  investigation.  Let  i  denote  the  rate  of  interest  assumed  in  computing 
the  Reserve;  and  let  i'  be  the  rate  of  interest  realized  on  the  Office  assets.  And  let 
(Pa;— e)  denote  the  Office  premium  less  its  current  expense,  and  px,  ihe,  net  premium. 
The  following  three-fold  expression  will  then  denote  the  Contrihition  to  Surplus : 

(V+i?x)  {i'—i)  +  {Px-e-p:c)  (1  +  *')  +  iqx+n-g'x+n)  (1-Vi). 


Here  the  first  term  makes  restitution  for  the  difference  of  interest  i' — i  on  the 
renewal  value  of  the  policy.  The  next  term  restores  the  loading  on  the  premium,  with 
a  year's  interest.  And  the  last  term  c6rrects  for  the  excess  of  the  tabular  rate  of  mor- 
tality qx+n  above  the  realized  rate  q'x-im-  In  the  preceding  illustration,  these  two  rates 
of  mortality  were  assumed  to  be  equal.  The  original  formula  differs  from  the  one  above 
by  the  subtraction  of  a  zero  equation,  so  that  the  numeric  results  will  be  precisely 
the  same. 


LIFE  ANNUITim  AND   imURANCES,  ^75 


SECTION    VIII. 

Life  Annuities.    Survivorship  and  Reversionary  Annuities. 

Successive  Lives. 

In  the  received  system  of  life  annuities,  the  annual  payment  is  made  at  the  end  of 
each  year  during  the  life  of  the  annuitant,  with  no  allowance  for  the  proportional  part 
of  the  year  of  death.  In  the  case  of  a  survivorship  annuity  on  the  life  x  to  commence 
on  the  death  of  y,  the  first  yearly  payment  is  made  at  the  end  of  the  year,  in  which  y 
dies,  and  the  last  payment  at  the  end  of  the  last  year  before  x  dies.  But  special 
formulas  have  been  investigated,  which  give  the  price  or  present  value  of  an  annuity 
payable  half-yearly  or  quarterly,  etc.,  and  with  a  proportional  part  to  the  day 
of  death. 

Life  Annuity.  To  recapitulate  from  Sections  III  and  V,  the  Present  Value  of 
an  annuity  of  $1  payable  at  the  end  of  each  year  during  life,  is 

fla;  =  %^-     On  two  Joint  Lives,  «^  =  ^^^jH, 


When  payable  at  the  beginning  of  each  year,  the  Present  Value  is 


xy 

Temporary  Annuity.  The  Present  Value  of  an  annuity  of  11  for  n  years,  on  a 
life  aged  x,  is 

n        Nai+l— Na;+»+l  _  .    ,   ^ra— 1         N"a;  — Na;+n 

««  = fv =  ax—^ax.         !+««      = fi • 

-L'a!  i-'a; 

Here  and  in  such  connections,  n  denotes  the  term  of  years,  and  is  not  used  as  an 
Algebraic  exponent.  On  Two  Joint  Lives  aged  x  and  y,  the  Present  Value  for 
n  years,  is 

n    Na;+l.y+l  —  Nj;+fi+i.y+n+i  „«— 1         ^■n/ — ^x+n.y+n 

O'Ty  — j^;      —  i--\-axy      — ^^r 

Deferred  Annuity.  The  Present  Value  of  a  life  annuity  of  $1,  deferred  for 
n  years,  the  first  payment  being  due  at  the  age-  x-{-n-\-lfis 


Nx+n+l  T)x+n 

Bx     ~    Bx 


(^x  —       T=i        —  ~T=;      .  fl^x+n- 


^x+n+l.y+n+1  ^x+n.y+n 

'xy,  iJxy 


"Oxy  —  pT —  — -p. -^x+re.y+ft. 

^xv .  ^xv 


The  divisor  to  give  the  annual  premium  for  n  payments,  will  be  1  +  aT'^.  •  And 
for  a  change  to  the  beginning  of  the  year,  or  first  payment  of  annuity  at  the  age x-\-n : 

Present  Value  =  ^^. 

I  -L'a; 

On  Joint  Lives,  Present  Value  =  ^y-^^". 


276  LIFE   ANNUITIES   AND    INSURANCES. 

Deferred  Temporary  Annuity.  The  Present  Value  of  a  temporary  annuity 
of  $1,  to  be  entered  upon  at  the  expiration  of  t  years,  and  then  to  continue  7i  years,  if 
the  annuitant  now  aged  x  shall  so  long  live,  is 

D^  -  D^  * 

Increasing  or  Decreasing  Annuity.  The  Present  Value  of  an  annuity  on 
the  life  x,  for  the  whole  term  of  life,  commencing  at  $a  and  increasing  ^h  annually,  is 
readily  proved  by  summations  founded  on  the  previous  formula,  to  be 

Single  Premium  = =:: 

-L'a; 

And  for  a  similar  life  annuity  decreasing  %b  annually,  we  have 
Single  Premium  = yt~" — " 

Ux 

The  Present  Value  of  a  temporary  annuity  on  the  life  x  for  n  years,  commencing 
at  $a  and  increasing  $b  each  year,  is 

a  ■  (Na;+i  —  Nx+n+l)  +  b  {Sx+i—Sx+n+i—n.  Nay+n+i) 

When  the  similar  annuity  decreases  $b  annually,  simply  reversing  the  sign  of  b  in 
the  last- formula,  will  give  the  present  value.     But  in  this  case  b  must  not  exceed 

,  that  the  annuity  may  not  finally  become  negative. 

For  the  Present  Value  of  an  annuity  of  $1,  increasing  annually  by  II  for  n  years, 
and  then  continuing  constant  at  $n  through  life,  we  have 

Single  Premium  =  §£±l^£±n±i. 
-L'a; 

The  Present  Value  of  an  Annuity  certai7i  for  n  years,  commencing  at  $a  and 
increasing  $b  each  year,  was  not  given  in  Part  I.  But  by  taking  the  derivative  D  of 
the  last  equation  on  page  59,  with  respect  to  v,  we  find  the  required  value  of  this 
increasing  annuity: 

{a—b)Y  +  bvDY  =  \a  +  nb  +  -.j. — -. r- 

The  value  of  the  similar  annuity  decreasing  $b  each  year,  is  found  by  reversing  the 
sign  of  b. 

Valuation  of  Annuity  Policies.  The  Present  Value  of  Single  and  Joint 
Life  Annuities  at  entry,  being  ax,  a^y,  etc.,  the  Eeserve  after  n  years  will  evidently  be 
Ox+n,  ax+n.y^n,  ctc.  In  like  manner,  the  Present  Value  of  a  Sur\'ivorship  Annuity  of 
$1  on  the  life  of  x  after  the  death  of  y,  being  ax—axy,  the  Eeserve  n  years  after  entry, 

will  be  aa;+n—«a;+n.y+n  • 

But  if  the  Survivorship  Annuity  of  |1  on  the  life  of.?:  after  the  death  of  y,  is  con- 
ditioned with  the  return  of  the  single  premium,  without  interest,  should  x  die  before  y, 
this  premium  and  the  Reserve  n  years  after  entry,  are  proved  to  be 


LIFE   ANNUITIES   AND    INSURANCES.  277 


ttx  —  dxy 


Single  Premium  =  — 


1 — A-xy 


Reserve  =  dx+n — <h;+n.y+nn ~--^x+n.y+n' 

1 — -^xy 

When  the  simple  Survivorship  Annuity  of  $1  on  the  life  of  x  after  the  death  of  ^, 
is  paid  for'  by  an  annual  premium  during  joint  life,  this  Premium  and  the  Reserve 
n  years  after  entry,  will  be 

Annual  Premium  =  r^ ^; 

1+Clxy 

Reserve  =  dx+n  —  dx+n.y+n — ^j    r~"       •  (1 +^x  +  w.y+7i/' 

-L  -+"  dxy 

The  premium  for  one  year  only,  to  secure  a  Survivorship  Annuity  in  case  y  dies 
in  the  first  year,  is  (1— J9y)  (fx,  or  qyOx.  At  some  ages,  this  rate  is  more,  and  at  other 
ages  less  than  the  average  premium  during  the  joint  lives.  In  the  latter  case,  the 
Company  would  not  be  fully  recompensed  in  the  first  years,  unless  the  policy  were 
continued  to  maturity.  The  present  divisor  to  give  the  annual  premium  is  l  +  Uxy',  if 
this  were  changed  to  l  +  Oxy,  the  ten  payment  premium  so  found,  would  generally 
prove  sufficient  in  the  first  years;  and  so  of  various  other  scales  of  premium. 

Under  an  arrangement  of  the  Survivorship  Annuity,  such  that  the  first  yearly 
payment  is  made  just  one  year  after  the  death  of  y,  or  more  generally  m  times  a  year 
thereafter,  and  a  proportional  part  is  to  be  paid  up  to  the  date  of  a;'s  death,  Mr.  Wool- 
house  finds  the  Present  Value 

This  is  the  formula  given  in  the  Journal,  Vol.  XV,  page  113.  Mr.  Sprague  had 
previously  determined  the  following  approximate  values,  according  as  the  annuity  is 
payable 

Yearly,  Half- Yearly,  "  Quarterly. 

{ax—axy)Vv,  {Ox  —  axy). ^'  («aj  — «a-y).  i^^- 

Note. — It  will  sometimes  be  required  that  the  common  life  annuity  be  extended  to  one  more  pay- 
ment, at  the  end  of  the  year  of  death.  The  present  value  of  such  payment  being  the  single  premium 
Ax  on  $1  insured,  the  present  value  of  the  extended  annuity  will  be  ax  +  Ax. 

In  case  the  annuity  is  to  be  extended  proportionally  to  the  day  of  death,  the  present  value  becomes 
ax-\-\Ax;  since  death  will  occur,  on  the  average,  at  the  middle  of  the  last  year.  This  is  the  method  of 
Francis  Bally.    A  slight  further  correction  is  given  by  the  formula  on  page  342. 

Annuity  on  the  Survivor  or  Last  of  any  Number  of  liiVEs.  Let  us 
take  first  the  case  of  two  lives,  of  the  present  ages  x  and  y.  Then  px, «  =  Ix+n-^lx  and 
Py^n'=  ly^n-^ly  will  denote  their  probabilities  of  living  to  the  end  of  any  future  year 
denoted  as  the  wth.  By  Sect.  I,  Principles  3,  4,  the  product  {l—fx^n)  ^—Py,n)  will 
express  the  probability  that  both  will  be  deceased  ;  consequently, 

1  —  (1  —px,  n)  (1  —Py,  n)  =  />x,  n  +  Vy,  n  —Px,  nPy,  n , 

expresses  the  probability  that  both  will  not  be  extinct,  or  that  one  at  least  will  be  living 
to  receive  the  nth  annual  payment     Therefore  multiplying  each  term  by  v^,  and 


378  LIFE  ANNUITIES   AND    INSURANCES. 

taking  the  sum  of  the  products  for  w  =  1,  2,  3, ,  we  find  the  required  value  on  the 

longest  of  two  lives  to  be  the  sum  of  the  two  single  annuities,  minus  the  joint  annuity ;  or, 

The  same  mode  of  solution,  illustrated  by  the  theory  of  the  higher  equations  of 
Algebra,  gives  the  value  of  an  annuity  on  the  longest  of  three  lives,  denoted  hy  a  line 
over  the  suffixes : 

^^  =  (^x+ay  +  az—{axy^-axz+ayz)+aryz* 

And  generally,  the  value  of  an  annuity  on  the  longest  of  any  number  of  lives,  is 
equal  to  the  sum  of  the  annuities  on  the  single  lives,  minus  the  sum  of  annuities  on 
the  joint  lives  combined  by  twos,  phis  the  sum  of  annuities  on  the  joint  lives  combined 
by  threes,  and  so  on ;  the  odd  orders  being  positive,  and  the  even  negative. 

Possibly  this  species  of  annuity  might  be  resolved  into  binomial  or  single  life 
factors,  like  the  elementary  probabilities  above,  aided  by  assumed  constants.  In 
another  expression,  if  C^  denote  the  sum  of  joint  life  annuities  on  m  lives  combined  n 
in  a  set,  then  evidently,  extending  to  n  such  terms, 

^m — ^wi  +  Cffj — Cffi-|-  .... 


xyz. 

VALUE    OP    AN    ANNUITY    ON    THE    LAST    n    SURVIVORS    OF    m    LIVES. 

For  an  annuity  to  commence  immediately  and  terminate  with  the  last  death 
but  one,  of  m  lives,  the  present  value  is  demonstrated  by  Milne,  Vol.  I,  pages  45,  126, 
to  be 

^m — 2.C»i-(-3.  Cm, — 4.  C,»+  .... 

Thus  the  present  value  of  an  annuity  to  end  with  the  last  death  but  one  of  two  lives, 
is  a^y-,  and  similarly  of  three  lives,  x,  y,  z^i\\Q  present  value  is 

ttpsy  -f-  Clxz  +  tt'yz  —  lidayz  • 

In  every  case,  the  algebraic  sum  of  the  coefficients  of  a  is  1,  to  indicate  one 
annuity  in  present  possession. 

And  generally,  to  commence  immediately  and  terminate  with  the  last  death  but 
n  —  \  of  m  given  lives,  the  present  value  of  the  annuity  is  the  series  of  m—n-\-l 
terms  of  C, 

nn  n^  +  l  ,  ^   ^^  +  1    pn  +  2  W  +  1    n-\-2   pw+3  , 

This  general  formula  is  proved  by  Milne,  pages  42,  126,  by  multiplying  ont  the 
probabilities  of  five  lives,  and  applying  the  rules  of  combination.  By  introducing  an 
auxiliary  t,  we  obtain  the  following  shorter  deynonstration  : 

Let  Px>  Py,  •  • .  ■,  denote  the  tabular  probabilities  that  the  m  lives  x,  y,  z, , 

will  survive  h  years.  And  let  the  continued  product  of  the  m  probabilities  of  decease 
{\—px)  (1— i?j/)  (1— />«)  ....  be  temporarily  denoted  by  P.  The  required  probability 
that  "  n  or  more  "  out  of  m  lives  will  survive  h  years,  will  be  the  sum  of  elementary 
products  of  the  form 

2w  factors  x  {m—n)  factors  =  'S.p^py {'^—Pz)  (1— jo«) =  P2  ^  .   _^^  

+  2  (w  +  1)  factors  X  {m—n—1)  factors  =         etc., 

+ 


LIFE  ANNUITIES   AND   INSURANCES.  279 

The  right-hand  expressions  after  P  represent  the  combinations  of  the  fractions 
taken  w  in  a  set,  w  + 1  in  a  set,  and  so  on  to  m  in  a  set.  By  comparison  with  the 
Algebraic  theory  of  the  roots  of  the  higher  equations,  these  combinations  will  be  the 
coefficients  of  t^,  ^'*+i, ^"»  in  the  development  of 

= + {t—iy^  CW+ (if— 1)'^+!  c(»+i) + (jf— 1)«+2.  c('*+2)  ^ + (if— 1)»».  cc"). 

Here  C(")  denotes  the  sum  of  the  combinations  of  the  m  factors  px^  Py, , 

taken  n  in  a  set;  etc.,  etc.  Developing  and  omitting  all  powers  of  t  lower  than  the 
wth ;  then  making  ^  =  1,  as  above  indicated,  Ave  find  the  precise  result  sought,  here 
denoted  by  P' :  < 

^      1-2  1.2-3  ^ 

Lastly  multiplying  by  v'^,  and  taking  the  sum  for  ^  =  1,  2,  3, ,  we  change  from 

probabilities  C^"^^  to  annuities  Cm ,  and  the  formula  on  the  preceding  page,  from  Milne, 
is  verified.    The  symbolic  form  is  evidently  C^  (1  +  C)-'*,  developed  as  far  as  C»». 

REVERSIONARY    ANNUITIES. 

General  Problem. — To  determine  the  present  value  of  an  annuity  dependent 
upon  the  joint  existence  of  the  last  n  survivors  out  of  m  lives  x,  y,  z,  . . . .,  after  the 

failure  of  the  joint  existence  of  the  last  n'  survivors  out  of  m'  other  lives  x,  y',  z', 

(Milne,  p.  130). 

The  leading  principle  of  solution  is  very  simple.  As  just  described,  let  P'  denote 
the  probability  that  n  or  more  of  the  m  lives  will  survive  h  years.  And  let  P"  denote 
the  like  probability  that  n'  or  more  of  the  m'  lives  will  survive  h  years;  then  1 — P"  is 
the  opposite  probability,  that  they  will  fail.  The  joint  probability  is  therefore 
P'  (1  — P").  Multiplying  this  by  v^,  and  taking  the  sum  for  all  values  of  h,  we  have  the 
required  value  of  the  annuity  in  terms  of  single  and  joint  annuities.  Also  the  required 
annuity  and  its  components  may  all  be  temporary  or  all  deferred  for  equal  periods. 

Example  1. — Eequired  the  value  of  an  annuity  on  the  life  of  x  to  commence  after 
the  death  of  y. 

Single  Premium  r::  ax—axy  Annual  Premium  = ^' 

1  +  flfary 

By  aid  of  the  above  type  P'  (1— P"),  this  solution  and  more  complex  ones  yet  to 
follow,  are  easily  written  by  inspection.  To  verify  the  present  result,  cancel  the 
annuity  on  x,  during  the  joint  lives.  This  latter  method  in  De  Morgan's  Essay  on 
Probabilities,  is  termed  ''  the  balancing  of  annuities."  ^ 

For  future  reference,  let  another  form  also  be  given,  which  is  easily  proved  by  substi- 
tuting for  N  below,  the  equivalent  series  of  D  and  canceling : 

dx — Ctxy  — YY\  ~~~        * 

lyLfx 

r.      _  (?y— ?y+l)  Na;-hl  +  (?y+l  — ^y+g)  J!^x+24-  •  »♦« 


280  LIFE   ANNUITIES   AND    INSURANCES. 

2.  Annuity  on  the  life  of  x  to  commence  after  the  first  death  oi  y  or  z'  the 
present  value  or 

Single  Premium  =  ttx—Oxyz'y  Annual  Premium  =  ^^^~^xyz 

1  -vClxyz 
v-T  Ux — uxiiz  — n    r  -i-v 


.X-U^Z-  ^^^jy 


X 


S.  Annuity  on  the  joint  lives  x,  y,  to  commence  after  the  death  of  z : 
Single  Premium  =  (ixy—dxyz'.  Annual  Premium  =  -— ^. 

1  '\-^xyz 

4.  Annuity  on  the  life  of  x  after  the  death  of  both  y  and  2 : 

Single  Premium     =  «a— «ary— «ar3  +  «aT^« 


Annual  Premium 


Ctx  —  (Ixy — dxz  -\-  ttxyz 


1  +  (^xy  "I"  ^X3  —  (^xyz 

5.  Annuity  on  the  survivor  of  x  and  y  after  the  death  of  2 : 

Single  Premium    z=  ax-\-ay— ctxy —axz— Oyz  +  cixyz- 

Annual  Premium  =  ^^+^y-«^-^^^gy£±fgJg. 

J-  ~r  f^xz  ~r  i^yz  —  Oxyz 

Verification  of  Formulas. — In  their  present  state,  the  algebraic  sura  of  the 
coefficients  of  a  in  the  single  premium  is  zero,  indicating  no  immediate  possession  of 
the  annuity.  And  the  only  change  from  the  present  state  must  occur  by  the  first 
death  of  either  x,  y,  or  z;  by  making  this  supposition  in  the  last  five  cases,  and  noting 
the  results,  the  solutions  given  above  are  again  verified.  The  same  methods  can  be 
further  applied  to  the  solutions  following. 

6.  Annuity  on  the  life  of  the  survivor  of  af  and  y,  that  is  on  either  one,  after  the 
death  of  the  other.     Give  an  annuity  to  both,  to  be  restored  as  long  as  both  are  alive: 

Single  Premium  =  aa;  +  «y—2«a;y,  Annual  Premium  =  ^-r-^ '-^' 


1  +  a.. 


xy 


7.  Annuity  to  commence  with  the  first  death  of  x,  y,  or  z,  and  to  end  with  ue 
joint  life  of  the  other  two,  that  is  with  the  second  death:  Grant  each  pair  a  joint  life 
annuity  to  be  restored  as  long  as  all  three  are  alive : 

Single  Premium    =•  axy-{-(ixz-\-Ch/z — ^^xyzf 
Annual  Premium  =  ^M±l^y^-^^^. 

-»•  -v^xyz 


LIFE  ANNUITIES   AND    INSURANCES.  281 


PARTITION    OF     ANNUITIES. 

8.  An  annuity  on  the  last  survivor  of  two  lives  x,  y,  is  to  be  equally  divided 

between  them  during  joint  life,  and  afterwards  to  go  to  the  survivor.     The  present 

value  of 

x'b  interest  =  a^—^axy,  y's  interest  =  %— ^«a^. 

Their  sum  evidently  makes  up  the  whole  value  of  the  annuity. 

9.  An  annuity  for  the  longest  life  is  to  be  divided  at  each  payment  equally  between 
the  survivors  of  three  lives,  x,  y,  z: 

Value  of  afs  share  =  ax—^  {axy + dxz)  +  i^xyz  • 

Here  x  may  denote  either  one  of  the  three  lives.  And  generally  for  equal  division 
of  such  annuity  between  the  survivors  of  m  lives  successively,  if  [  ]  denote  that  we 
exclude  from  Cm  as  before  defined,  every  combination  into  which  x  does  not  enter* 

x's  share  =  ax-i[Cl]+^[Cl]-i[(fm]  +  ....±-[Cl]. 

ft 

10.  Two  lives  x,  y,  possess  an  annuity  on  the  survivor  of  them.  If  either  dies 
before  a  third  person  z,  the  remaining  annuity  is  to  be  equally  divided  between  z  and 
the  survivor  during  their  joint  lives.     Required  the  value  of  z's  interest  • 

z's  interest  =  ^axz  +  ^yz—axyz.     (Milne,  p.  139.) 

11.  An  annuity  on  the  last  two  survivors  of  three  lives  x,  y,  z,  is  to  be  divided 
equally  among  them  while  all  are  living;  and  after  the  decease  of  any  one  of  them  is 
to  be  divided  equally  between  the  two  survivors  during  the  remainder  of  their  joint 
lives.     The  value  of 

x's  interest  =  ^xy+h^xz—^dxyz-     (Milne,  p.  140.) 

12.  An  annuity,  after  the  decease  of  x,  is  to  be  divided  equally  between  y  and  2 
during  their  joint  lives  ;  and  is  then  continued  to  the  last  survivor  for  his  life. 
(Milne,  p.  141.) 

y'&  interest  =  ap—axy—^yz-i-jaxyz. 

13.  An  annuity  on  the  last  survivor  of  x,  y,  z,  is  to  be  divided  equally  between  x 
and  y  during  their  joint  existence.  After  the  decease  of  either  of  them,  it  is  to  be 
divided  equally  between  z  if  then  living,  and  the  survivor  during  their  joint  existence. 
And  when  there  is  but  one  survivor  left  he  shall  receive  the  whole  of  the  remaining 
annuity.     (Milne,  p.  142.) 

a:'s  interest  =  ax—\axy—\axz-\-\cixyz. 

CONDITIONAL    PERIODS. 

H.  To  find  the  value  of  an  annuity  payable  during  the  joint  lives  of  a;,  y,  and  also 
during  t  years  after  the  death  of  y,  provided  x  shall  so  long  live. 

During  the  first  t  years,  whether  y  be  dead  or  living,  x  will  be  entitled  to  the 
temporary  life  annuity, 

Nar-t-i— Na;4.<-n  _  Da;_+« 


282  LIFE  ANNUITIES   AND   INSURANCES. 

After  this,  or  at  the  end  of  any  given  year  denoted  by  ^  +  n,  the  annual  payment 
will  depend  on  the  combined  chance  that  x  is  living,  and  that  y  was  alive  t  years 
previous.  This  expectation,  on  both  multiplying  and  dividing  by  ?a;+<,  also  summing 
with  respect  to  n,  to  the  end  of  the  life  table,  gives 

'x  'y  'x  ix  +  tiy  i^x 

Adding  this  to  the  former  result,  we  have  the  total  value, 

^X  +  t  ,  V 

(*x f=x —  \(tx+t — (tx+t.y)' 

15.  An  annuity  certain  for  the  term  of  15  years  is  to  be  enjoyed  by  P  and  his 
heirs,  during  the  joint  existence  of  two  lives  x,  y.  If  that  joint  existence  fail  before  the 
expiration  of  8  years,  the  annuity  is  to  go  to  Q  and  his  heirs  for  the  remainder  of  the 
terra  of  15  years.     To  find  the  present  value  of  P's  interest,  and  that  of  Q. 

The  value  of  P's  interest  for  the  first  8  years  is  evidently  the  temporary  annuity 
on  the  joint  lives  x,  y\  for  the  next  7  years,  P's  interest  is  the  deferred  annuity  certain 
for  7  years  multiplied  by  the  chance  that  x  and  y  will  both  live  through  the  first  period 
of  8  years  to  secure  it.    That  is, 

Fs  interest  =  «^_?^t8  [a,,^^^^-_:=f). 

The  value  of  Q's  interest  will  be  obtained  by  subtracting  P's  interest  from  the 
value  of  the  entire  annuity  — ; 

16.  A  reversionary  annuity  to  commence  on  the  death  of  x  and  continue  for  the 
remainder  of  the  life  of  y,  is  also  made  payable  for  t  years,  whether  y  is  alive  or  dead : 

y's  interest  =  Aa,.— ^^  ^tT  {(^y+t—ax.y+t)- 

I  Uy 

11.  To  find  the  single  and  annual  premiums  for  an  annuity  to  commence  at  the 
death  of  y,  and  continue  payable  during  the  remainder  of  a^'s  life,  but  to  be  payable 
only  if  y  dies  within  t  years. 

In  this  problem,  which  is  quoted  from  the  Journal,  Vol.  9,  page  302,  the  single 
premium  will  be 

iy  +  fiJx  +  t  /  \ 

Ux — ttxy pfj        ydx^t  —  (ix+t.y+t)- 

•    fy^x  ^ 

And  the  divisor  to  give  the  annual  premium,  payable  through  t  years,  if  the  joint 
life  so  long  continues,  will  be  l  +  a^^  .  We  may  observe  that  the  single  premium  is 
evidently  the  first  t  terms  of  the  series  before  stated  on  page  279. 

18.  Problem. — To  determine  the  present  value  of  an  annuity  on  the  life  of  x,  to 
commence  with  the  failure  of  the  joint  existence  of  y  and  z  provided  it  be  z  who 
dies  first. 

In  case  the  ages  of  y  and  z  are  equal,  the  probability  that  z  will  die  first  of  the 
two  is  ^.     Therefore  |  the  result  of  the  preceding  Problem  2,  on  p.  280,  gives  the  value; 

Annuity  on  a:  =  ^  {ax—dxyy)- 


LIFE   ANNUITIES   AND    INSURANCES.  283 

Secondly,  if  the  ages  of  y  and  z  are  unequal,  in  case  x  is  the  oldest  life,  and 
approximately  in  other  cases,  the  chance  that  z  will  die  first  of  the  two  is  usually  taken 
as  ^  in  practice.  So  that  \  of  the  result  of  Problem  4  gives  the  value  of  the  annuity 
on  X,  after  the  death  of  y.  Problem  3  gives  the  value  until  the  death  of  y  ;  and  the 
sum  of  the  two  will  express  the  total  value  : 

Annuity  on  x  =z  ^{ax+axy— axz — axyz) ; 
Annuity  on  a;  =  2 .-^ -TT"?  w  =  1,  2,  3, ; 

Iz  idly  Ux 

That  IS,  Annuity  on  a;  =  2 j  ^  " • 

tz  iy  Ux 

Another  solution  of  this  Problem  will  be  given  in  the  next  Section.  For  other 
combinations  of  Survivorship,  reference  may  be  made  to  the  works  of  Morgan,  Bailey, 
Milne,  Sang,  Farr ;  and  to  the  admirable  papers  of  Makeham  in  the  Journal,  Vols.  9, 
10,  12. 

ON    SUCCESSIVE    LIVES. 

Problem  1. — To  determine  the  present  value  of  a  deferred  income  of  $1  per 
annum  to  continue  forever,  the  first  payment  to  commence  at  the  end  of  the 
death  year  of  x. 

The  principal  -  when  multiplied  by  the  rate  i  gives  the  interest  $1  in  each  year 

perpetually.     Withdrawing  from  this  principal,  the  annuity  of  |1  during  the  life  of  x, 
we  have  the  required  result : 


Present  Value  z=  -—ax  =  (1  +  -I  Aa;. 


Here  the  last  member  is  found  by  merely  substituting  for  a  its  equal,  from  the 
common  formula 

1—iax 


Ax  =  1  — (1— v)(l  +  ax)  =  -J 


+  * 


Problem  2. — "  An  annuity  is  to  be  enjoyed  during  the  existence  of  a  life  aged  x, 
and  at  the  end  of  the  year  of  his  decease,  a  successor  aged  y  is  to  be  nominated,  who  is 
to  enjoy  the  annuity  during  his  life.  Required  the  present  value  of  the  annuity  on 
the  second  life  y." 

lu  the  system  of  compound  interest,  if  v"  is  the  factor  to  discount  a  sum  from 
the  end,  to  its  present  value  at  the  beginning  of  the  third  year,  v'  the  factor  to 
discount  through  the  second  year,  and  v  the  factor  to  discount  through  the  first 
year;  the  factor  to  discount  through  three  years  is  proved  to  be  the  product  vv'v". 
So,  the  single  premium  A  is  evidently  the  factor  to  discount  the  insurance  of  $1, 
from  the  end,  to  its  present  value  at  the  beginning  of  the  whole  term  of  insurance; 
and  AA'A"  would  represent  the  factor  to  discount  through  three  successive  periods 
of  life.  In  the  Problem  above,  the  value  of  II  annuity  during  the  life  y,  with  first 
payment  on  the  day  of  nomination,  1  +  %.  The  factor  to  discount  this  sum 
from  the  future  date  of  nomination,  to  the  present  time,  being  A^.,  we  have  the 
Present  Value  of  the  Annuity 


284  LIFE  ANNUITIES   AND    INSURANCES. 

During  the  second  life  =  A^  (l  +  fly)  =  A^;  (1+  •)  (1— Ay). 

During  the  two  successive  lives  =  rt^  +  Ax  (1  +  ay). 

For  Oy,  we  have  above  substituted  its  equal,  as  in  Problem  1.    If  a;,  1,  2, n — 1, 

n  designate  the  successive  lives  in  order,  the  present  value  of  $1  annuity  to  continue 
during  the  nth.  successive  life-time  beginning  with  an  immediate  payment,  will  be 

Aa;AiA2 A„_i(l  +  «n);  or      (1+-.J  Aa;(l— A„)  Ai  Aa A„_i. 

Problem  3. — Required  the  total  present  value  of  11  per  annum  during  n  suc- 
oessive  lives,  the  first  payment  to  commence  at  the  end  of  the  death  year  of  the 
present  life  x. 

The  result  sought  will  be  found  by  making  m  =  1,  2,  3, n,  in  the  last  expres- 
sion, and  taking  the  sum  of  all  the  terms.      Thus,   omitting  the   common   factor 

/1  +  -.)  A^,  and  making  w  =  1,  2,  3, n,  the  first  result  is  1  — Ai ;   the  second  is 

Ai— Ai  A2;  the  third  is  Ai  A3— Ai  A2A3,  etc.  From  these,  we  see  that  all  the  terms 
will  cancel  each  other,  except  the  first  and  the  last.  Hence  on  restoring  the  omitted 
factor. 

Present  Value  =  (l  +  •)  ^x  (1— A1A2A3 A»). 

Wlien  n  is  very  great  or  infinite,  the  right-hand  product  vanishes,  since  each  A  is 
less  than  unity,  leaving  a  result  which  is  independent  of  the  future  ages  to  be 
nominated : 


Present  Value  =  ( 1  +~.j  Aj 


When  the  successive  lives,  after  the  life  x,  are  all  to  be  of  the  same  age  y  at 
nomination,  the  formula  for  the  value  of  the  wth  successive  life,  given  at  the  end  of 
Problem  2,  becomes 

Aa;(l-{-rty)   Ay"\ 

-  In  like  manner,  the  formula  of  Problem  3,  for  the  sum  of  n  lives,  will  be 

(l  +  i)A,(l-Aj). 

Problem  4. — "  Instead  of  an  annuity,  a  fine  of  II  is  to  be  paid  at  the  end  of  the 
year  in  which  each  life  in  possession  fails,  being  the  time  when  the  next  sncceeding 
life  is  nominated.     Required  the  present  value  of  each  fine. 

By  Problem  2,  when  w  =  1,  Value  of  the  first  fine       =  Kx, 

w  =  2,         "        "     second  fine  =  Aa;  Ai , 

n  =  3,        «        «     third  fine     =Aa;AiA2. 

w  =  4,        "        "     fourth  fine  =  Ac  Ai  As  A3,  etc. 


LIFE  ANNUITIES   AND    INSURANCES.  285 

The  sum  of  the  terms  written,  will  evidently  be  the  present  value  of  the 
first  four  fines.  Each  term  is  readily  derived  from  that  which  precedes,  to  any 
extent. 

The  present  value  of  the  first  n  fines,  if  the  lives  are  all  of  the  same  age  at 
nomination,  will  be  the  sum  of  n  terms  above,  as  a  geometrical  series,  of  which 
the  ratio  is  Ay ;  and  the  sum  is 

-~ — 7—^ ;   or  if  w  be  infinite,  the  sum  is  :; -. — 

1— Ay  1— Ay 

By  subtracting  the  former  expression  from  the  latter,  we  obtain  the  present 
value  of  all  the  fines  after  the  nth,  that  is,  of  the  (w4-l)th  and  following  fines  to 
perpetuity : 

-A-a;  Ay 

I^a;' 

The  prece4ing  summary  is  based  chiefly  on  two  original  papers  by  Mr.  Peter  Gray 
in  the  Assurance  Magazine,  Vol.  2.  In  Vol.  21,  a  memoir  and  Table  for  the  Enfran- 
chisement of  Copyholds,  is  given  by  Edward  Smyth.  Further  problems  relating  to 
English  church  livings  and  copyholds  are  resolved  in  De  Morgan's  Essay  on  Proba- 
bilities, pages  228-236. 


SECTION    IX. 
Derivative   Formulas.     The    Continuo-as    Method. 

Besides  the  regular  Commutation  Formulas,  several  principles  of  mathematical 
analysis  have  conducted  to  other  formulas,  which  occasionally  offer  new  advantages. 
Especially  the  common  method  of  Algebraic  elimination  has  been  the  guide  to 
valuable  improvements.  For  example,  writing  x  and  then  a:  +  l  in  the  formula  for  the 
expectation  of  life,  we  obtained  two  equations,  from  which  the  series  common  to  both 
was  easily  eliminated,  leaving  the  simple  equation  between  ex  and  ex-^-x  shown  on 
page  243.  By  the  same  general  method,  and  in  other  ways,  the  following  Formulas  of 
Annual  Derivation  have  been  obtained : 

For  the  Expectation  of  Life,  <3a;—  ^  =  i'x  (^a;+i  +  i)- 

Annuity  on  a  Single  Life,  ax  =  vpx  (l  +  «a;+i). 

Annuity  on  Two  Joint  Lives,  axy  =  vpxPy  (l  +  «a;+i.j/+i)- 

Annuity  on  Three  Joint  Lives,  axyz  =  vpxPyPz  (l-f«x+i.y+i.a+i)- 

Temporary  Annuity,  a^  =  vpx  (1  +«"~i). 

Temporary  Annuity  on  Joint  Lives,  a^  =  vpxPy{l  +  ax+l.y+t). 

Insurance  by  Single  Premium  for  Life,        A^  =  vpx  \  — — l  +  A^+i  i  • 
By  Single  Premium  for  Term,  A^  =  vpx  \ 1  +  A^Ti  {•  • 


286  LIFE  ANNUITIES   AND    INSURANCES. 

By  Single  Premium  on  Joint  Lives,  Aay  =  vpxPy  (— — 1  +  A^+i  y+i)- 

Single  Premium  of  Survivorship  Insurance  of  II  to  be  paid  at  the  end  of  the  year 
in  which  x  dies,  provided  y  be  the  survivor,  * 

Ab  =  vv.Py  I  \  {^-\)  (^^  + 1)  +  A^^i  I . 

The  values  of  a;?^.  and  A  {ipo^)  are  already  given  in  Tables  XXVI  and  XLIIL 
And  at  the  oldest  age  of  the  life  table,  where  these  computations  usually  commence,  ^99  is 
0 ;   consequently  ^99  =  1^;   the  annuity  099  =  0 ;    the  single  premium   A99  =  v ;   and 

A^  =  \v  (l-f-/)y).  From  this  limit,  we  can  determine  the  other  values  in  a  connected 
series,  by  making  x  ■=^  98,  97,  96,  95,  ....,  in  successive  formulas.  The  operations 
will  be  greatly  aided  by  the  Addition  and  Subtraction  Logarithms  given  in  the  Tables 
and  Formulm  of  Peter  Gray,  whose  able  researches  first  directed  general  attention  to 
this  method. 

For  practical  illustration.  Tables  XLIV-XLVII  in  the  present  series,  were  com- 
puted by  the  formula  of  Temporary  Annuities,  a^  =  vfxi^-k-oi^x).  First  the  ages  99, 
98,  97,  96,  . . . . ,  were  written  at  the  head  of  so  many  columns ;  under  these,  the  values 
of  A  {v'p)  from  Table  XLIII  for  the  ages  one  year  younger,  were  copied,  once  for  all, 
to  be  repeatedly  added  each  in  the  same  column. 


TEMPORARY    ANNUITIES.      COMPUTATION    OF    JL(l  +  aD. 


PATKEirrs 

n 

96 

97 

98 

99 

Agb  X. 

L681936 

1627579 

1.585026 

L505846 

"^{vpx-x)  =  Xa. 

2 
3 

4 

0.153574 

0.141329 

0.120743 

A(l4-ai). 

L835510 

T.768908 

L705769 

Sum  =  Aa. 

0.200677 

0.178369 

A(l  +  a2). 

1.882613 

L805948 

Sum  =  Aa. 

0.214754 

A(l  +  a3). 

Here   at  4  per  cent,   interest,    A  (vj^gg)  =  L505846,    A  (r;?^)  =  L  585026,    , 

A  (H-«98)  =  0.120743,  A  (1  +  «^)  =  0.141329,  ....  At  the  first,  regarding  A  (vp)  as 
Xa,  we  look  out  A  (1  +  a)  in  Gray's  Table  and  copy  it  below,  one  column  to  the  left. 
Every  logarithm  A  (1  +  a)  so  found  is  next  added  to  A  (vp)  at  the  head  of  the  column, 
and  the  sum  written  underneath.  Again  regarding  each  sum  as  Aa,  the  corresponding 
A  (1  +  a)  is  then  found  by  Gray's  Table,  and  copied  as  before,  on  the  next  lower  line, 
one  column  to  the  left ;  and  so  on.  The  alternate  lines  present  a  complete  Table  of 
A(l  +  «x~^)  for  Temporary  Annuities.  When  n  is  1,  the  tabular  result  is  uniformly  0; 
and  at  the  foot  of  the  columns,  the  last  A  (1  +  a)  must  coincide  with  the  result  of  com- 
mon life  annuities.  To  prove  the  correctness  of  the  work,  while  in- progress,  every 
tenth  or  fifteenth  column  can  be  computed  by  the  independent  Commutation  formula 
or  otherwise,  for  comparison  and  correction. 

It  appears  scarcely  necessary  to  observe  in  the  use  of  Gray's  Tables,  when  the 
negative  index  of  the  argument  is  4,  5,  6,  etc.,  we  find  Log  (1  +  a;)  as  if  the  index 


LIFE   ANNUITIES   AND   INSURANCES.  387 

were  3,  and  prefix  to  the  result  of  Table  I,  as  many  decimal  cyphers  ;  or  in  the  use  of 
Table  II,  as  many  extra  decimal  9's,  as  the  excess  of  the  given  index  above  3,  denotes. 
Thus  when  Log  a:  is  5.500,  Log  {l-\-x)  is  0.0000137,  and  Log  {l—x)  is  1.9999862. 
There  are  Tables  to  seven  places  by  the  German  author  Zech,  and  by  Wittstein; 
Gray's  to  six  places  are  more  conveniently  arranged  for  practical  use. 

Formula  of  Valtjation. — Three  different  forms  have  been  published,  the  first 
by  Hon.  Elizur  Wright,  under  the  name  of  "  the  accumulation  formula,"  a  second  by 
Mr.  D.  P.  Fackler,  and  a  third  by  Mr.  Emory  McClintock.  To  demonstrate  the  last, 
let  i  denote  the  rate  of  interest;  and  v  tl^e  ratio  \-^{l-\-i).  Let  Yx+n  denote  the 
Keserve  at  the  end  of  n  years  on  each  $1  insured  at  the  age  of  entry  x,  with  the  net 
annual  Premium  P^, ;  so  that  Vx+w  +  Px  will  be  the  Reserve  just  after  the  Premium  is 
paid.  Assuming  Ix+n  persons  to  be  thus  insured  for  $1  each,  the  death  losses  in  the 
ensuing  twelve  months,  according  to  the  life  table,  will  be  Ix+n—lx+n+i-  Hence  the 
Reserve  with  a  year's  interest,  after  payment  of  the  $1  death  losses,  evidently  gives 

'«+«  (Vaj+w  +  Po;)  (1  +  *)  —  {Jx+n — '«+n+l)  =  '«+«+!  *a;+n+l' 

Dividing  by  lx+n+\  and  reducing,  we  have  the  required  formula: 

Va;+n+l  =  1— — [(v— Px)— Va;+n]. 

f^Px  +  n 

At  the  age  x,  just  before  the  first  premium  is  paid,  the  Reserve  V  is  evidently  0, 
which  is  the  initial  value  on  the  right  of  the  last  formula,  when  n  is  0.  Also  at  the 
end  of  the  last  year,  V  on  the  left  becomes  0  when  a  temporary  insurance  expires,  or 
1  when  an  endowment  matures,  or  1  when  a  common  life  policy  attains  the  oldest  age 
of  the  life  table.  Thus  the  computation  of  the  formula  may  commence  at  the  begin- 
ning, or  at  the  end  of  the  policy.     Table  XLIII  will  give  the  values  of  A  {vp). 

By  making  the  annual  Premium  P  to  be  0,  the  formula  becomes  applicable  to 
paid-up  Policies.  Consequently  one  year  before  maturity,  or  just  after  the  last  annual 
premium  is  paid,  the  Reserve  on  every  $1  of  endowment,  will  be  v. 

In  the  higher  analysis,  all  the  preceding  formulas  would  be  classed  among 
"equations  of  finite  differences  of  the  first  order;"  which  are  always  integrable, — 
Boole's  Finite  DiJEEerences,  Oh.  IX,  Art.  8.  But  the  integrals  are  already  known  in  the 
Commutation  and  other  forms. 


THE    CONTINUOUS    METHOD. 

Maclaurin,  Euler,  and  many  others  have  demonstrated  the  following  standard 
formula,  which  will  serve  the  double  purpose  of  summation,  and  conversely  of  quadra- 
ture. First,  let  the  values  of  the  ordinate  u  be  taken  at  the  distance  h  from  each 
other;  and  let  TJa  denote  the  special  sum  indicated;  then 

(A)  hJJh  =  h  (iWo  +  Uh-ht(ih+ +  U(n- l)A  +  iUnh) 

=  C+fudx+-^i^.^£-^y¥.^,+^hn^¥.'^^-..., 

For  the  present  applications,  let  nh  fall  beyond  the  oldest  age  of  the  life  table, 
where  Unh  and  its  differential  coefficients  all  vanish.  For,  by  Taylor's  Theorem,  when 
a  continuous  function  becomes  permanently  zero  beyond  a  certain  limit,  its  derivatives 


288  LIFE  ANNUITIES   AND    INSURANCES.       % 

also  vanish.     Taking  the  integral  of  the  right-hand  member  between  the  limits  nh  and 
0,  and  making  A  to  be  1, 

^nh  rill.  d^uQ 


^1  =  y  0  ^^^-^^'^-^^ 


dx      '  ^  " '  d3^ 

Subtracting  this  from  the  former  equation  integrated  between  the  same  limits, 
and  transposing, 

(B)  Ui  =  hJ5,+i,  {h^-1)  ^^-^i^  ih^-l)  ^+  . . . . 

Application-  to   Life   Annuities.— Referring  back   to   the  common   formula 

Da;«x  =  Na;+i  =  Dar+i  +  Daj+2+ ,    let  US    here   make    uo  =  T)x,  wi  =  D^+i,    etc. 

Then  will  Ui  =  p^+Da;+i+  . . . .  =  iD,,  +  Nx+i,    and    Ua  =  iT>x+'D^+h  +  'Dx+u+ 
Substituting  in  the  formula  (B),  dividing  by  Da;,  and  reducing, 

(C)  aa;  =  ^{T)x+h  +  'Dx+2h  +  'Dx+sh+  .■.•)-^^{h-l)—^\{k^-l){fi^  +  d). 

The  values  of  D  are  given  in  the  Commutation  Tables,  and  the  values  of  /*  and  5, 
in  Table  XLIIL  The  latter  represent  the  diflferential  coefficient  of  D^  or  IxV^,  divided 
by  Da;,  that  is,  of  log  Da;;  since  n  =  —dlx-—l:^x,  and  d  —  —log  v  =  log  (l  +  O-  Ac- 
cording to  W.  S.  B.  Woolhouse,  the  pioneer  of  this  mode  of  calculation,  in  the  Journal, 
Vol.  XI,  page  323,  the  best  intervals  to  adopt  for  h,  will  be  5,  7,  or  11  years.  In  the 
case  of  two  Joint  LivQS,  x,  y,  the  derivative  ft^.  will  become  [loey  ov  (tx-\-fiy;  and  so  on. 

Example. — Required  the  value  of  the  life  annuity  ax,  when  x  is  60  years,  and 
interest  is  5  per  cent. 

A  =  11 ;  flreo  =  i-(D7i  +  D82+D93)  +  5.-9.94(j«60  +  <5)  =  9.1322. 

A  =  7;  «6o  =  ^-(D67  +  D74  +  D8i  +  D88+D95)  +  3.-4(|«60  +  tJ)  =  9.1336. 

The  standard  value  from  Table  XXVIII  is  9.1322.  In  the  above  formula  for  11  year 
intervals,  the  last  coefficient  was  arbitrarily  changed  from  10  to  9.94  to  compensate  for 
omitted  terms.  The  annuity  so  computed  for  age  40  is  13.7601,  which  differs  very 
slightly  from  the  true  value  13.7602.  With  this  mode  of  amendment,  devised  by  the 
writer,  the  intervals  h  may  probably  be  taken  so  large  that  only  two  or  three  values  of 
D  will  be  needed.    Thus  for  thirty-five  or  other  ages  adjacent : 

20 
A  =  20;  ax  =  TT-P*+20+^a'+4o+Dx+6o) +  9.5-32.7023  {iix+H). 

Thus  with  slight  correction  of  the  last  coefficient,  through  a  single  central  value  of 
a,  this  method  (B)  may  also  be  extended  to  joint  lives  and  survivorships;  and  further 
trials  are  invited. 


Instalments. — Let  h  now  designate  a  fraction  —  of  1  year  or  of  II  annuity; 

and  let  the  equal  instalments  be  payable  at  the  end  of  each  interval  A  or  —  of  the 
year.     In  formula  (C),  the  present  value  of  the  1st  instalment  is  Da;+A-^Da;  when  the 


LIFE   ANNUITIES   AND    INSURANCES.  289 

instalment  is  1 ;  or  it  \s>  hy.'^x+h^^x  when  the  instalment  is  %h  px  -;  and  so  for 

the  following  terms  of  D,  which  evidently  make  up  the  required  present  value  «(»*). 
Therefore,  substituting  1-4-m  in  place  of  h,  and  transposing  the  terms,  we  find  the 

present  value  of  the  annuity  payable  in  instalments  of  $-  at  the  end  of  equal  intervals 
—  of  each  year,  ♦ 

(D)  «'  =''«+^2^-Tayf'*-+')- 

By  adding  - ,  we  evidently  obtain  the  present  value  of  the  annuity  payable  m 
times  a  year  in  advance.  This  wfll  also  be  the  divisor  of  the  single  premium  to  give 
the  premium  of  insurance  by  m  annual  instalments.     The  present  addition  of  —  gives 

Continuous  Annuities  dx-  When  the  equal  instalments  are  so  small  as  to  be 
payable  momently,  the  corresponding  value  of  the  annuity,  denoted  by  Ax ,  is  readily 
found  from  formula  (D),  by  making  the  number  of  intervals  m  very  great  or  infinite : 

(F)  «ar  =  «a;  +  i  — 1^  {l^x  +  (^). ^ 

axy  =  «ccy  +  i  — tV  (Ma;  +  /^y  +  (J). 

On  the  Survivor  of  Two  Lives,    d^  =  dx  +  dy—dxy, 

,       6 

=  ax  +  tty—axy-'r^—zrx' 

Continuous  Expectation  of  Life,    ex  =  ex—^f^x' 

^  =  ^xy — ^  {f^x-hH'y)' 

Complete  or  Apportionable  Annuities  cox.  The  characteristic  c  is  prefixed, 
when  the  annuity  is  to  be  paid  with  a  proportionate  part  to  the  instant  of  death.  A  close 
and  very  simple  approximation  for  this  case  has  already  been  given  in  the  Note  of 
page  277;  that  is,  cax  =  ax  +  ^Ax  =  {l—yv)ax-\-^v.  Here  the  proportionate  part, 
defined  by  the  actual  day  of  death,  is  to  be  paid  at  what  would  be  the  time  of  the  next 
regular  instalment  of  annuity. 

The  more  exact  solution  first  investigated  by  Mr.  Sprague  is  verified  by  Mr.  Wool- 
house  in  the  Journal,  Vol.  XY,  page  107,  substantially  as  follows :    Let  x'  denote  the 

age  at  the  beginning,  and  x'-}--  at  the  end  of  any  regular  interval.     And  let  x'-i-f 

denote  an  intermediate  age,  increasing  uniformly  to  x'  -{--  ,  so  that  if  death  should 

m 

occur,  U  will  be  the  proportionate  payment.     By  page  252,  ante,  and  since  M  is  a 

decreasing  function,  the  single  premium  to  insure  this  ^t  during  the  instant  dt,  is 

—t.dMx'+t^'Dx-     Or  integrating  by  parts  from  ^  =  0,  to  t  =  ~,  we  find  the  single 

premium  to  insure  through  this  interval  to  be 


290  LIFE   ANNUITIES   AND   INSURANCES. 

Ma^+l  +    fmUaZ+tdt, 


1" 

m 


both  terms  to  be  divided  by  Da; .  From  this  expression  we  next  find  the  sum  or  single 
premium  for  all  the  intervals  by  formula  (A),  which  gives  the  total  augmentation  of 
annuity : 


.2m     '^^  12w2   dx         •••  j    •     -^       2?w    -^     l%m? 

The  mark  over  M  denotes  its  continuous  value ;  and  so  of  the  single  premium  A. 
It  will  presently  be  shown  that  Ma;-^D^  =  Aa;  =  \—6.dx,  where  <5  :=  log  (l  +  «)  ;  also   • 
that  d^x  =  — v^.dlx.     Therefore,  adding  this  augmentation  to  formula  (D),  we  obtain 
the  complete  annuity  payable  with  a  proportionate  part  to  the  day  of  death : 

(G)  cai"'>  =  (l-2^)«-.+    ' 


12m2 


=(-.^.)(''-*-''^V 


12m^ 


Change  from  Ordinary  to  Contintjous  Annuities  and  Premiums. — By 
simply  changing  the  common  annuity  «x  to  «a;  +  i>  which  will  rarely  require  the 
slight  further  correction  shown  in  formula  (F),  we  obtain  the  continuous  annuity  ax- 
And  conversely,  Ox  =  (fx — i?  very  nearly. 

In  respect  to  Premiums,  the  operations  already  explained  on  page  264,  namely, 
A  :=  A-^-Vv,  and  A  =  A  Vv,  prove  to  be  sufficiently  exact  in  common  practice.  For 
illustration,  a  large  variety  of  single  premiums  are  represented  by  the  wxll  known  for- 
mula, A  :=  1  —  (1 — v){l-\-a).  Eliminating  the  annuity  a  by  comparison  with  the 
third  tjrpe  of  continuous  equation  stated  below,  we  have 

(H)  A  =  jA_A  +  ;;^  =  Anearly. 

At  the  age  of  40  years,  with  4  percent,  interest, /x(J-i-12  is  0.000030;  and  «y-f-(l— v) 
differs  from  ^/v  by  *2-^24  nearly,  Avhich  is  0.00006.  These  small  terms  being  neglecti- 
ble  except  in  rare  instances,  the  formula  A  =  A-^Vv,  is  so  far  verified,  with  its  con- 
verse A  =  A  Vv' 

Forms  of  Continuous  Single  Premiums. — Besides  these  simple  modes  of  trans- 
formation, the  continuous  method  presents  the  single  premium  under  four  new  forms. 
As  will  be  demonstrated  presently,  according  to  Mr.  Woolhouse's  analysis  in  the  Jour- 
nal, Vol.  XV,  pages  123,  409,  the  Jirsi  form,  separating  the  symbols  of  operatioiT,  is 

(I)  A=(^,-^)«-  +  (^,-|)a+.... 

This  type  will  be  of  general  application,  if  A,  a,  depend  on  all  the  lives ;  while 

X,  y,   ,  designate  only  each  life,  by  whose  death  the  insurance  would  become 

payable.    Thus, 

A    -ad-^^-  A     -f«4-uU/    _^_^.     etc 


LIFE   ANNUITIES   AND    INSURANCES.  291 

A^  =  l^xttxy ^  ;  A-  _  HyCl^cy ^- 

-j-l  .  "'ttxyz  T"  1    -  ddxyz , 


A—  =  ^«  axyz ^— •  ^aya  +  ^xyz  +  ^xyz  —  -^'^«- 


The  second  and  i(AiV<^  forms  following  apply  exclusively  to  absolute  assurances, 
having  the  common  relation  A  =  1  — (1— r)  (1+a) : 

(J)  Xx  =  l—6dx'  'Kxy=l—Ux,j',  Aseyz  =  1—^dxyz;      etc. 

(K)  ^.  =  cj(J-e/.+g);  Axy  =  6(]-axy+^-''^);    etc. 

Here  «  denotes  the  ordinary  tabular  annuity  ;   and  in  both,  S  =  Nap.  log.  (l  +  «). 

The  fourth  type  is  but  another  form  of  the  first,  where  x,  y, ,  designate  only  each 

particular  life,  by  whose  death  the  insurance  would  become  payable.     Thus, 

(L)       A,  =  -|-^(«;        A^  =  -t^(^-«^)-r/|(^^^'^>'  "^• 

The  derivatives  with  respect  to  age,  as  x,  which  occur  in  the  preceding  equations, 
(unlike  derivatives  with  respect  to  v),  are  here  determined  with  sufficient  accuracy  by 
first  differences.    Thus, 

„.        da                A^rt  ,   A% 
Since  -J-  —  A« K--{- 


dx~  2     '     3 

ddx          ^  ,                            \                            dttxy       dOmi  ^  I  ,  , 

—  -^z=.\yax-\ — flfoj+lj;  -^ t —  =:  ^  (Oas— l.y— l — «a!  +  l.y  +  l)  ;      CtC. 

""  ~^  ~  ^  (^'^^-i  y~^+iy)'  — ~^  —  ^  i^^v-i  —  (^x.y+i);    etc. 

dlx  'x—1  —  Ix  +  t  a\^  'x—iax—l.y — 'x+lttx+Ly 

fix  — J-  —  ^j  A(ry  —  ^ 

As  heretofore,  the  single  premium,  when  divided  by  1  + ««,  for  a  single  life,  or  by 
1+axy  for  two  joint  lives,  will  give  the  annual  premium. 

Demonstrations.— It  is  shown  in  the  Differential  and  Integral  Calculus,  in  relation 
to  the  area  of  a  curve  whose  ordinate  is  denoted  by  //,  that  fydx  represents  the  sum  of 
yAx,  when  the  difference  of  abscissas  a  a;  is  diminished  to  its  limit.  Accordingly,  let 
the  commutation  Da;  =  ,y.     In  the  common  sum  of  annual  values,  Na,  =  D^+Dai+i 

+  Da!+2+ ,  the  value  of  Arr  is  1  year  or  1.     Diminishing  Aa;  to  its  limit  dx  or  dt, 

we  have  the  continuous  value  N  =  fDx+tdt. 

In  the  similar  sum,  Ma,  =  (4,— /x+i)  ?^^^  +  (/a5+i  — ^aj+a)  v*+^+ ,  the  value  of 

AX  is  represented  by  Ix—^x+i.    Diminishing  this   a   to  its  limit  —dlx,  since  l^  is  a 
decreasing  function,  we  obtain  the  continuous  value ;  then  integrating  by  parts, 


292  LIFE  ANNUITIES   AND    INSURANCES. 

M  =  —fdl.if  =  —lif^log  V  flvf^dx. 

Dividing  by  Da,,  we  verify  the  second  type  of  equations,  before  noted,  A=l— (J.«. 
For  another  standard  example  or  application : 

loi.ax  =  Ix+t-vKdf;  Ix'-^x  =  —fvKdlx+t' 

Integrating  by  parts,  and  observing  that  v  =  e^og^;  6  =  — log  v  =  log  (l  +  ^); 

^ Aa,  =  — v" ■lx+t  +  log  vf  Ix+t- v*dt. 
Applying  the  limits  ^  =  00  and  t  =  0,  also  substituting  l»  dx  for  its  equal, 

?a,Aa,  =  4  +  log  V.Zaj-«a,;  A^=zl— 6. da,. 

In  another  form,  noting  the  principle  of  the  Calculus  that  —^  =     j±^ ^  a,nd 
differentiating  the  first  equation  with  respect  to  x^  then  substituting  in  the  second, 

,    -T-   _       d  {Ix  dx)  -T-   _       .       ddx 

1  1        1         A 

By  substitution  of  the  common  annuity,  since  ^  =  -.+  - — —^  nearly, 
•^  *"  <5        t     2      12  *' 


^x  =  l-6.d^-^6(^j-ax  +  l^' 


In  this  manner  the  four  previous  forms  of  equation  are  demonstrated,  and  the 
methods  of  integration  are  general.  For  the  insurance  of  $1  payable  on  the  death  of  x 
if  y  be  living : 

l9ilydxy  =  flx  +  tly^^tV*dt', 
IxlyA-sy  ^   — J  iy  +  tV^  -d  Ix  +  t  • 

For  three  lives,        Ix  ly  h  k^z  =  — /  ^y+<  hrt  v^  •  d  Ix+t  • 

ApPLiCATioi^s  OF  THE  Law  OF  MORTALITY. — The  preceding  results  are  evidently 
general,  and  adapted  to  any  life  table.  But  according  to  the  law  of  Makeham,  on 
page  237,  with  hyperbolic  logarithms,  the  value  of  ^  is  found  as  follows: 

Na,  =  /Bx.dx  =  fh{vsY.e-^.dx', 
if    w  =  log  - .  g* ;  du  ■=  log  q .  udx. 

Let  r  =  l^i-(^  + 1.  (vsY  =  e"  ^""^  ^""^  =  n^-^ .  (log  -)  "^ 

Changing  entirely  from  the  variable  a;  to  w,  we  obtain  the  known  form  of  the 
Gamma  function,  or  second  Eulerian  integral,  tabulated  by  Legendre,  with  an  outline 
Table  in  De  Morgan's  Calculus,  page  587.     By  the  latter  treatise,  pages  577,  590: 


LIFE   ANNUITIES   AND    INSURANCES.  293 

/« 
E-^.u^-^.du  =  r(r-i)  =  r(r)-j-(r— 1)  =  r(i+r)-i-r(r— 1). 
0 

/=0  /TOO  />|^ 

—  J     —  j   ,  we  have 


log? 


log  a      J  u 


1  "^,       1     r'^r'^r(r  +  l)"^r(r+l)(r  +  2)'^'*"  f 


r.loff —  log  — 

^  vs  °  vs 

Dividing  by  Do.- ,  of  course,  gives  the  annuity  dx .  For  numeric  calculations, 
reference  may  be  made  to  more  full  developments  in  the  Journal,  by  Mr.  Makeham,  in 
volume  XVII,  page  305,  and  by  Mr.  McClintock,  in  volume  XVIII,  page  242.  An 
interesting  feature  is  the  rapid  convergence  of  the  series  in  the  earlier  ages  of  manhood. 
At  age  40,  u  is  0.030813;  at  60,  u  is  0.20622;  at  80,  u  is  1.3801. 

Integration  of  (N)  by  parts  will  easily  show  the  following  Relation  between  two  life 
annuities,  at  equal  ages,  but  at  rates  of  interest  differing  nearly  10  per  cent.,  or  as  the 
rate  of  v  differs  from  that  of  v';  the  logarithms  are  hyperbolic: 

:^  1  ,  log  q  ,         s"  log  q 

For  ;  I  joint  lives ;  log  --;,'  a^  +  - — y'  log a^  =  1 ;         - — t-  =  0. 9532326, 

to  q      J-  pxy-'-  q      ■■- 

For  one  life ;  log  — .  cby  +  u.  log q.  dy'  =  l\v'  =  vq;  u  =  log—.  g-*'=  — - —     Z' 

Demonstration  of  the  Formula  of  Survivorship  Insurance  on  P.  263.  Having 
tabulated  the  coefficients  a'  and  b',  let  us  here  adopt  the  notation,  and  the  two  auxiliary 
ages,  X,  y,  stated  on  page  263.     The  probability  of  the  m  lives  all  surviving  the  time  t 

is     J     J  - — — —  or  s'^Kg^^^^  -i);  and  the  probability  of  the  n  other  lives  surviving  the 

toj/ .  ta// .... 

time  t  is  entirely  similar.     Hence  by  the  same  reasoning  as  for  two  single  lives,  x,  y : 
-T-l r  ^  {^<^+t  •  ^'«f'^t   •  • . )  ly'+t  ■  ly"+t  •  •  •  •     , 

^  la/ •  Ix" •  ■  •  •  h/.ly't .  .  .  . 

=  —/{m  log  s.dt-\-\ogg.q^. dq^) . 6('"+'») Kg^*^^) (s'-i). 

Here  the  differential  has  been  more  conveniently  found  by  the  latter  form,  of  the 
identity  rf?  =  l.d  log  ?  =  <?  log  I . I.     Interchanging  the  lives  m  and  n, 

~^{y'y"..^^«f'..  =  —f{n\(igs.dt-\-\Qgg.qy.dq^')  «(»»+") « . ^(2*+«^) (? -D. 
Eliminating  the  last  term  of  the  two  equations, 

§-»  A(a,/a;".  .)y'y". .  —q^  ^{y'y" ..)v/x" ..  =  —  {m(^—nq^)  log  5 .  a(B'..j^... 

At  the  end,  a  has  been  written  in  place  of  the  equivalent  integral  on  all  the  lives. 


294  LIFE   ANNUITIES   AND    INSURANCES. 

Also  \x'x"..)y'y"..  +  \y'y" ..)x'x" ..  =  ^x'..y'..'     Eliminating  the  middle  term  by  compar- 
ison with  the  preceding  equation, 

(S)  {(t  +  qy)-\x'x"..)yy"..  =  g^-A.x'..y\.  —  {mqy—7iq^)  log  s.«a>'..y'... 

Again,  eliminating  a,  by  the  relation  A.r'..y'..  =  1 — 6da/,.y>,,,  we  obtain  the  general 

formula  on  page  263,  which  was  to  be  demonstrated.     Multiplying  by  ■y/v  as  there 
described, 


,      1^  ,,  _     m        mgv-^—n/    1         1         1\ 

^^s'  ~  m-{-n       qy-''  +  \\m  +  n'^'6'  ^^  ~s)' 


5^^  =  a'  +  i'Aa^ 


xy 


The  Table  of  a'  and  AJ'  on  page  263  is  based  on  the  values  m  z=  n  =  1.  But  if 
a"  and  h"  denote  the  values  in  any  case  where  the  numbers  of  lives  m  and  w  are  equal, 
we  have  a"  =  na' ;  b"  =  b'—{n  —  l)  a'-^Vv. 

Probability  of  Survivorship.-  For  two  lives,  the  probability  that  y  will  sur- 
vive X  is  strictly  the  value  of  A—  when  v  is  1,  and  <J  is  0.     The  former  equation  A  =  1 

^6. a  thus  becomes  A  =  1;  which  is  the  proper  result  to  be  substituted  in  the  pre- 
ceding solution  (S),  also  changing  dxy  to  e^y.  The  required  value  will  always  be  ^, 
when  the  ages  are  equal. 

For  a  near  approximation  in  other  cases,  let  T  denote  the  "Probable  Life  "of  the 
age  X — 5  years,  given  in  Table  XXVI.  Then  ly-5+r-^ly-5  will  approximate  to  the 
probability  A—  that  the  younger  life  y  will  survive  the  older  x.  And  1— A—  will  be 
the  opposite  probability  that  the  older  will  survive  the  younger.  At  the  ages  50,  30, 
for  example,  x—5  or  45  guides  to  T,  25.86.  Whence  ly.^+T-i-ly.^  or  A^  is  0.785 ; 
and  the  chance  that  the  older  x  will  outlive  the  younger  y  is  1— A^  or  0.215. 

Solution  for  Survivorship  Annuities.  The  preceding  expressions  for  a'  and  ¥ 
have  the  singular  property  of  remaining  constant  for  the  duration  of  the  given  lives. 
Being  easily  tabulated,  they  appear  adapted  for  an  important  part  in  the  system  of 
survivorships.  For  illustration,  let  the  last  problem  on  page  282  be  resolved  by  this 
method.  Firstly,  supposing. death  to  occur  on  an  average  at  the  middle  of  a  policy 
year,  and  the  first  payment  of  annuity  to  the  survivor  to  be  made  six  months  after,  or 
at  the  end  of  the  year,  the  present  value  may  be  considered  equivalent  to  that  of  a  con- 
tinuous annuity  commencing  at  death  or  survivorship. — Page  290. 

Problem. — To  determine  the  present  value  of  an  annuity  on  the  life  of  x,  to  com- 
mence with  the  failure  of  the  joint  existence  of  y  and  z,  provided  it  be  z  who  dies  first. 
Let  yz'dx  denote  the  required  value.     By  the  continuous  method, 

/dlz+flyn'^x+t  _  _    Pd  h+t  •  ly+t  •  Ix+t  •  V*  •  dx+t  ^ 

Iz  iy  Ux  *^  •'Z  ly  'x 

=  /dAz+t.y+t.x+t  •  dx+t  =  b  /dAz+t.y+t.x+t  •  dx+t  • 

'Here  the  differentiation  refers  to  the  variable  time  t;  and  b'  enters  by  the  substi- 
tution of  a'  4-  b'A  from  the  previous  investigation.     Interchanging  y  and  z, 


LIFE  ANNUITIES  AND  INSURANCES.  295 

Adding  the  last  two  equations,  and  substituting  from  page  280, 

Dividing  the  second  preceding  equation  by  this,  and  reducing. 

The  required  annuity,      yz'Cbx  =  t-, r  {(^x—dxyz) ;      — ^ — {^x — a^yz)  ■=yz'Cix' 

0  +  b  q^  +  q^ 

In  this  problem  for  three  lives,  x,  y^  z  (Milne  V.),  the  value  of  g,  which 
defines  V  and  6",  differs  from  the  cognate  value  for  two  lives  on  page  294. 
Also  the  series  on  page  280,  line  5,  and  283,  line  8,  have  the  above  ratio  of 
mean  terms  nearly.  But  accurate  examples  solved  with  the  Thirty  Offices' 
Table  disclose  the  following  adjustment,  where  the  correction  (a?)  may  differ 
slightly  from  its  mean  value  0.0150.  From  the  representative  examples  below, 
it  appears  sufficient  when  the  youngest  age  is  x  to  take  {x)  =  0.01 47,  When  x  is 
the  intermediate  age,  take  (a;)==0.0L53.  And  when  x  is  the  oldest  age  of  the 
three,  take  (x)  =0.0149,  in  the  value  of  q,  which  here  completes  the  solution.* 

log  Pa, 

A  complimentary  equation  is  found  by  transposing  y  and  z  in  the  exact 
series  on  page  283,  line  8,  and  taking  the  sum  of  results  compared  with  page 
280,  line  5,  thus; 

zydx '^  Cl^ Clxyz yz'CI'xJ  yz'(^x~—Q.'  zy^^xJ  yy'O^x^^^  '^\flx~^0,xyy)' 

In  a  first  example  of  the  general  problem  let  the  age  of  the  annuitant  x  be 
45  years,  of  the  decedent  z  60,  and  of  the  survivor  y  30.  Secondly,  let  x  be  30, 
let  z  be  60  and  y  45.  Thirdly,  let  x  be  47,  let  z  be  30  and  y  23  years.  By  the 
Thirty  Offices'  Tables,  with  interest  at  four  per  cent.,  the  present  value  of  the 
required  annuities  found  by  the  exact  series  on  page  283  is  5.1742,  6.9146  and 
1.2815  in  order.  The  corresponding  values  of  ax — a^y/^were  6.1356,  9.2668  and 
2.3553;  and  the  exact  values  of  q  1.0577,  1.0745  and  1.0255  respectively. 

*  Value  of  q — (x).  From  above  add  (x)  to  give  q,  for  the  sum  of  ages  (y+z): 
{y+z  =  4:0)  1.0068,(45)1.0080,  (50)  1.0102,  (55)1.0118,  (60)  1.0147,  (65)  1.0187, 
(70)  1.0225,  (75)  1.0275,  (80)  1.0311,  (85)  1.0355,  (90)  1.0424,  (95)  1.0483,  (100) 
1.0545,  (105)  1.0598,  (110)  1.0658,  (115)  1.0704,  (L20)  1.0756,  (125)  1.0798,  (1*30) 
1.0830,  (135)  1.0852,  (140)  1.0«86,  (145)  1.0904,  (150)  1.0922. 

The  last  solution  becomes  important  in  view  of  Mr.  Makeham's  statements 
In  the  Journal,  Vols.  9  and  10:  "  If  we  should  ever  possess  a  complete  table  of 
the  values  of  the  simple  survivorship  assurance  A^  and  also  of  the  annuity 
%l\x  or>«'«;r,  we  should  be  able  to  calculate  the  numeric  value  of  double  survivor- 
ships in  any  case  with  the  greatest  facility. "     "A  satisfactory  solution  has  never 


296  LIFE  INSURANCE  AND  ANNUITIES. 

yet  been  published^  determining  the  value  of  a  reversion  on  x  subject  to  y 
surviving  during  the  life-time  of  j;." — 3Ii1ne,  Problem  V. 

Among  numerous  applications  to  wills  and  probate  business  the  following 
illustration  is  here  adjusted  from  Griffith  Davies:  "  Suppose  z,  aged  45,  to  be 
entitled  to  an  estate  in  the  event  of  his  surviving  his  father,  y,  aged  60,  and 
desirous  of  providing  an  annuity  of  $500  to  his  wife,  x,  aged  30,  to  commence 
at  his  death  in  the  event  of  his  dying  before  his  father;  it  is  required  to 
determine  the  present  value  of  his  wife's  contingent  annuity." 

This  value  $1,176  shows  at  how  little  cost  a  provision  can  be  secured 
against  the  contingency  to  which  the  wife  is  exposed.  It  is  surprising  that 
such  insurances  are  not  more  frequent. 


SECTION    X. 

Insurance  on  Lives  according  to  the  Order  of  Survivorship. 

Problem  I. — Insurance  on  the  Longest  or  Survivor  of  Two  Lives. 
The  premiums  are  already  defined  on  pages  257  and  278,  including  the  reserves 
on  page  271,  to  be  reviewed,  and  especially  the  general  mode  of  solution  shown 
on  page  261. 

Problems  II.-VII.— A  General  Insurance  of  $1  on  One  of  Several 
Lives. — Such  are  the  insurances  payable  at  the  end  of  the  year  of  fiy^st  deaths 
or  of  second  death,  or  of  third  death,  or  of  the  last  death  hut  one.  Their 
annuities,  given  on  page  278,  may  be  used  to  enter  Orchard's  Tables  (or  the 
common  formulas  of  single  life),  to  obtain  the  proper  single  or  annual  premium. 
Note  especially  Problem  V.,  already  resolved.  These  general  insurances  are 
comparatively  few  in  number.  The  standard  treatise  of  Milne  (London,  1815) 
resolves  the  more  numerous  class  of  problems  which  depend  on  a  particular  or 
assigned  order  of  survivorship.  Many  of  his  solutions  have  since  been  simpli- 
fied by  Makeham  and  others;  and  his  system  of  numbering  the  particular 
problems  is  conveniently  retained  here,  with  select  formulas. 

Problem  VIII. — Required  the  Single  Premium  to  insure  $1,  to  be  received  at 
the  end  of  the  year  in  which  x  dies,  provided  another  life  y  be  then  living. 
Especially  note  that  the  life  y  can  be  replaced  hy  y  z,  or  any  number  of  joint 
lives,  as  in  Problem  X.  Extensions  to  four  lives  are  given  by  Makeham  in  the 
Journal  (London),  Vol.  Xll.  The  accurate  formula  of  Milne,  already  copied 
on  page  261,  is  expressed  in  three  terms,  followed  by  our  new  method:  Then 
another  was  discovered  by  the  writer  for  correction,  in  combining  page  291, 
lines  1 3  and  19,  with  the  well-known  2/jr=  ?;r— i  +  Ix+i  an<I  2ajrj,  =  «;r— 1.>  +  (ix  + 1^. 

Thus:  Single  premium=Ai;y==  '^~  ^~  — a^-y-i  +  C.      On  trial,  6=0.01 ;  c  =0.4. 

Px—\ 

Computed  A 0.5  0.6  0.7  0.8  A. 

Correction  C,  add  0.0005        .0012        .0021         .0032     6 A  (A— c). 


LIFE  INSURANCE  AND  ANNUITIES.  297 

Problem  IX. — Insurance  of  $1  on  the  particular  life  a-,  provided  he  die 
last  of  the  two  lives  a;,  y.  Verify  below,  or  on  page  262,  by  supposing  x  to  die 
first  or  last:  Single  premium=A;,r — Ai^.     Annual  premium  divisor,  1-^axy. 


Survivorships  of  Three  Lives. — For  more  convenient  reference,  the 
following  Problems  of  Milne,  with  improved  solutions  hy  Makeham  and  others, 
are  here  denoted  by  index  notation.  The  condition  of  first,  second  or  third 
death  is  defined  by  the  suffixes  1,  2,  3,  under  the  proper  letter;  also,  the  life  z 
is  not  insured  like  that  of  x  or  y.     In  {3'^)  either  x  or  y  may  fail  first  or  second. 


Problem  (10) 
xyz    ' 
1 

(11) 
xyz 

2 

(12) 

XIJZ 

3 

(13) 
'  xyz 
1.2 

(14) 
xyz 
1.3 

(15) 
xyz 
2.3 

(16) 
X'yz 
1   1 

(17)   (18) 
X'yz       X'yz 
2  2    3  3 

(19) 

(20> 

(21) 

(22) 

(23) 

(24) 

(25) 

(26)   (2_7) 

xyz 
2  1 

X  yz 
1.21 

xyz 
32 

xyz 
1.3  1 

xyz 
2.3  1 

xyz 

1 

xyz 
3 

xy    z   xyz 
2     1.2 

(28) 

(^9) 

(30) 

(31) 

(32). 

(33) 

(34)     (35) 

xyz 
1-3 

xyz 
2-3 

xyz 

2 

xyz 
1 

x-y   z 
1-2  1-2 

X'y    z 
1-3  1-3 

;   X'y    z         X  yz. 
2-3  2-3    1.2  1 

Problem  X. — Insurance  of  $1,  payable  if  x  dies  first  of  the  three  lives  x, 
y^  z.  For  a  new  method  of  solution,  discovered  by  the  writer  in  1898,  simply 
annex  z  to  y  and  z — I  to  y — 1,  and  then  proceed  as  in  Problem  VIII.  By  the 
Method  of  pages  263,  294;  while  the  divisor  to  give  the  annual  Premium  is 

l  +  a;ry^;  and  at  4  percent,  interest,  ^  \ocr  -=0.15812:  Nap.log -=0.0027466 


S 


Ai    ri'-\-h'A  I      ^      (m+n)  q^    -/v    ,  _1        -,,  1 

ivz=«+^^^>^.        a-^m—^^,     /^  .log-.       h'=——-_ 


q^'+qy+q^'    <^  '  s'  q'^+qy-hq^      -/v 

Problem  XI. — Insurance  of  $1,  payable  if  x  dies  second  of  the  three  lives 
x^  y,  z.  The  solution  of  Milne  by  symbols  is  readily  verified  by  deaths.  The 
divisor  to  give  the  annual  premium  is  1  +  €1;^^  +  ci^z  —  a^^yz- 

Single  premium  =  A^^+  A^^—  2  A^^^. 

Problem  XII. — To  determine  the  present  value  of  $1,  payable  upon  x 
failing  the  last  of  three  proposed  lives,  a-,  y,  z.  Solution:  Substituting  from 
Problem  XI.  and  transposing,  evidently,  A^^^+  A^^^-f-A3^^==A.^;  page  280,  line  9: 

Problem  XIII. — To  determine  the  present  value  of  $1,  payable  upon  x 
failing  either  first  or  second  of  the  lives  x,  i/,  z.  Grant  a  single  insurance  on  x, 
less  another  by  Problem  XII.  if  y  and  z  die  before  x. 

Single  premium  =  A^  —  A|.  ^ 


298  LIFE  INSURANCE  AND  ANNUITIES. 

Problem  XIV, — Insurance  of  $1,  payable  upon  x  failing  ihe  first  or  last  of 
the  lives  x,  y,  z.     Grant  a  single  insurance  on  a*,  less  another  by  Problem  XI, 

Single  premium  ^  A^  —  ^ly^« 

Problem  XV.  — Insurance  of  $1,  payable  upon  x  failing  either  the  second  or 
third  of  the  lives  x,  y,  z. 

Single  premium  =  A^  —  ^L^.     (Problem  X, ) 

Problem  XVI, — Insurance  of  $1,  payable  on  either  x  or  y  failing  the  first 
of  three  lives  x,  y,  z.     Evidently, 

Single  premium  =  A^^^  +  A^i^  ==  A^^^  —  A^^]. 

Problem  XVII, — Insurance  of  $1,  payable  on  either  a;  or  ^  failing  the  second 
of  three  lives  x,  t/,  z. 

Single  premium  =  A^^^  +  A^^^.     (Problem  XI.) 

Problem  XVIII, — Insurance  of  $1,  payable  on  either  x  or  ^failing  the  last  of. 
three  lives  x,  y,  z. 

Single  premium  =  A^^^  +  A^j^.     (Problem  XII, ) 

Problem  XIX, — Insurance  of  $1,  payable  on  x  failing  second  of  the  lives 
X,  y,  z,  provided  z  fail  first.  If  either  x  or  y  dies  first,  the  two  terms  of  the 
premium  below  cancel  or  vanish.  If  z  dies  first,  the  last  term  vanishes;  leaving 
the  first  subject  to  the  death  of  x,  as  the  second  in  order. 

Single  premium  =  A^^  —  A^^^. 

Problem  XX. — Insurance  of  $1,  payable  upon  x  failing  either  first  or 
second  of  the  lives  x,y,3j  provided,  in  the  latter  case,  that  y  fail  first.     By 

symbols,  ^(A]^^  +  A^]  =  A^).     . 

Single  premium  =A^^. 

Problem  XXI. — We  come  now  to  the  more  difficult  problems  of  Milne, 
simplified  by  Makeham  in  the  Journal,  Vols.  X  and  XII,  for  computation,  as 
follows :  To  determine  the  present  value  of  $1  payable  upon  x  failing  last  of 
the  three  lives  x,  y,  z,  provided  that  y  fail  second. 

Single  premium  =  A^^^  —  A^j^  —  A^^  —  (l—v)  ^^a^. 

Problem  XXII. — To  determine  the  present  value  of  $1,  payable  upon  x 
failing  either  first  or  last  of  the  three  lives  x,  y,  z,  provided  that  in  the  latter 
case  z  fail  first. 

Single  premium  =  2A^^^  +  A^^i  —  K\y  —  (1— ^•)^y«;r« 

t 


LIFE  INSURANCE  AND  ANNUITIES.  299 

Problem  XXIII. — To  determine  the  present  value  of  $1,  payable  upon  x 
failing  either  second  or  third,  provided  that  z  fail  first  of  the  three  lives  x,  y,  z. 

Single  premium  ==  A^^i  —  ( 1  —  ^' )  ^^  a^. 

Problem  XXIV. — To  determine  the  present  value  of  $1,  payable  upon  the 
failure  of  the  last  survivor  of  the  two  lives  x^  ij^  provided  that  they  both  survive 
a  third  life,  z. 

Single  premium  =  A^^^  -  A^^  +  A^  +  ^^a^  —  (1  -^)^^a^ 

Problem  XXV. — To  determine  the  present  value  of  $1,  payable  at  the 
failure  of  the  last  survivor  of  the  two  lives  x^  y,  provided  that  they  both  fail 
before  a  third  life,  z. 

,  Single  premium  =  A^^  +  A^^  —  A^^^  —  A^^^. 

Problem  XXVI. — To  find  the  present  value  of  $1,  payable  upon  the  failure 
of  the  last  survivor  of  the  two  lives  x,  i/,  provided  that  one  of  them  fail  before 
and  the  other  after  a  third  life,  z. 

Single  premium  =  A^  +  A^  —  A^^  —  AJ,^  —  2 A^^^  +  (1— v)  {^^a^  —  ^^,a^) 

Problem  XXVII. — Insurance  of  $1  on  the  survivor  of  two  lives,  x,  y, 
provided  that  a  third  life  z  fail,  either  first  or  second  of  the  three. 

Single  premium  =A  ^  +  A^  —  A^^  +  A^^^  —  A^^  —  A^^  —  A^^^. 

Problem  XXVIII. — Insurance  of  $1  on  the  survivor  ©f  *W0  lives,  x,  y^ 
provided  that  a  third  life  z  fail,  either  first  or  last  of  the  three. 

Single  premium  =  A^^+  Aj,^—  A^^  +  2A^^^  —  {l-v)  {y^a^  +  ^^a^). 

Problem  XXIX. — Insurance  of  $1  on  the  survivor  of  two  lives,  x,  y, 
provided  a  third  life  z  fail,  either  second  or  last  of  the  three. 

Single  premium  ==  A^  —  A^^l  —  (1— ^0(^y«;r  +  :,^y)  • 

Problem  XXX. — Insurance  of  $i  on  the  survivor  of  two  lives,  x,  y, 
provided  that  y  fail  after  a  third  life,  z.     See  page  257. 

Single  premium  ==  A-  —  AJ^  +  (1— v)  ^^a^. 

Problem  XXXI. — Insurance  of  $1  on  the  survivor  of  Xy  t/,  provided  that 
y  fail  before  a  third  life,  z. 

Single  premium  =  A  j,, —  (1 — v)  ^^a^ 


300  LIFE  INSURANCE  AND  ANNUITIES. 

Problem  XXXII. — Insurance  of  $1  upon  either  x  or  y  failing  either  first 
or  second  of  three  lives,  x,  y,  z.     Evidently,  ^ 

Single  premium  =  A^^^  +  A^j^  +  Ay  +  A^]  =  A^^. 

Problem  XXXIII. — Insurance  of  $1,  payable  upon  either  x  or  y  failing 
either  first  or  last  of  the  three  lives,  x,  y,  z.     See  page  257. 

Single  premium  =  A-  +  (1—?;)  i^ya^  +  ^^A^). 

Problem  XXXIV. — Insurance  of  $1,  payable  upon  either  x  or  y  failing 
either  second  or  third  qf  the  three  lives,  x,  y,  z. 

Single  premium  =  A^^  —  {l—v)  {^^a^  +  ^^,a^). 


NOTES  AND   ADDITIONS. 

Among  the  ADDITIONS  to  the  present  Revised  Edition  of  1899  will  be 
found  the  critical  correction  of  the  usual  few  Errata  discovered  during  the 
past  twelve  years;  the  instructive  Draw^ing  on  page  2;  Return  Premiums 
developed  on  page  253;  Paid-up  Insurance  on  pages  271,  272;  new  modes 
of  Integration  on  pages  293,  295;  new  explanation  of  Least  Squares  on 
page  '*2o4;  and  especially  Section  X.  On  Survivorships,  wherein  the  new 
formulas  open  a  wide  field  for  this  species  of  Life  Insurance. 

On  the  Law  of  Mortality. — Besides  Final  Series  and  other  new 
researches  given  in  the  text,  a  comparison  of  pages  *212  and  301  suggests  that 
the  convenience  of  Makeham's  Formula  may  be  united  to  entire  generality  of 
Formula,  by  vanishing  exponentials.  Let  us  begin  with  the  primitive  equation 
on  page  239,  line  4,  which  has  the  form  of  Newton's  Law  of  the  Radiation  of 
Heat.  In  its  second  integral  on  page  237,  line  38,  after  the  manner  of 
Lagrange's  variable  parameters,  substitute  thus, 

x\s  =  xXsi  4-  x^Xs^  +  X^XSg  +  

Then  the  equations  of  condition  for  the  whole  life  are  reducible  by  Least 
Squares.  And  as  in  Meteorology  the  climatic  cycle  of  35  years  is  needed  to  de- 
termine the  constants,  so  in  Mortality  the  experience  of  one,  two,  (three  score 
years  and  ten)  or  more  cycles  may  be  required  for  the  highest  accuracy. 

Historical. — The  Life  Insurance  Year  Book  (Spectator  Co.,  New  York) 
has  the  following  notes  by  the  author:  "  For  1887,  pages  321-324,  American 
Life  Tables  from  combinations  of  the  Census.  For  1888,  pages  117-123,  On 
the  Measure  of  Mortality  and  on  Recent  Vital  Statistics.  For  1897,  pages  140- 
143,  A  Perpetual  Calendar,  and  Notes  on  Ancient  Chronology." 

Continued  from  The  Spectator  (Weekly):  For  Sept.  17,  1891,  Reductions 
of  the  Thirty  American  Offices.  Conversion  from  Calendar  to  Policy  years. 
For  April  1 1,  1889,  Ages  of  Entry  in  Life  Insurance.  For  May  17,  1894,  Waves 
in  Meteorology  and  Mortality— Compare  page  240,  lines  2-5. — Cycle  of  35  years. 
— Deaths  by  Brain  and  Nervous  Diseases  are  one-seventh  part  of  the  whole. 
For  Dec.  11,  1890,  Man  and  Longevity  in  America. 


'212a 


FEW    TABLE     LXXII. 


301 


PRESENT  VALUE    (ajrx)    OF  JOINT   LIFE  ANNUITIES  ON  TWO  EQUAL  LIVES.      CONTAINING 
MONTHLY  DIFFERENCES,  M.  D.,  AND  THE   CORRECTION  FROM   PAGE   258. 


Is 

3 

M.D. 

3/2 

M.D. 

4 

M.D. 

•3  « 

0  ® 

3 

M.D. 

^y^ 

M.D. 

4 

M.D. 

a<  be 

Per  Ct. 

Subt. 

Per  Ct. 

Subt. 

Per  Ct. 

Subt. 

Per  Ct. 

Subt. 

Per  Ct. 

Subt. 

Per  Ct. 

Subt. 

10 

18.1553 

75,5 

16.7903 

61,1 

15.5954 

49,8 

55 

8.9127 

262,0 

8.5937 

245,0 

8.2936 

229,5 

11 

1S.0647 

78,3 

16.7170 

63,7 

15.5357 

52,1 

56 

8.5983 

262,6 

8.2997 

246,3 

8.0182 

231,0 

12 

17.9707 

82,0 

16.6406 

66,9 

15.4732 

54,9 

57 

8.2832 

262,4 

8.0041 

246,4 

7.7410 

232,0 

13 

17.8723 

85,3 

16.5603 

69,9 

15.4073 

57,6 

58 

7.9683 

261,9 

7.7084 

246,8 

7.4626 

232,7 

14 

17.7699 

88,7 

16.4764 

72,8 

15.3382 

60,3 

59 

7.6540 

261,1 

7.4123 

246,4 

7.1834 

232,9 

15 

17.6635 

92,4 

16.3890 

76,2 

15.2658 

63,2 

60 

7.3407 

259,1 

7.1166 

245,7 

6.9039 

232,6 

16 

17.5526 

96,3 

16.2976 

79,8 

15.1900 

66,5 

61 

7.0298 

258,0 

6.8218 

244,1 

6.6248 

231,8 

17 

17.4370 

100,2 

16.2018 

83,3 

15.1102 

69,6 

62 

6.7202 

255,2 

6.5289 

242,6 

6.3467 

230,6 

18 

17.3168 

104,2 

16.1019 

86,9 

15.0267 

72,8 

63 

6.4140 

252,2 

6.2378 

240,1 

6.0700 

229,0 

19 

17.1918 

108,4 

15.9976 

90,8 

14.9393 

76,4 

64 

6.1114 

248,8 

5.9497 

237,3 

5.7952 

226,7 

20 

17.0617 

112,5 

15.8887 

94,6 

14.8476 

79,8 

65 

5.8130 

244,7 

5.6649 

233,9 

5.5232 

223,8 

21 

16.9267 

116,8 

15.7752 

98,5 

14.7518 

83,5 

66 

5.5194 

240,3 

5.3842 

230,3 

5.2546 

220,8 

22 

Id. 7865 

121,4 

15.6570 

102,8 

14.6516 

87,3 

67 

5.2310 

235,4 

5.1078 

225,9 

4.9896 

217,0 

23 

16.6408 

125,9 

15.5337 

106,9 

14.5468 

91,3 

68 

4.9486 

230,4 

4.8367 

221,6 

4.7292 

213.2 

24 

16.4897 

130^5 

15.4054 

111,2 

14.4373 

95,2 

69 

4.6721 

224,4 

4.5708 

216,3 

4.4733 

208,5 

25 

16.3331 

135,6 

15.2719 

115,9 

14.3230 

99,4 

70 

4.4028 

218,6 

4.3113 

211,0 

4.2231 

203,8 

26 

16.1704 

140,1 

15.1328 

120,3 

14.2037 

103,7 

71 

4.1405 

212,1 

4.0581 

205,1 

3.9786 

198,4 

27 

16.0023 

145,3 

14.9885 

125,0 

14.0793 

108,2 

72 

3.8860 

208,8 

3.8120 

199,1 

3.7405 

192,9 

28 

15.8280 

150,2 

14.8385 

129,8 

13.9495 

112,7 

73 

3.6393 

198,8 

3.5731 

192,9 

3.5090 

187,2 

29 

15.6477 

155,1 

14.6827 

134,5 

13.8142 

116,9 

74 

3.4007 

191,3 

3.3416 

186,0 

3.2843 

180,8 

30 

15.4616 

160,6 

14.5213 

139,5 

13.6739 

121,8 

75 

3.1711 

184,3 

3.1184 

179,3 

3.0674 

174,5 

31 

15.2690 

165,6 

14.3539 

144,5 

13.5277 

126,6 

76 

2.9500 

177,0 

2.9033 

172,5 

2.8580 

168,2 

32 

15.0704 

171,1 

14.1805 

149,8 

13.3758 

131,5 

77 

2.7376 

169,2 

2.6963 

165,2 

2.6562 

161,2 

33 

14.8651 

176,2 

14.0008 

154,8 

13.2180 

136,4 

78 

2.5345 

161,7 

2.4981 

158,0 

2.4627 

154,5 

34 

14.6537 

181,5 

13.8151 

159,9 

13.0543 

141,4 

79 

2.3405 

154,1 

2.3085 

150,8 

2.2773 

147,6 

35 

14.4359 

186,5 

13.6232 

164,8 

12.8846 

146,2 

80 

2.1556 

146,5 

2.1276 

143,6 

2.1002 

140,7 

SQ 

14.2121 

192,0 

13.4254 

170,2 

12.7092 

151,4 

81 

1.9798 

139,3 

1.9553 

136,7 

1.9314 

134,1 

37 

13.9817 

197,5 

13.2211 

175,7 

12.5275 

156,8 

82 

1.8126 

131,7 

1.7913 

129,3 

1.7705 

127,0 

38 

13.7447 

202,4 

13.0103 

180,7 

12.3394 

161,7 

83 

1.6546 

125,2 

1.6361 

123,1 

1.6181 

121,1 

39 

13.5018 

207,7 

12.7935 

185,8 

12.1454 

166,7 

84 

1.5044 

118,5 

1.4884 

116,6 

1.4728 

114,7 

40 

13.2526 

212,5 

12.5705 

190,8 

11.9453 

171,8 

85 

1.3622 

113,2 

1.3485 

111,5 

1.3351 

109,8 

41 

12.9976 

217,8 

12.3416 

196,1 

11.7392 

176,9 

86 

1.2264 

110,5 

1.2147 

108,8 

1.2033 

107,3 

42 

12.7362 

222,3 

12.1063 

200,7 

11.5269 

181,7 

87 

1.0938 

109,6 

1.0841 

108,1 

1.0745 

106,8 

43 

12.4695 

227,2 

11  8655 

205,8 

11.3089 

186,7 

88 

0.9623 

119,1 

0.9544 

117,8 

0.9464 

116,5 

44 

12.1968 

231,4 

11.6185 

210,2 

11.0848 

191,4 

89 

.8194 

101,7 

.8131 

100,2 

0.8066 

99,7 

45 

11.9191 

235,9 

11.3662 

214,8 

10.8551 

196,1 

90 

.6974 

79,9 

.6929 

79,8 

0.6870 

78,3 

43 

11.6360 

240,8 

11.1085 

219,2 

10.6198 

200,6 

91 

.6015 

71,8 

.5972 

71,2 

0.5931 

70,6 

47 

11.3481 

243,7 

10.8455 

223,3 

10.3791 

204,8 

92 

.5153 

67,7 

.5118 

67,1 

0.5084 

66,5 

48 

11.0557 

247,2 

10.5776 

227,0 

10.1334 

208,9 

93 

.4341 

61,1 

.4313 

60,6 

0.4286 

60,1 

49 

10.7591 

250,5 

10.3052 

230,6 

9.8827 

212,8 

94 

.3608 

55,5 

.3586 

55,0 

0.3565 

54,9 

60 

10.4585 

253,2 

10.0285 

233,9 

9.6273 

216,3 

95 

.2942 

62,0 

.2920 

61,5 

0.2906 

61,3 

51 

10.1546 

255,9 

9.7478 

236,8 

9.3678 

219,6 

96 

.2198 

40,8 

.2188 

39,5 

0.2170 

39,1 

52 

9.8476 

257,9 

9.4636 

239,4 

9.1043 

222,6 

97 

.1708 

63,9 

.1714 

53,3 

0.1701 

45,6 

53 

9.5381 

259,8 

9.1763 

241,8 

8.8372 

225,3 

98 

.1061 

00,8 

.1074 

00,3 

0.1154 

23,8 

54 

9.2263 

261,3 

8.8862 

243,7 

.  8.5668 

227,7 

99 

0.0868 

NOTATION. 


i  =  interest  on  11  or  any  other  monetary  unit  for  one  year. 

V  =  :. :  =  the  present  value  of  1  due  a  year  hence. 

6 —  log  (l  +  i)  =  'Nap\og  {l-\-i),  the   nominal  yearly  rate  of  interest  when 
compounded  momently. 

Log  A  =  AA  =  notation  for  the  common  logarithm  of  A. 

log  A  =:  Nap  log  A  =  notation  for  the  hyperbolic  or  Napier  logarithm. 

e  =  2.718  281  828  =  the  number  whose  hyperbolic  logarithm  is  1. 

M  =  A£  =  0.434  294  482. 

AM  =  1.637  784  311.  

4  =  number  living  according  to  the  Life  Table,  at  the  precise  age  x. 

dx  =  lx—lx+\  =  the  number  of  persons  dying  between  the  ages  x  and  x  +  1. 

Ig-y  =:  Ix.ly  =  uumbeT  living  in  the  Joint  Life  Table  at  the  combination  of  ages  x,  y. 

dxy  =  lxy—lx+\.y+Ti  =  annual  decrement  in  the  Joint  Life  Table. 

Px  =  -4^  =  -^— ^  =  the  probability  of  a  person  whose  age  is  x  living  one  year. 

'x  Ix 

g'ar  =  y  =  ^  7  ^^^  =  1  —Px  =  the  probability  of  x  dying  within  one  year. 

'a;  ix 

Pxy  =  '^t  '  j^-  =  the  probability  of  the  joint  existence  of  two  lives  x  and  t/,  con- 

Ix-  iy 

tinuing  one  year. 
qxy  =  1—pxy  =  the  probability  that  one  of  the  lives  x,  y,  may  die  within  one  year. 

^x  =  —  1—^  =  ~  j~  log  ^x  =  limiting  ratio  of  mortality  at  the  age  x< 
Ix  ax  dx 

l^x  = ^^ =  - — ^j—— »  approximately. 

Px,  n  =  -y^  =  the  probability  that  a  life  aged  x,  may  survive  n  years. 
1  —Px,  n  =  the  probability  of  x  dying  within  n  years. 

Pxy,  n  =  '""^;"''/—  =  the  probability  that  both  x  and  y  will  survive  n  years. 


NOTATION.  303 

Co,  =  1+  '^"^       '»+^-r  ■  •  •;  _  |.j^g  «  expectation  "  or  average  duration  of  life. 

e^—^  =  the  "curtate  expectation  "  of  life  after  the  age  x. 

Tx  =  the  "probable  life"  after  the  age  x,  defined  by  ?as+T  =  i?<». 


ttx  =  the  present  value  of  $1  Annuity  due  at  the  end  of  each  year  during  the  life  x. 

l-\-ax  =  the  present  value  of  11' annuity  due  at  the  beginning  of  each  year  during 
the  life  x. 

a^  =  the  present  value  of  a  temporary  annuity  for  the  next  n  years,  if  x  shall  so 
long  live. 

1  -t-a-^-i  =  the  value  of  the  same,  when  the  annuity  is  due  at  the  beginning  of  each  year. 

%a.  =  the  present  value  of  a  deferred  annuity ;  that  is,  of  a  life  annuity  on  a;  to 
commence  at  the  age  x-\-n. 

ttxy  =  the  value  of  an  annuity  during  the  joint  existence  of  x  and  y. 

a~  =  ax  +  tty — ttxy  =  the  value  of  an  annuity  on  the  longest"  life. 

«(»»)  =  the  value  of  $1  annuity,  when  payable  by  m  instalments  in  each  year. 

—  +  «("*>  =  the  value  of  the  same,  when  the  instalments  are  payable  in  advance. 

ca^''*'  =  complete  annuity  providing  for  a  proportionate  payment  to  the  day  of  death. 

dx  =  the  value  of  a  continuous  annuity  of  |1  per  annum,  for  instalments  supposed 
payable  momently. 


Ax  =  the  single  premium  to  insure  $1  payable  at  the  end  of  the  policy  year  in 
which  X  shall  die. 

TT-B  or  Pa;  =  annual  premium  to  insure  II  on  the  life  of  x.     In  some  cases  it  denotes  the 
premium  to  insure  11000, 

j^(^)  _  siijgie  premium  of  Endowment  Insurance  of  $1  for  m  years. 

A—  =  single  premium  of  insurance  "  on  x  against  y,"  that  is,  of  $1  payable  on  the 
death  of  x,  if  y  be  the  survivor. 


Note  1. — Generally  x  denotes  the  age  of  entry,  when  the  risk  commences  j  x  +  n  the  age  of 
valuation  of  the  policy ;  and  m  or  n  +  m  the  total  period  of  insurance. 

The  suffixes  x,  xy,  . . . .,  are  often  omitted  where  the  meaning  is  obvious. 

Note  2. — The  notation  relative  to  other  conditions  is  usually  explained  on  the  several  pages 
where  it  is  introduced  and  applied. 


ao4 


INTERPOLATION    BY    FINITE    DIFFERENCES. 


From  the  series  r^  h,  c,  d,  e,  etc.,  whose  terms  are  a  unit's  distauce  from  each 
other,  to  find  any  intermediate  term  denoted  by  u : 

Let  X  be  the  integral  or  the  fractional  distance  of  u  from  the  first  term  a,  and 
A,  A^  A^  etc.,  the  first  terms  of  the  differences.    That  is, 

A  =zh—a,  the  first  difference; 
a'^  =  c— 2J  +  ff,  the  first  of  the  second  differences; 
A^  =  cl—Zc-\-Zh—a,  the  first  of  the  third  differences;  etc.  Then, 


u  =  a-\-x^  4 


x{x-l)         x{x-l){x-2)         x{x-l){x-^){x-d)  ^^ 
2  "^  2x3  "^  2x3x4 


aH 


Note. — The  derivative  du-i-dx  at  any  point  as  at  c,  may  be  found  by  differentiating  with  respect 
to  u  and  x  as  the  only  variables,  and  at  c  making  x  =  2.  The  well  known  values  of  /^  were  thus 
found. 

The  first  terra  a  can  generally  be  so  located  that  the  required  term  ^^  shall  be  near 
the  middle  of  the  employed  portion  of  the  series. 


DOUBLE     INTERPOLATION. 

Let  U  denote  the  term  to  be  interpolated  at  the  junction  of  a;,  y;  where  x  is  the 
horizontal,  and  y  the  vertical  distance  from  the  term  a.  We  might  apply  the  preceding 
formula  to  insert  a  term  u  at  the  distance  x  from  a,  then  a  term  u'  at  the  distance  x 

from  a',  etc.    The  same  formula  applied  to  u,  u,  u", would  evidently  give  U  at 

the  vertical  distance  y  from  u.     But  the  result  will  be  the  same,  if 


A  =  h—a,  a2  =  {c—h)  —  (b—a), 

A'  =  b'—a'.  etc. 

6  =  a— a,  (J2  =(«"—«')  —  (a' — a), 

x(x — 1) 


h 
V 
h" 


d 
d' 
d" 


U  =  a-{-xA  +  yd  +  xy{A'—A)-\-' 


2 


AH 


3^(^-1) 


<P+.... 


NUMBERS    OFTEN    USED    IN    CALCULATIONS. 


RATE  OF 
INTEREST. 

NUMBERS. 

^       LOGARITHMS. 

V. 

1-v., 

Xv. 

A(l_.;). 

3 

per  cent. 

■  .9708  7379 

.0291  2621 

L987  1628 

2.464  2840 

3i 

a         i( 

.9661  8357 

.0338  1643 

1.985  0597 

2.529  1277 

4 

11         a 

.9615  3846 

.0384  6154 

1.982  9667 

2.585  0267 

H 

i(         a 

.9569  3780 

.0430  6220 

1.980  8837 

2.634  0962 

5 

(I         « 

.9523  8095 

.0476  1905 

1.978  8107 

2.677  7807 

6 

U             (( 

.9433  9623 

.0566  0377 

L974  6941 

2.752  8454 

7 

cc         a 

.9345  7944 

.0654  2056 

1.970  6162 

2.815  7143 

8 

((         i( 

.9259  2593 

.0740  7407 

1.966  5762 

2.869  6662 

9 

a         ci 

.9174  3119 

.0825  6881 

1.962  5J735 

2.916  8161 

10 

i(         ii 

.9090  9091 

.0909  0909 

1.958  6073 

2.958  6073 

TABLES    IN    PART    SECOND. 


THIRTY   OFFICES'  EXPERIENCE: 

MALE  LIFE, Tables  XXVI-LXIV.  Pages     *2-*203 

JOINT  LIVES,     -    -    -    -         f-        LXV-LXXVI.  "    *204^*223 

FEMALE  LIFE,  -    -    -    -         «        LXXVII-LXXVIII,       "    *224-*227 


MISCELLANEOUS, Tables  LXXIX-LXXXIL  Pages  *228-*253 


*3 


TABLE     XXYI 


MALE    LIFE    TABLE.       FROM    EXPERIENCE    OF    LOSSES    AND    AMOUNTS    INSURED. 
EXPECTATION    OF    LIFE    AND    PROBABLE    LIFE. 


Living. 

Decre- 

Prob. of  Dec. 

Prob.  of  Living. 

Expectation 

Probable 

Age  added 

AGE. 

ment. 

Ix  —  ~j-' 
tar 

lx+\ 
Ix 

of  Life. 

Life. 

to  Ex- 

AQE. 

X. 

Ix. 

dx- 

Yearg. 

Years. 

pectation. 
Years. 

X. 

10 

100,  odo 

.6'48  ' 

0.006479 

0.993521 

49.994 

55.40 

59.99 

10 

11 

99,352 

646 

.006502 

.993498 

49.316 

54.56 

60.32 

11 

12 

98,706 

643 

.006516 

.993484 

48.637 

53.73 

60.64 

12 

13 

98,063 

641 

.006536 

.993464 

47.952 

52.89 

60.95 

13 

14 

97,422 

640 

.006568 

.993432 

47.264 

52.05 

61.26 

14 

15 

96,782 

638 

0.006593 

0.993407 

46.573 

51.21 

61.57 

15 

16 

96,144 

636 

.006614 

.993386 

45.880 

50.36 

61.88 

16 

17 

95,508 

635 

.006648 

.993352 

45.183 

49.52 

62.18 

17 

18 

94,873 

634 

.006683 

.993317 

44.481 

48.68 

62.48 

18 

19 

94,239 

633 

.006717 

.993283 

43.777 

47.83 

62.78 

19 

20 

93,606 

633 

0.006763 

0.993237 

43.069 

46.99 

63.07 

20 

21 

92,973 

633 

.006808 

.993192 

42.359 

46.14 

63.36 

21 

22 

92,340 

6.33 

.006856 

.993144 

41.646 

45.29 

63.65 

22 

23 

91,707 

634 

.006911 

.993089 

40.930 

44.43 

63.93 

23 

24 

91,073 

635 

.006973 

.993027 

40.211 

43.58 

64.21 

24 

25 

90,438 

,636 
639 

0.007032 
.007115 

0.992968 
.992885 

39.490 

38.766 

42.73 

41.88 

64.49 

64.77 

25  1 

26  ! 

26 

89,802 

27 

89,163 

641 

.007190 

.99:^810 

88.040 

65.04 

27 

28 

88,522 

644. 

.0072.75 

.992725 

37.312 

40.18 

65.51 

28 

29 

87,878 

649 

.007385 

.992615 

36.582 

39.33 

65.58 

29 

30 

87,229 

653 

0. 007485  ■ 

0.992515 

35.850. 

38.48 

65.85 

30 

31 

86,576 

658 

.007602 

.992398 

35.117 

37.62 

66.12 

31 

32 

85,918 

664 

.007727 

.992273 

34.383 

36.77 

66.38 

32 

33 

85,254 

671 

.007871 

.992129 

33.646 

35.93 

66.65 

33 

34 

84,583 

t':^' 

.'}0.<0'y7 

.931973 

32.910 

35.08 

66.91 

34 

35 

83,904 

689 

0.008212 

0.991788 

32.172 

34.23 

67.17 

35 

36 

83,215 

698 

.008390 

.991610 

31.434 

33.38 

67.43 

36 

37 

82,517 

709 

.008591 

.991409 

30.696 

32.53 

67.70 

37 

38 

81,808 

722 

.008826 

.991174 

29.957 

3L69 

67.96 

38 

39 

81,086 

736 

.009077 

.990923 

29.219 

30.85 

68.22 

39 

40 

80,35P 

752 

0.009360 

0.990640 

28.482 

30.01 

68.48 

40 

41 

79,598 

768 

.009647 

.990353 

27.747 

29.17 

68.75 

41 

42 

78,830 

788 

.009998 

.990002 

27.013 

28.34 

69.01 

42 

43 

78,042 

808 

.010351 

.989649 

26.280 

27..51 

69.28 

43 

44 

77,234 

831 

.010761 

.989239 

25.550 

26.68 

.  69.55 

44 

45 

76,403 

856 

0.011203 

0.988797 

24.822 

25.86 

69.82 

45 

46 

75,547 

883 

.011688 

.988312 

24.090 

25.05 

70.09 

46 

47 

74,664 

913 

.012227 

.987773 

2.3.377 

•24.23 

70.38 

47 

48 

73,751 

945 

.012814 

.987186 

22.660 

23,42 

70.66 

48 

49 

72,806 

980 

.013459 

.986541 

21.948 

22.62 

70.95 

49 

50 

71,826 

1,018 

0.014175 

0.985825 

21.241 

21.83 

71.24 

50 

51 

70,808 

1,059 

.014955 

.985045- 

20.539 

21.04 

71,54 

51 

52 

69,749 

1,103 

.015814 

.984186 

19.843 

20.26 

71.84 

52 

53 

68,646 

1,150 

.016752 

.983248 

19.154 

19,49 

72.15 

53 

54 

67,496 

1,200 

^ — 

.017779 

.982221 

18.471 

18.73 

72.47 

54 

TABLE     XXYI. 


*3 


MALE    LIFE    TABLE.       FROM    EXPERIENCE    OF    LOSSES    AND    AMOUNTS    INSURED. 
EXPECTATION    OF    LIFE   AND    PROBABLE    LIFE. 


Living. 

Decre- 

Prob. of  Dec. 

Prob.  of  Living. 

Expectation 

Probable 

Age  added 

AaE. 

ment. 

qx  —  ^' 

I'X 

Px  —     J     ' 
ix 

of  Life. 

Life. 

'^to  Ex- 

AGE. 

X. 

55 

Ix. 

dx. 

Years. 

Years. 

pectation. 
Years. 

X. 

66,296 

1,255 

0.018930 

0.981070 

17.797 

17.97 

72.80 

55 

56 

65,041 

1,312 

.020172 

.979828 

17.130 

17.23 

73.13 

56 

57 

63,729 

1,374 

.021560 

.978440 

16.473 

16.50 

73.47 

57 

58 

62,355 

1,438 

.023060 

.976940 

15.825 

15.78 

73.83 

58 

59 

60,917 

1,505 

.024707 

.975293 

15.187 

15.07 

74.19 

59 

60 

59,412 

1,576 

0.026527 

0.973473 

14.559 

14.37 

74.56 

60 

61 

57,836 

1,650 

.028529 

.971471 

13.942 

13.69 

74.94 

61 

62 

56,186 

1,725 

.030700 

.969300 

13.336 

13.03 

75.34 

62 

63, 

54,461 

1,803 

.033108 

.966892 

12.743 

12.38 

75.74 

63 

64 

52,658 

1,882 

.035740 

.964260 

12.162 

11.74 

76.16 

64 

65 

50,776 

1,962 

0.038640 

0.961360 

11.595 

11.12 

76.60 

65 

66 

48,814 

2,040 

.041789 

.958211 

11.040 

10.52 

77.04 

66 

67 

46,774 

2,118 

.045282 

.954718 

10.500 

9.94 

77.50 

67 

68 

44,656 

2,190 

.049043 

.950957 

9.974 

9.37 

77.97 

68 

69 

42,466 

2,261 

.053242 

.946758 

9.463 

8.83 

78.46 

69 

70 

40,205 

2,323 

0.057778 

0.942222 

8.967 

8.30 

78.97 

70 

!  71 

37,882 

2,378 

.062775 

.937225 

8.486 

7.80 

79.49 

71 

72 

35,504 

2,422 

.068216 

.931784 

8.021 

7.31 

80.02 

72 

73 

33,082 

2,453 

.074149 

.925851 

7.572 

6.84 

80.57 

73 

74 

30,629 

2,472 

.080709 

.919291 

7.138 

6.40 

81.14 

74 

75 

28,157 

2,472 

0.087792 

0.912208 

6.721 

5.97 

81.72 

75 

76 

25,685 

2,453 

.095503 

.904497 

6.320 

5.57 

82.32 

76 

77 

23,232 

2,416 

.103996 

.896004 

5.934 

5.19 

82.93 

77 

78 

20,816 

2,356 

.113181 

.886819 

5.565 

4.82 

83.57 

78 

79 

18,460 

2,274 

.123185 

.876815 

5.211 

4.49 

84.21 

79 

80 

16,186 

2,170 

0.134068 

0.865932  . 

4.873 

4.16 

84.87 

80 

81 

14,016 

2,044 

.145833 

.854167 

4.550 

3.85 

85.55 

81 

82 

11,972 

1,900 

.158704 

.841296 

4.242 

3.57 

86.24 

82 

i  83 

10,072 

1,737 

.172458 

.827542 

3.947 

3.30 

86.95 

83 

84 

8,335 

1,563 

.187523 

.812477 

3.666 

3.03 

87.67 

84 

85 

6,772 

1,379 

0.203633 

0.796367 

3.396 

2.81 

88.40 

85 

86 

5,393 

1,191 

.220841 

.779159 

3.137 

2.60 

89.14 

86 

87 

4,202 

1,008 

.239885 

.760115 

2.885 

2.38 

89.89 

87 

88 

3,194 

829 

.259550 

.740450 

2.637 

2.14 

90.64 

88 

89 

2,365 

692 

.292600 

.707400 

2.386 

1.89 

91.39 

89 

90 

1,673 

549 

0.328154 

0.671846 

2.166 

1.71 

92.17 

90 

91 

1,124 

403 

.358541 

.641459 

1.980 

1.57 

92.98 

91 

92 

721 

281 

.389736 

.610264 

1.808 

1.43 

93.81 

92 

93 

440 

187 

.425000 

.575000 

1.643 

1.28 

94.64 

93 

94 

253 

117 

.462451 

.537549 

1.488 

1.14 

95.49 

94 

95 

136 

68 

0.500000 

0.500000 

1.338 

1.00 

96.34 

95 

96 

68 

38 

.558824 

.441176 

1.176 

0.90 

97.18 

96 

97 

30 

18 

.600000 

.400000 

1.033 

0.83 

98.03 

97 

98 

12 

8 

.666666 

.333334 

0.833 

0.75 

98.83 

98 

99 

4 

4 

1.000000 

.000000 

0.500 

0.50 

99.50 

99 

H 


TABLE    XXYII. 

COMMON  LOGARITHMS  (A)  OF  THE  PRECEDING  LIFE  TABLE. 


AQE. 

.,  1 

,  1 

AGE. 

Z. 

10 

Xl^. 

ix 

Xdx- 

^qx- 

^Px- 

A — 
J^x 

X. 

10 

5.000000 

5".  000000 

2.811575 

\    3.811575 

1.997177 

0.002823 

11 

4.997177 

.002823 

.810233 

1   .813056 

7167 

2833 

11 

12 

.994344 

.005656 

.808211 

.813867 

7161 

2839 

12 

13 

.991505 

.008495 

.806858 

.815353 

7152 

2848 

13 

14 

.988657 

.011343 

.806180 

.817523 

7138 

2862 

14 

15 

4.985795 

5.014205 

2.804821 

3.819026 

1.997127 

0.002873 

15 

16 

.982922 

.017078 

.803457 

.820535 

7118 

2882 

16 

17 

.980040 

.019960 

.802774 

'      .822734 

7103 

2897 

17 

18 

.977143 

.022857 

.802089 

.824946 

7088 

2912 

18 

19 

.974231 

.025769 

.801404 

1  .827173 

7073 

2927 

19 

20 

4.971304 

5.028696 

2.801404 

1  3.830100 

1.997053 

0.002947 

20 

21 

.968357 

.031643 

.801404 

1  .833047 

7033 

2967 

21 

22 

.965390 

.034610 

.801404 

i   .836014 

7012 

2988 

22 

23 

.962402 

.037598 

.802089 

.839687 

6988 

3012 

23 

24 

.959390 

.040610 

.802774 

.843384 

6961 

3039 

24 

25 

4.956351 

5.043649 

2.803457 

3.847106 

1.996935 

0.003065 

25 

26 

.953286 

.046714 

.805501 

i  .852215 

6899 

3101 

26 

27 

.950185 

.049815 

.806858 

'      .856673 

6866 

3134 

27 

28 

.947051 

.052949 

.808886 

.861835 

6829 

3171 

28 

29 

.943880 

.056120 

.812245 

.868365 

6781 

3219 

29 

30 

4.940661 

5.059339 

2.814913 

3.874252 

1.996737 

0.003263 

30 

31 

.937398 

.062602 

.818226 

.880828 

6686 

3314 

31 

32 

,934084 

.065916 

.822168 

.888084 

6631 

3369 

32 

33 

.930715 

.069285 

.826723 

.896008 

6568 

3432 

33 

34 

.927283 

.072717 

.831870 

.904587 

6500 

3500 

34 

35 

4.923783 

5.076217 

2.838219 

3.914436 

1.996419 

0.003581 

35 

36 

.920202 

.079798 

.843855 

.923653 

6341 

3659 

36 

37 

.916543 

.083457 

.850646 

.934103 

6253 

3747 

37 

38 

.912796 

.087204 

.858537 

.945741 

6150 

3850 

38 

39 

.908946 

-.091054 

.866878 

.957932 

6040 

3960 

39 

40 

4.904986 

5.095014 

2.876218 

3.971232 

1.995916 

0.004084 

40 

41 

.900902 

.099098 

.885361 

.984459 

5790 

4210 

41 

42 

.896692 

.103308 

.896526 

.999834 

5636 

4364 

42 

43 

.892328 

.107672 

.907411 

2.015083 

5481 

4519 

43 

44 

.887809 

.112191 

.919601 

.031792 

5301 

4699 

44 

45 

4.883110 

5.116890 

2.932474 

2.049364 

1.995107 

0.004893 

45 

46 

.878217 

.121783 

.945961 

.067744 

4894 

5106 

46 

47 

.873111 

.126889 

.960471 

.087360 

4657 

5343 

47 

48 

.867768 

.132232 

.975432 

.107664 

4399 

5601 

48 

49 

.862167 

.137833 

.991226 

.129059 

4115 

5885 

49 

50 

4.856282 

5.143718 

3.007748 

2.151466 

1.993800 

0.006200 

50 

51 

.850082 

.149918 

.024896 

.174814 

3456 

6544 

51 

52 

.843538 

.156462 

.042576 

.199038 

3077 

6923 

52  , 

53 

.836615 

,163385 

.060698 

.224083 

2663 

7337 

53 

54 

.829278 

.170722 

.079181 

.249903 

2209 

7791 

54 

f5 


TABLE    XXYII. 

COMMON   LOGARITHMS  (X)  OF  THE  PRECEDING  LIFE  TABLE. 


AGE. 
X. 

55 

A?^. 

A4- 

^x- 

^Px- 

^i- 

AGE 

X. 

55 

4.821487 

5.178513 

3.098644 

2.277157 

1.991700 

0.008300 

56 

.813187 

.186813 

.117934 

.304747 

.991150 

.008850 

56 

57 

.804337 

.195663 

.137987 

.333650 

.990534 

.009466 

57 

58 

.794871 

.205129 

.157759 

.362888 

.989868 

.010132 

58 

59 

.784739 

.215261 

.177537 

.392798 

.989135 

.010865 

59 

60 

4.773874 

5.226126 

3.197556 

2.423682 

1.988324 

0.011676 

60 

61 

.762198 

.237802 

.217484 

.455286 

.987430 

.012570 

61 

62 

.749628 

.250372 

.236789 

.487161 

.986458 

.013542 

62 

63 

.736086 

.263914 

.255996 

.519910 

.985378 

.014622 

63 

64 

.721464 

.278536 

.274620 

.553156 

.984194 

.015806 

64 

65 

4.705658 

5.294342 

3.292699 

2.587041 

1.982886 

0.017114 

65 

66 

■  .688544 

.311456 

.309630 

.621086 

.981461 

.018539 

66 

67 

.670005 

.329995 

.325926 

.655921 

.979875 

.  .020125 

67 

68 

.649880 

.350120 

.340444 

.690564 

.978161 

.021839 

68 

69 

.628041 

.371959 

.354301 

.726260 

.976239 

.023761 

69 

70 

4.604280 

5.395720 

3.366049 

2.761769 

1.974153 

0.025847 

70 

71 

.578433 

.421567 

.376212 

.797779 

.971844 

.028156 

71 

72 

.550277 

.449723 

.384174 

.833897 

.969315 

.030685 

72 

73 

.519592 

.480408 

.389698 

.870106 

.966541 

.033459 

73 

74 

.486133 

.513867 

.393049 

.906916 

.963453 

.036547 

74 

75 

4.449586 

5.550414 

3.393049 

2.943463 

1.960094 

0.039906 

75 

76 

.409680 

.590320 

.389698 

.980018 

.956407 

.043593 

76 

77 

.366087 

.633913 

.383097 

1.017010 

.952310 

,047690 

77 

78 

.318397 

.681603 

.372175 

.053778 

.947835 

.052165 

78 

79 

•266232 

.733768 

.356791 

.090559 

.942908 

.057092 

79 

80 

4.209140 

5.790860 

3.336460 

1.127320 

1.937484 

0.062516 

80 

81 

.146624 

.853376 

.310481 

.163857 

.931543 

.068457 

81 

82 

.078167 

.921833 

.278754 

.200587 

.924949 

.075051 

82 

83 

.003116 

.996884 

.239800 

.236684 

.917790 

.082210 

83 

84 

-3.920906 

4.079094 

.193959 

.273053 

.909811 

.090189 

84 

85 

3.830717 

4.169283 

3.139564 

1.308847 

1,901113 

0.098887 

85 

86 

.731830 

.268170 

.075912 

.344082 

.891626 

.108374 

86 

87 

.623456 

.376544 

.003461 

.380005 

.880879 

.119121 

87 

88 

.504335 

.495665 

2.918555 

.414220 

.869496 

.130504 

88 

89 

.373831 

.626169 

.840106 

.466275 

.849665  ■ 

.150335 

89 

90 

3.223496 

4.776504 

2.739572 

1.516076 

1.827270 

0.172730 

90 

91 

.J050766 

.949234 

.605305 

.554539 

.807169 

.192831 

91 

92 

2.857935 

3.142065 

.448706 

.590771 

.785518 

.214482 

92 

93 

.643453 

.356547 

.271842 

.628389 

.759668 

.240332 

93 

94 

.403121 

.596879 

068186 

.665065 

.730418 

.269582 

94 

95 

2.133539 

3.866461 

1.832509 

1.698970 

1.698970 

0.301030 

95  1 

96 

1.832509 

2.167491 

.579784 

.747275 

.644612 

.355388 

96  i 

97 

.477121 

.522879 

.255273 

.778152 

.602060 

.397940 

97 ; 

98 

.079181 

.920819 

0.903090 

.823909 

.522879 

.477121 

98 

99 

0.602060 

1.397940 

.602060 

0.000000 

QO 

00 

99 

TABLE     XXYIII. 

Pik^SSNT  VALUE  (a)  OF   ANNUITY  OF   $1,   PAYABLE   AT  THE    END  OF  EACH    YEAR 

DURING    LIFE. 


AGE.  I 

1 

10 

11 

12 
13 
14 

15 
16 
17 
18 
19 

20 
21 
22 
23 
24 

25 
26 
27 
28 
29 


3 
•erCent., 


30 
31 
32 
33 
34^ 


35 
36 
37 
38 
39 

40 
41 
42 
43 

44 

45 
46 
47 
48 
49 

50 
51 
52 
53 
64 


23.7680 
23.6406 
23.5093 
23.3732 
23.2329 

23.0881 
22.9386 
22.7840 
22.6246 
22.4602 

22.2904 
22.1154 
21.9351 
21.7491 
21.5575 

21.3601 
21.1568 
20.9476 


Per  Cent. 


21.5905 
21.4920 
21.3897 
21.2835 
21.1734 

•a.  0594 
20.9411 
20.8183 
20.6912 
20.5595 

20.4230 
20.2817 
20.1355 
19.9841 
19.8274 

19.6655 
19.4980 
19.3250 
20. 7323!  19. 1462 
20.5107jl8.9616 

^0.2832118.7713 
20.0492  18.5747 
19.8089|18.3721 
19.5621  18.1632 
19.3088  17.9481 


19.0490 

18.7830 

18.5101 

H8.2306 

17.9448 

17.6524 
17.3538 
17.0485 
16.7372 
16.4197 

16.0963 
15.7669 
15.4321 
15.0917 
14.7463 

14.3959 
14.0410 
13.6818 
13.3187 
12.9519 


4 
Per  Cent 


19.7316 
19.6547 
19.5747 
19.4912 
19.4042 

19.3138 
19.2196 
19.1216 
19.0195 
18.9133 

18.8029 
18.6882 
18.5689 
18.4450 
18.3163 


Per  Cent 


5 
Per  Cent. 


18.1334:16.7497 
18.0729 1 16. 7018 
18.0098  16.6517 


17.9437 
17.8745 

17.8023 
17.7270 
17.6480 
17.5656 
17.4795 


16.5990 
16.5436 


6 
Per  Cent. 


14.4869 
14.4562 
14.4238 
14.3896 
14.3533 


16.4856  14.3151 
16.4248  14.2747 
16.3609  i  14.2319 
16.2938  14.1868 
16.2236  14.1392 


Per  Cent.  '  Per  Cent. 


10 
Percent. 


17.3896  16.1500  14.0889 


17.2959 1 16.0730 
17.1981115.9923 


17.0961 
16.9898 


15.9079 


14.0359 
13.9800 
13.9212 


15.8195  13.8591 


18. 1827 !  16. 8789  15. 7271 :  13. 7939 
18.0440 116.7634  15.6305  13.7250 
17. 9002 1 16. 6433  15. 5296  13. 6528 
17.7510 1 16.5182  15.4241  13.5768 
17.5964' 16.3880  15.3140  13.4969 


17.4364 
17.2706 


16.2529 
16.1124 


17.0990 115.9664 
16. 9214i  15.8148 
16.7379 115.6576 


17.7266 
17.4989 
17.2646 
17.0237 
16.7765 

16.5227 
16.2625 
15.9957 
15.7227 
15.4432 

15.1576 
14.8659 
14.5682 
14.2647 
13.9556 

13.6411 
13.3216 
12.9971 
12.6682 
12.3350 


16.3527  15.3259 


15.1993  13.4131 
15.0797  13.3251 
14.9550  13.2328 
14.8250,13.1360 
14.6897  13.0346 


16.5483115.4946  14. 5490;  12. 9285 


14.40301 12.8176 


16.1507  15.1511 114.2510  12.7017 
15. 9423  14. 9702,!  14. 0933 1 12. 5804 
15. 7276 114.7830  13.9297  12.4540 

15.5065 1 14. 5897  13. 7602 1 12.3222 
15.2792 114.3903  13.5847 1 12.1849 
15.0451  14. 1844  i  13.4028  i  12.0418 
14.8050  13. 9724 !  13. 2151  i  11. 8932 
14.5582 113.7538 113.0210  11.7387 


14.3052 1 13.5291 1 12.8208 
14.0460 1 13.2981  12.6144 
13. 7806 1 13. 0609  12.4017 


13.5092 
13.2320 

12.9490 
12.6606 
12.3669 
12.0682 
11.7648 


12.8176 
12.5683 

12.3129 
12.0521 
11.7857 
11.5139 
11.2370 


12.1829 
11.9582 

11.7274 

11.4908 
11.2485 
11.0007 
10.7475 


11.5784 
11.4121 
11.2399 
11.0618 
10.8777 

10.6877 
10.4918 
10.2902 
10.0829 
9.8699 


12.7276 111.3299 
12.7074 1 11.3161 
12. 6858 1 11.3014 
12.6629  11.2855 
12.6385  11.2686 


12.6125 
12.5850 
12.5556 
12.5244 
12.4913 

12.4560 
12.4187 
12.3822 
12.3373 
12.2928 

12.2427 
12.1954 
12.1426 
12.0867 
12.0276 

11.9652 
11.8993 
11.8298 
11.7565 
11.6792 

11.5979 
11.5125 
11.4226 
11.3281 
11.2290 

11.1251 
11.0163 
10.9023 
10.7832 
10.6587 

10.5289 
10.3936 
10.2527 
10.1061 
9.9540 

9.7960 
9.6325 
9.4632 
9.2883 
9.1079 


11.2505 
11.2312 
11.2105 
11.1884 
11.1647 

11.1394 
11.1125 
11.0838 
11.0531 
11.0204 


AGE. 


9.2650 
9.2580 
9.2504 
9.2422 
9.2333 

9.2238 
9.2135 
9.2023 
9.1903 
9.1774 

9.1634 
9.1483 
9.1322 
9.1148 
9.0960 


10.9856  9. 0758 1 
10.9485  9.0541 
10.9091:9.0309 
10.8671;  9.0059 
10.8226 1 8.9791 

10.7753  8.9505  i 
10.7251  8.9198' 
10. 6718 18.8870 
10. 6153 18. 8518 
10.5555  8.8142 

10. 4922 1 8. 7741 1 
10.4254  8.7.314 
10.3547:8.6858 
10.2800-8.6372 
10.2012  j  8. 5855 

10.118218.5306 

10.0309,8.4723 

9.9389  8.4103 

9.842418.3447 

9.741018.2752 

9.634818.2018 
9.523418.1242 
9.406918.0423 
9.2853  7.9560 
9.1583  7.8652 

9.0258  7.7698 
8.8881  7.6696 
8.7449  7.5647 
8.5962  7.4549 
8.442117.3401 


10 
11 
12 
13 

14 

15 
16 
17 
18 
19 

20 
21 
22 
23 
24 

25 
26 
27 
28 
29 

30 
31 
32 
33 
34 

35 
36 
37 
38 
39 

40 
41 
42 
43 

44 

45 
46 
47 
48 
49 

50 
51 
52 
53 

FA 


Formula,    «»  = 


Da, 


TABLE    XXYIII. 


•7 


PRESENT  VALUE  (a)  OF  ANNUITY  OF  $1,    PAYABLE  AT  THE  END  OF  EACH    YEAR 

DURING    LIFE. 


AGE. 

3 
Per  Cent. 

3V 
Per  Cent. 

4 
Per  Cent. 

U 
Per  Cent. 

5 
Per  Cent. 

6 
Per  Cent. 

7 
Per  Cent. 

8 
Per  Cent. 

10 
Per  Cent. 

AGE. 

55 

55 

12.5820 

- 
11.9978 

11.4569 

10-9552 

10.4892 

9.6515 

8.9218 

8.2825 

7.2203 

56 

12.2095 

11.6573 

11.1451 

10.6691 

10.2262 

9.4280 

8.7305 

8.1177 

7.0955 

56 

57 

11.8347 

11.3137 

10.8295 

10.3788 

9.9586 

9.1994 

8.5340 

7.9476 

6.9658 

57 

58 

11.4583 

10.9677 

10.5108 

10.0848 

9.6869 

8.9663 

8.3326 

7.7725 

6.8312 

58 

59 

11.0806 

10.6195 

10.1893 

9.7874 

9.4113 

8.7286 

8.1263 

7.5925 

6.6916 

59 

60 

10.7021 

10.2696 

9.8653 

9.4869 

9.1322 

8.4867 

7.9155 

7.4076 

6.5473 

60 

61 

10.3236 

9.9187 

9.5395 

9.1839 

8.8501 

8.2410 

7.7003 

7.2182 

6.3983 

61 

62 

9.9456 

9.5674 

9.2125 

8.8791 

8.5655 

7.9920 

7.4813 

7.0246 

6.2448 

62 

63 

9.5684 

9.2158 

8.8844 

8.5725 

8.2787 

7.7398 

7.2585 

6.8268 

6.0868 

63 

64 

9.1929 

8.8650 

8.5562 

8.2650 

7.9902 

7.4851 

7.0326 

6.6254 

5.9248 

64 

65 

8.8197 

8.5154 

8.2282 

7.9571 

7.7007 

7.2283 

6.8037 

6.4206 

5.7588 

65 

66 

8.4494 

8.1676 

7.9013 

7.6493 

7.4107 

6.9700 

6.5726 

6,2130 

5.5893 

66 

67 

8.0824 

7.8222 

7.5757 

7.3422 

7.1206 

6.7104 

6.3394 

6.0027  '  5.4164 

67 

68 

7.7198 

7.4799 

7.2525 

7.0365 

6.8313 

6.4504 

6.1049 

5.790415.2406 

68 

69 

7.3614 

7.1410 

6.9315 

6.7323 

6.5428 

6.1901 

5.8691 

5.5762 

5.0620 

69 

70 

7.0087 

6.8066 

6.6142 

6.4309 

6.2562 

5.9305 

5.6331 

5.3609 

4.8813 

70 

71 

6.6616 

6.4768 

6.3006 

6.1324 

5.9719 

5.6718 

5.3970 

5.1448 

4.6987 

71 

72 

6.3210 

6.1525 

5.9915 

5.8376 

5.6905 

5.4148 

5.1616 

4.9286 

4.51471' 72  1 

73 

5.9873 

5.8340 

5.6873 

5.5469 

5.4124 

5.1599 

4.9273 

4.7126 

4.3298 

73 

74 

5.6608 

5.5218 

5.3885 

5.2607 

5.1382 

4.9075 

4.6944 

4.4972 

4.1442 

74 

75 

5.3425 

5.2168 

5.0961 

4.9801 

4.8687 

4.6586 

4.4640 

4.2834 

3.9588 

75 

76 

5.0324 

4.9190 

4.8100 

4.7051 

4.6042 

4.4134 

4.2362 

4.0712 

3.7738 

76 

77 

4.7307 

4.6287 

4.5306 

4.4360 

4.3448 

4.1722 

4.0113 

3.8612 

3.5895 

77 

78 

4.4381 

4.3468 

4.2587 

4.1737 

4.0916 

3.9358 

3.7903 

3.6541 

3.4067 

78 

79 

4.1547 

4.0731 

3.9943 

3.9181 

3.8445 

3.7044 

3.5732 

3.4501 

3.2256 

79 

80 

3.8806 

3.8079 

3.7376 

3.6696 

3.6038 

3.4783 

3.3605 

3.2496 

3.0467 

80 

81 

3.6158 

3.5514 

3.4890 

3.4285 

3.3699 

3.2579 

3.1524 

3.0529 

2.8702 

81 

82 

3.3601 

3.3032 

3.2480 

3.1945 

3.1425 

3.0429 

2.9489 

2.8601 

2.6963 

82 

83 

3.1138 

3.0638 

3.0152 

2.9679 

2.9220 

2.8340 

2.7506 

2.6716 

2.5254 

83 

84 

2.8756 

2.8318 

2.7893 

2.7478 

2.7075 

2.6300 

2.5565 

2.4866 

2.3568 

84 

85 

2.6455 

2.6074 

2.5704 

2.5343 

2.4990 

2.4313 

2.3668 

2.3053 

2.1909 

85 

86 

2.4216 

2.3888 

2.3567 

2.3255 

2.2950 

2.2361 

2.180G 

2.1264 

2.0262 

86 

87 

2.2012 

2.1731 

2.1457 

2.1189 

2.0927 

2.0421 

1.9937 

1.9474 

1.8606 

87 

88 

1.9827 

1.9590 

1.9357 

1.9130 

1.8908 

1.8478 

1.8065 

1.7669 

1.6925 

88 

89 

1.7581 

1.7383 

1.7189 

1.6999 

1.6813 

1.6452 

1.6105 

1.5772 

1.5143 

89 

90 

1.5598 

1.5432 

1.5270 

1.5111 

1.4955 

1.4652 

1.4361 

1.4080 

1.3548 

90 

91 

1.3913 

1.3774 

1.3638 

1.3504 

1.3373 

1.3117 

1.2871 

1.2633 

1.2182 

91 

92 

1.2340 

1.2225 

1.2111 

1.1999 

1.1890 

1.1676 

1.1470 

1.1270 

1.0890 

92 

93 

1.0828 

1.0733 

1.0639 

1.0547 

1.0457 

1.0281 

1.0110 

.9945 

.9629 

93 

94 

.9395 

.9319 

.9243 

.9169 

.9096 

.8953 

.8814 

.8679 

.8421 

94 

95 

.8002 

.7942 

.7883 

.7825 

.7767 

.7654 

.7544 

.7438 

.7233 

95 

96 

.6485 

.6440 

.6397 

.6353 

.6310 

.6227 

.6145 

.6065 

.5912 

96 

97 

.5140 

.5109 

.5079 

.5049 

.5019 

.4960 

.4903 

.4847 

.4841 

97- 

98 

.3236 

.3221 

.3205 

.3190 

.3175 

.3145 

.3115 

.3087 

.3031 

98 

99 

.0000 

•  .0000 

.0000 

.0000 

.0000 

.0000 

.0000 

.0000 

.0000 

99 

TABLE    XXIX. 

ANNUAL  PREMIUM  (tt)  TO  INSURE   $1000,   PAYABLE  AT  THE   END  OP  THE    POLICY 
YEAR    IN    WHICH    THE    LIFE    FAILS. 


AaE. 

3  Per  Cent. 

3^  Per  Cent 

4  Per  Cent. 

^  Per  Cent. 

5  Per  Cent. 

6  Per  Cent. 

AGE. 

1 

10 

10 

11.2486 

10.4500 

9.7739 

9.2026 

8.7201 

7.9672 

11 

11.4571 

10.6440 

9.9535 

9.3682 

8.8723 

8.0952 

11 

12 

11.6747 

10.8470 

10.1419 

9.5422 

9.0327  ■ 

8.2308 

12 

13 

11.9023 

11.0598 

10.3400 

9.7260 

9.2026 

8.3754 

13 

14 

12.1400 

11.2827 

10.5480 

9.9194 

9.3819 

8.5289 

14 

15 

12.3881 

11.5158 

10.7660 

10.1227 

9.5709 

8.6913 

15 

16 

12.6474 

11.7601 

10.9953 

10.3369 

9.7706 

8.8640 

16 

17 

12.9188 

12.0166 

11.2364 

10.5629 

9.9819 

9.0478 

17 

18 

13.2025 

12.2852 

11.4897 

10.8010 

10.2050 

9.2428 

18 

19 

13.4993 

12.5668 

11.7560 

11.0518 

10.4407 

9.4499 

19 

20 

13.8099 

12.8625 

12.0361 

11.3163 

10.6899 

9.6701 

20 

21 

14.1349 

13.1724 

12.3304 

11.5950 

10.9531 

9.9037 

21 

22 

14.4752 

13.4974 

12.6399 

11.8887 

11.2311 

10.1517 

22 

23 

14.8317 

13.8388 

12.9656 

12.1985 

11.5251 

10.4152 

23 

24 

15.2050 

14.1972 

13.3082 

12.5250 

11.8357 

10.6949 

24 

25 

15.5963 

14.5733 

13.6687 

12.8696 

12.1641 

10.9919 

25 

26 

16.0068 

14.9689 

14.0485 

13.2333 

12.5117 

11.3079 

26 

27 

16.4369 

15.3842 

14.4479 

13.6166 

12.8786 

11.6426 

27 

28 

16.8883 

15.8206 

14.8689 

14.0214 

13.2671 

11.9986 

28 

29 

17.3623 

16.2797 

15.3125 

14.4487 

13.6780 

12.3769 

29 

30 

17.8592 

16.7621 

15.7791 

14.8991 

14.1119 

12.7777 

30 

31 

18.3814 

17.2699 

16.2712 

15.3751 

14.5713 

13.2038 

31 

32 

18.9302 

17.8042 

16.7902 

15.8779 

15.0575 

13.6566 

32 

33 

19.5070 

18.3670 

17.3376 

16.4092 

15.5722 

14.1376 

33 

34 

20.1136 

18.9593 

17.9149 

16.9706 

16.1170 

14.6487 

34 

35 

20.7516 

19.5836 

18.5241 

17.5638 

16.6936 

15.1916 

35 

36 

21.4224 

20.2407 

19.1663 

18.1901 

17.3035 

15.7674 

36 

37 

22.1294 

20.9342 

19.8452 

18.8533 

17.9504 

16.8801 

37 

38 

22.8743 

21.6661 

20.5624 

19.5549 

18.6357 

17.0316 

38 

39 

23.6590 

22.4378 

21.3199 

20.2971 

19.3616 

17.7235 

39 

40 

24.4863 

23.2526 

22.1206 

21.0825 

20.1309 

18.4590 

40 

41 

25.3587 

24.1126 

22.9667 

21.9137 

20.9462 

19.2406 

41 

42 

26.2802 

25.0220 

23.8627 

22.7949 

21.8117 

20.0726 

42 

43 

27.2524 

25.9825 

24.8099 

23.7276 

22.7287 

20.9564 

43 

44 

28.2801 

26.9989 

25.8133 

24.7167 

23.7026 

21.8972 

44 

45 

29.3662 

28.0738 

26.8757 

25.7651 

24.7359 

22.8979 

45 

46 

30.5150 

29.2118 

28.0014 

26.8771 

25.8330 

23.9627 

46 

47 

31.7306 

30.4173 

29.1948 

28.0572 

26.9985 

25.0962 

47 

48 

33.0174 

31.6942 

30.4602 

29.3094 

28.2364 

26.3026 

48 

49 

34.3809 

33.0482 

31.8029 

30.6395 

29.5524 

27.5876 

49 

50 

35.8261 

34.4845 

33.2283 

32.0524 

30.9517 

28.9564 

50 

51 

37.3590 

36.0085 

34.7419 

33.5538 

32.4399 

30.4147 

51 

52 

38.9855 

37.6268 

36.3501 

35.1505 

34.0235 

31.9688 

52 

53 

40.7128 

39.3463 

38.0599 

36.8490 

35.7093 

33.6257 

53 

54 

42.5485 

41.1744 

39.8789 

38.6571 

37.5051 

35.3931 

54 

Formula,    ttx  = 


lOOOMar 


r=  1000 


ir^-^-(i-')| 


TABLE    XXIX. 

ANNUAL  PREMIUM  (tt)  TO  INSURE   $1000,   PAYABLE  AT  THE    END  OF  THE    POLJClt 
YEAR    IN    WHICH    THE    LIFE    FAILS. 


.i^U'i.i 

3  Per  Cent. 

3^  Per  Cent. 

4  Per  Cent. 

4^  Per  Cent. 

5  Per  Ceat. 

6  Per  Cent. 

AGE. 

55 

44.5008 

43.1199 

41.8154 

40.5834 

39.4191 

37.2798 

55 

56 

46.5771 

45.1894 

43.8764 

42.6342 

41.4585 

39.2920 

56 

57 

48.7878 

47.3939 

46.0730 

44.8211 

43.6340 

41.4411 

57 

58 

51.1416 

49.7418 

48.4132 

47.1516 

45.9537 

43.7349 

58 

59 

53.6509 

52.2457 

50.9095 

49.6389 

48.4302 

46.1862 

59 

60 

56.3282 

54.9175 

53.5745 

52.2951 

51.0760 

48.8073 

60 

61 

59.1848 

57.7696 

56.4196 

55.1317 

53.9026 

51.6097 

61 

62 

62.2349 

60.8148 

59.4582 

58.1621 

56.9232 

54.6062  ' 

62 

63 

65.4953 

64.0706 

62.7079 

61.4038 

60.1552 

57.8148 

63 

64 

68.9809 

67.5521 

66.1832 

64.8709 

63.6129 

61.2493 

64 

65 

72.7102 

71.2769 

69.9017 

68.5817 

67.3143 

64.9276 

65 

66 

76.7006 

75.2633 

73.8817 

72.5538 

71.2768 

68.8667 

66 

67 

80.9763 

79.5344 

78.1464 

76.8106 

75.5240 

73.0907 

67 

68 

85.5559 

84.1089 

82.7146 

81.3703 

80.0741 

77.6169 

68 

69 

90.4709 

89.0189 

87.6177 

86.2649 

84.9587 

82.4772 

69 

70 

95.7386 

94.2812 

92.8725 

91.5105 

90.1937 

87.6870 

70 

71 

101.395 

99.9310 

98.5145 

97.1422 

95.8145 

93.2814 

71 

72 

107.467 

105.996 

104.570 

103.188 

101.848 

99.2869 

72 

73 

113.991 

112.511 

111.075 

109.682 

108.329 

105.738 

73 

74 

121.006 

119.516 

118.069 

116.663 

115.296 

112.673 

74 

75 

128.540 

127.039 

125.579 

124.158 

122.776 

120.118 

75 

76 

136.645 

135.131 

133.656 

132.219 

130.819 

128.1^3 

76 

77 

145.373 

143.843 

142.352 

140.897 

139.477 

136.739 

77 

78 

154.760 

153.212 

151.701 

150.225 

148.784 

145.998 

78 

79 

164.871 

163.302 

161.769 

160.269 

158.802 

155.964 

79 

80 

175.769 

.174.174 

172.614 

171.087 

169.592 

166.694 

80 

81 

187.521 

185.898 

184.307 

182.749 

181.221 

178.257 

81  1 

82 

200.225 

198.567 

196.942 

195.348 

193.783 

190.743 

82 

83 

213.958 

212.260 

210.594 

208.958 

207.351 

204.224 

83 

84 

228.899 

227.155 

225.442 

223.759 

222.103 

218.877 

84 

85 

245.187 

243.390 

241.622 

239.883 

238.173 

234.835 

85 

86 

263.137 

261.279 

259.448 

257.648 

255.874 

252.409 

86 

87 

283.260 

281.333 

279.436 

277.565 

275.722 

272.117 

87 

88 

306.139 

304.140 

302.168 

300.223 

298.305 

294.543 

88 

89 

333.449 

331.380 

329.342 

327.326 

325.339 

321.442 

89 

90 

361.532 

359.385 

357.261 

355.167 

353.099 

349.040 

90 

91 

389.061 

386.811 

384.586 

382.396 

380.228 

375.972 

91 

1  ^ 

^  418.501 

416.137 

413.801 

411.495 

409.214 

404.733 

92 

i^ 

151.009 

448.516 

446.049 

443.614 

441.206 

436.468 

93 

b-x 

486.463 

483.818 

481.198 

478.615 

476.056 

471.023 

94 

95 

526.353 

523.527 

520.729 

517.963 

515.226 

509.839 

95 

1  9^ 

577.487 

574.439 

671.434 

568.437 

565.488 

559.670 

96 

W 

631.366 

628.022 

624.715 

621.445 

618.210 

611.838 

97 

98 

726.375 

722.578 

718.820 

715.099 

711.420 

704.177 

98 

;  99 

• —  -— 

970.868 

966.189 

861.537 

956.947 

952.384 

943.405 

99 

•10 


TABLE    XXX. 


SINGLE  PREMIUM    (A)  TO  INSURE    $1,000,   PAYABLE   AT    THE   END   OP  THE  POLICY 
YEAR  IN   WHICH  THE   LIFE  FAILS. 


A&E. 

3  Per  Cent. 

3i  Per  Cent. 

4  Per  Cent. 

4^  Per  Cent. 

5  Per  Cent. 

6  Per  Cent. 

AOE, 

10 

10 

278.604 

236.069 

202.630 

176.078 

154.779 

123.387 

11 

282.310 

239.403 

205.587 

178.678 

157.055 

125.120 

11 

12 

286.139 

242.859 

208.665 

181.396 

159.443 

126.951 

12 

13 

290.098 

246.450 

211.878 

184.246 

161.956 

128.893 

13 

14 

294.189 

250.175 

215.224 

187.224 

164.593 

130.946 

14 

15 

298.404 

254.030 

218.699 

190.329 

167.352 

133.108 

15 

16 

302.761 

258.031 

222.321 

193.579 

170.250 

135.395 

16 

17 

307.260 

262.181 

226.095 

196.977 

173.294 

137.815 

17 

18 

311.903 

266.480 

230.019 

200.526 

176.483 

140.369 

18 

19 

316.695 

270.935 

234.101 

204.232 

179.827 

143.064 

19 

20 

321.639 

275.552 

238.349 

208.103 

183.332 

145.911 

20 

21 

326.735 

280.329 

242.763 

212.140 

187.001 

148.911 

21 

22 

331.989 

285.275 

247.348 

216.351 

190.842 

152.072 

22 

23 

337.407 

290.395 

252.116 

220.745 

194.865 

155.407 

23 

24 

342.986 

295.690 

257.065 

225.322 

199.071 , 

158.917 

24 

25 

348.735 

301.166 

262.203 

230.094 

203.470 

162.613 

25 

26 

354.658 

306.832 

267.540 

235.069 

208.075 

166.508 

26 

27 

360.751 

312.680 

273.069 

240.241 

212.878 

170.597 

27 

28 

367.023 

318.727 

278.806 

245.629 

217.899 

174.901 

28 

29 

373.475 

324.971 

284.756 

251.234 

223.143 

179.426 

29 

30 

380.101 

331.407 

290.909 

257.053 

228.603 

184.166 

30 

31 

386.914 

338.051 

297.284 

263.104 

234.301 

189.146 

31 

32 

393.916 

344.905 

303.886 

269.391 

240.242 

194.372 

32 

33 

401.104 

351.967 

310.714 

275.917 

246.430 

199.850 

33 

34 

408.482 

359.244 

317.773 

282.688 

252.871 

205.589 

34 

35 

416.049 

366.733 

325.066 

289.707 

259.570 

211.595 

35 

36 

423.799 

374.432 

332.588 

296.970 

266.526 

217.868 

36 

37 

431.748 

382.357 

340.359 

304.501 

273.761 

224.435 

37 

38 

439.886 

390.502 

348.373 

312.294 

281.273 

231.296 

38 

39 

448.214 

398.864 

356.630 

320.349 

289.063 

238.453 

39 

40 

456.727 

407.446 

365.134 

328.672 

297.136 

245.915 

40 

41 

465.427 

416.243 

373.879 

337.259 

305.493 

253.685 

41 

42 

474.317 

425.266 

382.879 

346.127 

314.150 

261.783 

42 

43 

483.382 

434.498 

392.119 

355.257 

323.091 

270.195 

43 

44 

492.630 

443.947 

401.608 

364.666 

332.333 

278.941 

44 

45 

502.052 

453.608 

411.338 

374.344 

341.868 

288.018 

45 

46 

511.642 

463.473 

421.309 

384.292 

351.699 

297.427 

46 

47 

521.399 

473.540 

431.516 

394.509 

361.825 

307.175 

47 

48 

531.308 

483.802 

441.953 

404.985 

372.239 

317.257 

48 

49 

541.371 

494.255 

452.618 

415.724 

382.945 

327.678 

49 

50 

551.574 

504.889 

463.500 

426.712 

393.934 

338.432 

60 

61 

561.916 

515.697 

474.594 

437.949 

405.201 

349,520 

61 

52 

572.377 

526.667 

485.889 

449.423 

416.738 

360.933 

62 

53 

582.952 

537.792 

497.376 

461.124 

428.538 

372.669 

53 

54 

593.632 

549.060 

509.046 

473.048 

440.592 

384.721 

64 

FoEMULA,    Ax  =  12^M?  =  1000  I  1  _  (1  _  t,)  (1+a^)  | 


xy 


TABLE    XXX. 


♦11 


SINGLE  PREMIUM  (A)  TO  INSURE  $1,000,    PAYABLE   AT    THE  END    OF  THE  POLICY 

YEAR  IN   WHICH  THE  LIFE  FAILS. 


AQE. 

55 

3  Per  Cent. 

3^  Per  Cent. 

4  Per  Cent. 

4^  Per  Cent. 

5  Per  Cent. 

6  Per  Cent. 

AGE. 
55 

604.410 

560.462 

520.890 

485.184 

452.895 

397.085 

56 

615.259 

571.976 

532.882 

497.502 

465.421 

409.736 

56 

57 

620.174 

583.596 

545.019 

510.008 

478.165 

422.674 

57 

58 

637.137 

595.295 

557.277 

522.666 

491.101 

435.873 

58 

59 

648.137 

607.069 

569.642 

535.472 

504.222 

449.325 

59 

60 

659.160 

618.901 

582.103 

548.412 

'517.514 

463.019 

60 

61 

670.187 

630.769 

594.636 

561.458 

530.947 

476.925 

61 

62 

681.197 

642.651 

607.214 

574.587 

544.499 

491.020 

62 

63 

692.182 

654.535 

619.829 

587.787 

558.159 

505.290 

63 

64 

703.118 

666.403 

632.458 

601.030 

571.895 

519.709 

64 

65 

713.991 

678.225 

645.069 

614.291 

585.681 

534.246 

65 

66 

724.776 

689.986 

657.643 

627.542  . 

599.490 

548.868 

66 

67 

735.462 

701.665 

670.162 

640.767 

613.303 

563.560 

67 

68 

746.028 

713.239 

682.598 

653.931 

627.081 

578.278 

68 

69 

756.464 

724.701 

694.941 

667.029 

640.823 

593.017 

69 

70 

766.738 

736.011 

707.148 

680.010 

654.466 

607.711 

70 

71 

776.848 

747.162 

719.211 

692.861 

668.007 

622.352 

71 

72 

786.769 

758.131 

731.099 

1  ,705.558 

681.408 

636.901 

72 

73 

796.488 

768.897 

742.795 

718.075 

694.647 

651.328 

73 

74 

805.996 

779.455 

754.288 

730.397 

707.706 

665.613 

74 

75 

815.267 

789.771 

765.535 

742.484 

720.536 

679.701 

75 

76 

824.297 

799.840 

776.539 

754.324 

733.133 

693.581 

76 

77 

833.086 

809.653 

787.285 

765.914 

745.482 

707.235 

77 

78 

841.606 

819.189 

797.743 

777.213 

757.544 

720.616 

78 

79 

849.863 

828.446 

807.914 

788.216 

769.311 

733.713 

79 

80 

857.847 

837.410 

817.783  ' 

798.914 

780.770 

746.509 

80 

81 

865.558 

846.089 

827.346  ' 

809.299 

791.910 

758.990 

81 

82 

873.004 

854.480 

836.614 

819.377 

802.738 

771.156 

82 

83 

880.181 

862.577 

845.569 

829.131 

813.237 

782.984 

83 

84 

887.117 

870.420 

854.256 

838.610 

823.450 

794.528 

84 

85 

893.822 

878.011 

862.677  , 

847.807 

833.376 

805.777 

85 

86 

900.343 

885.407 

870.893 

856.799 

843.098 

816.823 

86 

87 

906.761 

892.697 

879.012 

865.693 

852.727 

827.805 

87 

88 

913.125 

899.941 

887.089 

874.559 

862.341 

838.786 

88 

89 

919.670 

907.403 

895.433 

883.737 

872.320 

850.272 

89 

90 

925.444  ■ 

'  914.000 

902.805 

891.865 

881.165  ' 

860.459 

90 

91 

930.356 

919.606 

909.076 

898.785 

888.700 

869.147 

91 

92 

934.934 

924.845 

914.958 

905.268 

895.761 

877.308 

92 

93 

939.338 

929.891 

920.617 

911.517 

902.585 

885.201 

93 

94 

943.509 

934.674 

925.985 

917.453 

909.065 

892.719 

94 

95 

947.563 

939.325 

931.219 

923.245 

915.396 

900.072 

95 

96 

951.985 

944.407 

936.936 

929.580 

922.331 

908.151 

96 

97 

955.903 

948.903 

942.005 

935.197 

928.483 

915.324 

97 

98 

961.449 

955.294 

949.212 

943.203 

937.266 

925.612 

98 

99 

970.868 

966.189 

961.537 

956.947 

952.384 

043.405 

99 

*12 


TABLE    XXXI. 

REVERSION,   OR  LIFE  INSURANCE  EQUIVALENT  TO  SINGLE  PREMIUM  OF  1. 


g 

3 

3i 

4 

H 

5 

6 

3 

H 

4 

H 

5 

6 

10 

Per  Ct. 

PerCt. 

Per  Ct. 

PerCt. 

PerCt. 

Per  Ct. 

<1 

Per  Ct. 

Per  Ct. 

Per  Ct. 

PerCt. 

Per  Ct. 

fer  Ct. 

3.5893 

4.2360 

4.9351 

5.6793 

6.4608 

8.1046 

55 

1.6545 

1.7842 

1.9198 

2.0611 

2.2080 

2.5184 

11 

.5432 

.1771 

.8641 

.5967 

.3672 

7.9923 

56 

.6253 

.7483 

.8766 

.0100 

.1486 

.4406 

12 

.4948 

.1177 

.7924 

.5128 

.2718 

.8771 

57 

.5970 

.7135 

.8348 

1.9608 

.0913 

.3659 

13 

.4471 

.0576 

.7197 

.4275 

.1745 

.7584 

58 

.5695 

.6798 

.7944 

.9133 

.0362 

.2942 

14 

.3992 

3.9972 

.6463 

.3412 

.0756 

.6367 

59 

.5429 

.6473 

.7555 

.8675 

1.9833 

.2256 

15 

3.3512 

3.9366 

4.5725 

5.2541 

5.9754 

7.5127 

60 

1.5171 

1.6158 

1.7179 

1.8234 

1.9323 

2.1597 

16 

.3029 

.8755 

.4980 

.1659 

.8737 

.3858 

61 

.4921 

.5854 

.6817 

.7811 

.8834 

.0968 

17 

.2545 

.8142 

.4229 

.0767 

.7705 

.2561 

62 

.4680 

.5561 

.6469 

.7404 

.8366 

.0366 

18 

.2061 

.7527 

.3475 

4.9869 

.6663 

.1241 

63 

.4447 

.5278 

.6133 

.7013 

.7916 

1.9791 

19 

.1576 

.6910 

.2717 

.8964 

.5609 

6.9899 

64 

.4222 

.5006 

.5811 

.6638 

.7486 

.9242 

20 

3.1091 

3.6291 

4.1955 

4.8053 

5.4546 

6.8535 

65 

1.4006 

1.4745 

1.5502 

1.6279 

1.7074 

1.8718 

21 

.0606 

.5672 

.1192 

.7139 

.3476 

.7154 

66 

.3797 

.4493 

.5206 

.5935 

.6681 

.8219 

22 

.0122 

.5054 

.0429 

.6221 

.2399 

.5758 

67 

.3597 

.4252 

.4922 

.5606 

.6305 

.7744 

23 

2.9638 

.4436 

3.9664 

.5301 

.1318 

.4347 

68 

.3404 

.4021 

.4650 

.5292 

.5947 

.7293 

24 

.9155 

.3819 

.8901 

.4381 

.0233 

.2926 

69 

.3219 

.3799 

.4390 

.4992 

.5605 

.6863 

25 

2.8675 

3.3204 

3.8138 

4.3461 

4.9147 

6.1496 

70 

1.3042 

1.3587 

1.4141 

1.4706 

1.5280 

1.6455 

26 

.8196 

.2591 

.7378 

.2541 

.8060 

.0057 

71 

.2872 

.3384 

.3904 

.4433 

.4970 

.6068 

27 

.7720 

.1982 

.6621 

.1625 

.6975 

5.8618 

72 

.2710 

.3190 

.3678 

.4173 

.4675 

.5701 

28 

.7246 

.1375 

.5867 

.0712 

.5893 

.7175 

73 

.2555 

.3006 

.3463 

.3926 

.4396 

.5353 

29 

.6776 

.0772 

.5118 

3.9804 

.4814 

.5733 

74 

.2407 

.2830 

.3258 

.3691 

.4130 

.5024 

30 

2.6309 

3.0174 

3.4375 

3.8902 

4.3744 

5.4299 

75 

1.2266 

1.2662 

1.3063 

1.3468 

1.3879 

1.4712 

31 

.5846 

2.9581 

.3638 

.8008 

.2680 

.2869 

76 

.2132 

.2503 

.2878 

.3257 

.3640 

.4418 

32 

.5386 

.8993 

.2907 

.7121 

.1625 

.1448 

77 

.2004 

.2351 

.2702 

.3056 

.3414 

.4140 

33 

.4931 

.8412 

.2184 

.6243 

.0579 

.0038 

78 

.1882 

.2207 

.2535 

.2866 

.3201 

.3877 

34 

.4481 

.7836 

.1469 

.5375 

3.9546 

4.8641 

79 

.1767 

.2071 

.2378 

.2687 

.2999 

.3629 

35 

2.4036 

2.7268 

3.0763 

3.4518 

3.8525 

4.7260 

80 

1.1657 

1.1942 

1.2228 

1.2517 

1.2808 

1.3396 

36 

.3596 

.6707 

.0067 

.3673 

.7520 

.5899 

81 

.1553 

.1819 

.2087 

.2356 

.2628 

.3175 

37 

.3162 

.6154 

2.9381 

,.2841 

.6528 

.4556 

82 

.1455 

.1703 

.1953 

.2204 

.2457 

.2968 

38 

.2733 

.5608 

.8705 

.2021 

.5553 

.3235 

83 

.1361 

.1593 

.1826 

.2061 

.2297 

.2772 

39 

.2311 

.5071 

.8040 

.1216 

.4595 

.1937 

84 

.1272 

.1489 

.1706 

.1924 

.2144 

.2586 

40 

2.1895 

2.4543 

2.7387 

3.0425 

3.3655 

4.0664 

85 

1.1188 

1.1389 

1.1592 

1.1795 

1.1999 

1.2410 

41 

.1486 

.4024 

.6747 

2.9651 

.2734 

3.9419 

86 

.1107 

.1294 

.1482 

.1671 

.1861 

.2243 

42 

.1083 

.3515 

.6118 

.8891 

.1832 

.8200 

87 

.1028 

.1202 

.1376 

.1551 

.1727 

.2080 

43 

.0688 

.3015 

.5502 

.8149 

.0951 

.7010 

88 

.0951 

.1112 

.1273 

.1434 

.1596 

.1922 

44 

.0299 

.2525 

.4900 

.7422 

.0090 

.5850 

89 

.0874 

.1020 

.1168 

.1316 

.1464 

.1761 

45 

1.9918 

2.2046 

2.4311 

2.6713 

2.9251 

3.4720 

90 

1.0806 

1.0941 

1.1077 

1.1212 

1.1349 

1.1622 

46 

.9545 

.1576 

.3736 

.6022 

.8433 

.3622 

91 

.0749 

.0874 

.1000 

.1126 

.1252 

.1506 

47 

.9179 

.1117 

.3174 

.5348 

.7638 

.2555 

92 

.0696 

.0813 

.0929 

.1046 

.1164 

.1399 

48 

.8821 

.0670 

.2627 

.4692 

.6864 

.1520 

93 

.0646 

.0754 

.0862 

.0971 

.1079 

.1297 

49 

.8471 

.0233 

.2094 

.4054 

.6113 

.0518 

94 

.0599 

.0699 

.0799 

.0900 

.1000 

.1202 

50 

1.8130 

1.9806 

2.1575 

2.3435 

2.5385 

2.9548 

95 

1.0553 

1.0646 

1.0739 

1.0831 

1.0924 

1.1110 

51 

.7796 

.9391 

.1071 

.2834 

.4679 

.8611 

96 

.0504 

.0589 

.0673 

.0758 

.0842 

.1011 

52 

.7471 

.8987 

.0581 

.2251 

.3996 

.7706 

97 

.0461 

.0539 

.0616 

.0693 

.0770 

.0925 

53 

.7154 

.8595 

.0106 

.1686 

.3335 

.6833 

98 

.0401 

.0468 

.0535 

.0602 

.0669 

.0804 

54 

.6845 

.8213 

1.9645 

1 

.1139 

.2697 

.5993 

99 

.0300 

.0350 

.0400 

.0450 

.0500 

.0600 

Formula, 


1000 


*13 


TABLE    XXXII, 


ANNUITY    WHICH  1,000   WILL   PURCHASE,    PAYABLE   AT   THE   END  OF   EACH   YEAB 

DURING    LIFE. 


% 

10 

3 

PerCt. 

3i 
Per  Ct. 

4 
Per  Ct. 

Per^t. 

5 
Per  Ct. 

6 
Per  Ct. 

< 

3 
Per  Ct. 

Per  Ct. 

4 
Per  Ct. 

PerCt. 

5 
Per  Ct. 

6 
PerCt. 

43.07 

46.33 

50.68 

55.15 

59.70 

69.03 

55 

79.48 

83.35 

87.28 

91.28 

95.34 

103.6 

11 

42.30 

46.53 

50.88 

55.33 

59.87 

69.17 

56 

81.90 

85.78 

89.73 

93.73 

97.79 

106.1 

12 

43.54 

46.75 

51.09 

55.53 

60.05 

69.33 

57 

84.50 

88.39 

92.34 

96.35 

100.4 

108.7 

13 

43.78 

46.99 

51.31 

55.73 

60.35 

69.50 

58 

87.37 

91.18 

95,14 

99.16 

103.3 

111.5 

14 

43.04 

47.33 

51.54 

55.95 

60.45 

69.67 

59 

90.35 

94.17 

98.14 

102.3 

106.3 

114.6 

15 

43.31 

47.49 

51.78 

56.17 

60.66 

69.86 

60 

93.44 

97.37 

101.4 

105.4 

109.5 

117.8 

16 

43.59 

47.75 

52.03 

56.41 

60.88 

70.05 

61 

96.87 

100.8 

104.8 

108.9 

113.0 

131.3 

17 

43.89 

48.03 

52.30 

56.66 

61.13 

70.27 

62 

100.6 

104.5 

108.5 

113.6 

116.7 

125.1 

18 

44.30 

48.33 

52.58 

56.93 

61.37 

70.49 

63 

104.5 

108.5 

112.6 

116.7 

120.8 

129.2 

19 

44.53 

48.64 

53.87 

57.31 

61.64 

70.73 

64 

108.8 

113.8 

116.9 

121.0 

125.2 

133.6 

20 

44.86 

48.96 

53.18 

57.51 

61.93 

70.98 

65 

113.4 

117.4 

121.5 

135.7 

129.9 

138.3 

21 

45.33 

49.31 

53.51 

57.83 

63.33 

71.25 

66 

118.4 

133.4 

136.6 

130.7 

134.9 

143.5 

22 

45.59 

49.66 

53.85 

58.15 

63.53 

71.53 

67 

133.7 

137.8 

132.0 

136.3 

140.4 

149.0 

23 

45.98 

50.04 

54.33 

58.49 

63.86 

71.83 

68 

139.5 

133.7 

137.9 

143.1 

146.4 

155.0 

24 

46.39 

50.44 

54.60 

58.86 

63.31 

72.16 

69 

135.8 

140.0 

144.3 

148.5 

153.8 

161.5 

25 

46.83 

50.85 

55.00 

59.25 

63.59 

72.50 

70 

143.7 

146.9 

151.2 

155.5 

159.8 

168.6 

26 

47.37 

51.39 

55.43 

59.65 

63.98 

72.86 

71 

150.1 

154.4 

158.7 

163.1 

167.5 

176.3 

27 

47.74 

51.75 

55.87 

60.08 

64.39 

73.35 

72 

158.3 

163.5 

166.9 

171.3 

175.7 

184.7 

28 

48.33 

53.33 

56.34 

60.54 

64.83 

73.66 

73 

167.0 

171.4 

175.8 

180.3 

184.8 

193.8 

29 

48.76 

53.74 

56.83 

61.03 

65.30 

74.09 

74 

176.6 

181.1 

185.6 

190.1 

194.6 

203.8 

30 

49.30 

53.37 

57.35 

61.53 

65.79 

74.55 

75 

187.3 

191.7 

196.2 

300.8 

205.4 

214.7 

31 

49.88 

53.84 

57.90 

63.06 

66.31 

75.05 

76 

198.7 

303.3 

207.9 

313.5 

317.2 

226.6 

32 

50.48 

54.43 

58.48 

62.63 

66.87 

75.57 

77 

311.4 

316.0 

220.7 

335.4 

230.2 

239.7 

33 

51.13 

55.06 

59.10 

63.23 

67.45 

76.13 

78 

335.3 

330.1 

234.8 

339.6 

244.4 

254.1 

34 

51.79 

55.73 

59.75 

63,87 

68.08 

76.72 

79 

340.7 

345.5 

250.4 

355.3 

360.1 

370.0 

35 

53.50 

56.41 

60.43 

64.54 

68.73 

77.35 

80 

357.7 

363.6 

267.5 

373.5 

377.5 

387.5 

36 

53.34 

57.15 

61.15 

65.25 

69.43 

78.02 

81 

376.6 

381.6 

286.6 

391.7 

396.7 

307.0 

37 

54.03 

57.92 

61.93 

66.00 

70.17 

78.73 

82 

397.6 

303.7 

307.9 

313.0 

318.3 

338.6 

38 

54.85 

58.74 

63.73 

66.80 

70.96 

79.49 

83 

331.3 

326.4 

331.7 

336.9 

343.3 

352.9 

39 

55.73 

59.61 

63.58 

67.65 

71.79 

80.30 

84 

347.8 

353.1 

358.5 

363.9 

369.3 

380.2 

40 

56.65 

60.53 

64.49 

68.54 

73.67 

81.15 

85 

378.0 

383.5 

389.1 

394.6 

400.3 

411.3 

41 

57.63 

61.49 

65.45 

69.49 

73.61 

83.07 

86 

413.0 

418.6 

424.3 

430.0 

435.7 

447.2 

42 

58.66 

63.52 

66.47 

70.50 

74.61 

83.04 

87 

454.3 

460.2 

466.1 

471.9 

477.9 

489.7 

43 

59.75 

63.60 

67.55 

71.57 

75.67 

84.08 

88 

504.4 

510.5 

516.6 

533.7 

538.9 

541.2 

44 

60.90 

64.75 

68.69 

72.71 

76.80 

85.19 

89 

568.8 

675.3 

581.8 

588.3 

594.8 

607.8 

45 

63.13 

65.97 

69.91 

73.92 

78.00 

86.37 

90 

641.1 

648.0 

654.9 

661.8 

668.7 

682.5 

46 

63.43 

67.27 

71.30 

75.20 

79.27 

87  63 

91 

718.8 

726.0 

733.3 

740.5 

747.8 

762.3 

47 

64.80 

68.64 

73.57 

76.56 

80.63 

88.97 

92 

810.4 

818.0 

825.7 

833.4 

841.1 

856.4 

48 

66.36 

70.10 

74.03 

78.02 

82.08 

90.40 

93 

923.6 

931.7 

939.9 

948.1 

956.3 

972.7 

49 

67.81 

71.66 

75.57 

79.57 

83.63 

91.93 

94 

1064. 

1073. 

1082. 

1091. 

1099. 

1117. 

50 

69.46 

73.31 

77.33 

81.33 

85.27 

93.57 

95 

1350. 

1259. 

1269. 

1378. 

1388. 

1307. 

51 

71.33 

75.07 

78.99 

83.97 

87.03 

95.31 

96 

1543. 

1553. 

1563. 

1574. 

1585. 

1606. 

52 

73.09 

76.94 

80.86 

84.85 

88.90 

97.18 

97 

1945. 

1957. 

1969. 

1981. 

1993. 

2016. 

53 

75.08 

78.94 

83.86 

86.85 

90.90 

99.18 

98 

3090. 

3105. 

3120. 

3135. 

3150. 

3180. 

54 



77.31 

81.07 

85.00 

88.99 

93.05 

101.3 

99 

0000. 

0000. 

0000. 

0000. 

0000. 

0000. 

Formula, 


1000       1000  D, 


ttx 


Nx+] 


14 


TABLE    XXXIII. 

COMMUTATION  COLUMNS.        3  PER  CENT. 


AGE. 

D.. 

N.. 

s^. 

c^. 

Mo:. 

Ex. 

AGE. 

10 

10 

74,409.3 

1,842,967.6 

38,012,941.3 

468.129 

20,730.738 

735,794.660 

11 

71,774.1 

1,768,558.3 

36,169,973.7 

453.092 

20,262.609 

715,063.922 

11 

12 

69,230.4 

1,696,784.2 

34,401,415.4 

437.852 

19,809.517 

694,801.313 

12 

13 

66,776.2 

1,627,553.8 

32,704,631.2 

•423.777 

19,371.665 

674,991.796 

13 

14 

64,407.3 

1,560,777.6 

31,077,077.4 

410.792 

18,947.888 

655,620.131 

14 

15 

62,120.8 

1,496,370.3 

29,516,299.8 

397.581 

18,537.096 

636,672.243 

15 

16 

59,913.7 

1,434,249.5 

28,019,929.5 

384.790 

18,139.515  ■   618,135.147 

16 

17 

57,784.0 

1,374,335.8 

26,585,680.0 

372.996 

17,754.725  i  599,995.632 

17 

18 

55,727.9 

1,316,551.8 

25,211,344.2 

361.561 

17,381.729 

582.240.907 

18 

19 

53,743.1 

1,260,823.9 

23,894,792.4 

350.477 

17,020.168 

564,859.178 

19 

20 

51,827.5 

1,207,080.8 

22,633,968.5 

340.269 

16,669.691 

547,839.010 

20 

21 

49,977.6 

1,155,253.3 

21,426,887.7 

330.358 

16,329.422 

531,169.319 

21 

22 

48,191.5 

1,105,275.7 

20,271,634.4 

320.736 

15,999.064 

514,839.897 

22 

23 

46,467.1 

1,057,084.2 

19,166,358.7 

311.886 

15,678.328 

498,840.833 

23 

24 

44,801.9 

1,010,617.1 

18,109,274.5 

303.279 

15,366.442 

483,162.505 

24 

25 

43,193.7 

965,815.2 

17,098,657.4 

294.910 

15,063.163 

467,796.063 

25 

26 

41,640.7 

922,621.5 

16,132,842.2 

287.671 

14,768.253 

452,732.900 

26 

27 

40,140.2 

880,980.8 

15,210,220.7 

280.166 

14,480.582 

437,964.647 

27 

28 

38,690.8 

840,840.6 

14,329,239.9 

273.279 

14,200.416 

423,484.065 

28 

29 

37,290.7 

802,149.8 

13,488,399.3 

267.380 

13,927.137 

409,283.649 

29 

30 

35,937.2 

764,859.1 

12,686,249.5 

261.192 

13,659.757 

395,356.512 

30 

31 

34,629.4 

728,921.9 

11,921,390.4 

255.526 

13,398.565 

381,696.755 

31 

32 

33,365.1 

694,292.5 

11,192,468.5 

^50.345 

13,143.039 

368,298.190 

32 

33 

32,143.1 

660,927.4 

10,498,176.0 

245.616 

12,892.694 

355,155.151 

33 

34 

30,961.1 

628,784.3 

9,837,248.6 

241.305 

12,647.078 

342,262.457 

34 

35 

29,818.2 

597,823.2 

9,208,464.3 

237.727 

12,405.773 

329,615.379 

35 

36 

28,711.9 

568,005.0 

8,610,641.1 

233.818 

12,168.046 

317,209.606 

36 

37 

27,641.8 

539,293.1 

8,042,636.1 

230.585 

11,934.228 

305,041.560 

37 

38 

26,606.1 

511,651.3 

7,503,343.0 

227.974 

11,703.643 

293,107.332 

38 

39' 

'25,603.2 

485,045.2 

6,991,691.7 

225.626 

11,475.669 

281,403.689 

39 

40 

24,631.8 

459,442.0 

6,506,646.5 

te.816 

11,250.043 

269,928.020 

40 

41 

23,690.6 

434,810.2 

6,047,204.5 

221.921 

11,026.227 

258,677.977 

41 

42 

22,778.6 

411,119.6 

5,612,394.3 

221.068 

10,804.306 

247,651.750 

42 

43 

21,894.1 

388,341.0 

5,201,274.7 

220.076 

10,583.238 

236,847.444 

43 

44 

21,036.4 

366,446.9 

4,812,933.7 

219.749 

10,363.162 

226,264.206 

44 

45 

20,203.9 

345,410.5 

4,446,486.8 

219.766 

10,143.413 

215,901.044 

45 

46 

19,395.7 

325,206.6 

4,101,076.3 

220.096 

9,923.647 

205,757.631 

46 

47 

18,610.6 

305,810.9 

3,775,869.7 

220.945 

9,703.551 

195,833.984 

47 

48 

17,847.7 

287,200.3 

3,470,058.8 

222.028 

9,482.606 

186,130.433 

48 

49 

17,105.8 

269,352.6 

3,182,858.5 

223.545 

9,260.578 

176,647.827 

49 

50 

16,384.1 

252,246.8 

2,913,505.9 

225.449 

9,037.033 

167,387.249 

50 

51 

15,681.3 

235,862.7 

2,661,259.1 

227.699 

8,811.584 

158,350.216 

51 

52 

14,997.0 

220,181.4 

2,425,396.4 

230.252 

8,583.885 

149,538.632 

52 

53 

14,329.9 

205,184.4 

2,205,215.0 

233.071 

8,353.633 

140,954.747 

53 

54 

13,679.5 

190,854.5 

2,000,030.6 

236.121 

8,120.562 

132,601.114 

54 

Formulas,    'Dx=v%;  Na,=Dx  +  Da,+i-f- 


S->=Na,  +  Na,+i-f 


TABLE     XXXIII. 


COMMUTATION    COLUMNS.         3    PER   CEFT. 


♦15 


AGE.. 

55 

D^. 

No,.  ■ 

Sx. 

0^. 

M^. 

Rx. 

AGE. 

13,044.8 

177,175.0 

1,809,176.1 

239.750 

7,884.441 

124,480.552 

55 

56 

12,425.2 

164,130.2 

1,632,001.1 

243.339 

7,644.691 

116,596.111 

56 

57 

11,820.0 

151,705.0 

1,467,870.9 

247.416 

7,401.352 

108,951.420 

57 

58 

11,228.3 

139,885.0 

1,316,165.9 

251.398 

7,153.936 

101,550.068 

58 

59 

10,649.8 

128,656.7 

1,176,280.9 

255.448 

6,902.538 

94,396.132  i  59 

1 

60 

10,084.2 

118,006.89 

1,047,624.22 

259.708 

6,647.090 

87,493.594 

60 

61 

9,530.75 

107,922.69 

929,617.33 

263.983 

6,387.382 

80,846.504 

61 

62 

8,989.18 

98,391.94 

821,694.64 

267.944 

6,123.399 

74,459.122 

62 

63 

8,459.43 

89,402.76 

723,302.70 

271.903 

5,855.455 

68,335.723 

63 

64 

7,941.12 

80,943.33 

633,899.94 

275.550 

5,583.552 

62,480.268 

64 

65 

7,434.26 

73,002.21 

552,956.61 

278.896 

5,308.002 

56,896.716 

65 

66 

6,938.84 

65,567.95 

479,954.40 

281.537 

5,029.106 

51,588.714 

66 

67 

6,455.22 

58,629.11 

414,386.45 

283.789 

4,747.569 

46,559.608 

67 

68 

5,983.40 

52,173.89 

355,757.34 

284.889 

4,463.780 

41,812.039 

68 

69 

5,524.25 

46,190.49 

303,583.45 

285.558 

4,178.891 

37,348.259 

69 

70 

5,077.78 

40,666.24 

257,392.96 

284.844 

3,893.833 

33,169.368 

70 

71 

4,645.05 

35,588.46 

216,726.72 

283.095 

3,608.489 

29,276.035  |  71 

72 

4,226.65 

30,943.41 

181,138.26 

279.935 

3,325.394 

25,667.546  |  72 

73 

3,823.61 

26,716.76 

150,19^.85 

275.260 

3,045.459 

22,342.152 

73 

74 

3,436.99 

22,893.15 

123,478.09 

269.313 

2,770.199 

19,296.693 

74 

75 

3,067.56 

19,456.1.6 

100^584.94 

261.468 

2,500.886 

16,526.494 

75 

76 

2,716.76 

16,388.60 

81,128.78 

251.902 

2,239.418 

14,025.608 

76 

77 

2,385.73 

13,671.84 

64,740.18 

240.876 

1,987.516 

11,786.190 

77 

78 

2,075.36 

11,286.11 

51,068.34 

228.052 

1,746.640 

9,798.674 

78 

79 

1,786.86 

9,210.75 

39,782.23 

213.704 

1,518.588 

8,052.034 

79 

80 

1,521.12 

7,423.887 

30,571.484 

197.991 

1,304.884 

6,533.446 

80 

81 

1,278.82 

5,902.767 

23,147.597 

181.063 

1,106.893 

5,228.562 

81 

82 

1,060.51 

4,623.947 

17,244.830 

163.404 

925.830 

4,121.669 

82 

83 

866.216 

3,563.437 

12,620.883 

145.035 

762.426 

3,195.839 

83 

84 

695.951 

2,697.221 

9,057.446 

126.705 

617.391 

2,433.413 

84 

85 

548.976 

2,001.270 

6,360.225 

108.533 

490.686 

1,816.022 

85 

86 

424.452 

1,452.294 

4,358.955 

91.0068 

382.153 

1,325.336 

86 

87 

321.083 

1,027.842 

2,906.661 

74.7799 

291.1461 

943.1827 

87 

88 

236.951 

706.759 

1,878.819 

59.7092 

216.3662 

652.0366 

88 

89 

170.341 

469.808 

1,172.060 

48.3900 

156.6570 

435.6704 

89 

90 

116.9892 

299.4671 

702.2519 

37.2722 

108.2670 

279.0134 

90 

91 

76.3096 

182.4779 

402.7850 

26.5633 

70.9948 

170.7464 

91 

92 

47.5237 

106,1683 

220.3071 

17.9823 

44.4315 

99.7516 

92 

93 

28.1573 

58.6446 

114.1388 

11.6183 

26.4492 

55.3201 

93 

94 

15.7189 

30.4873 

55.4942 

7.05748 

14.83089 

28.87092 

94 

95 

8.20357 

14.76840 

25.00690 

3.98231 

7.77341 

14.04003 

95 

96 

3.98231 

6.56483 

10.23852 

2.16059 

3.79110 

6.26662  96 

97 

1.70573 

2.58252 

3.67369 

.993631 

1.630512 

2.475523  97 

98 

.662419 

.876794 

1.091169 

.428751 

.636881 

.8450111  98 

99 

.214375 

.214375 

.214375 

.208130 

.208130 

.208130  99 

Cx^ilx—lx+ljv^"-^;     Ma,=Ca.+Ca,+i  + 


Ra.=Ma,  +  Ma;+i  + 


^16 


TABLE     XXXiri. 

LOGARITHMS  OF  COMMUTATION  COLUMNS.        3  PER  CENT. 


1 

AGE. 

- 

AiNa;. 

1 

1 

A{jx. 

AMa;. 

Axis. 

A&E 
10 

10 

4.871627 

6.265518 

7.579931 

2.670366 

4.316615 

5.866757 

11 

4.855968 

6.247619 

7.558349 

2.656186 

4.306695 

5.854345 

11 

12 

4.840297 

6.229627 

7.536576 

2.641327 

4.296874 

5.841861 

12 

13 

4.824622 

6.211535 

7.514609 

2.627137 

4.287167 

5.829298 

13 

14 

4.808935 

6.193341 

7.492440 

2.613622 

4.277561 

5.816652 

14 

15 

4.793237 

6.175039 

7.470062 

2.599425 

4.268042 

5.803916 

15 

16 

4.777526 

6.156625 

7.447467 

2  585224 

4.258626 

5.791084 

16 

17 

4.761808 

6.138093 

7.424648 

2.571704 

4.249314 

5.778148 

17 

18 

4.746073 

6.119438 

7.401596 

2.558182 

4.240093 

5.765103 

18 

19 

4.730323 

6.100654 

7.378303 

2.544659 

4.230964 

5.751940 

19 

20 

4.714559 

6.081736 

7.354760 

2.531822 

4.221928 

5.738653 

20 

21 

4.698776 

6.062677 

7.330959 

2.518985 

4.212971 

5. 725233 

21 

22 

4.682971 

6.043471 

7.306889 

2.506148 

4.204094 

5.711672 

22 

23 

4.667146 

6.024110 

7.282539 

2.493996 

4.195300 

5.697962 

23 

24 

4.651296 

6.004587 

7.257901 

2.481843 

4.186573 

5.684093 

24 

25 

4.635421 

5.984894 

7.232962 

2.469689 

4.177916 

5.670056 

25 

26 

4.619518 

5.965024 

7.207711 

2.458896 

4.169328 

5.655842 

26 

27 

4.603580 

5.944966 

7.182135 

2.447416 

4.160787 

5.641439 

27 

28 

4.587608 

5.924714 

7.156223 

2.436606 

4.152301 

5.626837 

28 

29 

4.571601 

5.904255 

7.129961 

2.427128 

4.143862 

5.612025 

29 

30 

4.555544 

5.883581 

7.103334 

2.416959 

4.135443 

5.596989 

30 

31 

4.539445 

5.862681 

7.076327 

2.407435 

4.127059 

5.581718 

31 

32 

4.523292 

5.841542 

7.048926 

2.398540 

4.118696 

5.566200 

32 

33 

4.507087 

5.820154 

7.021114 

2.390257 

4.110344 

5.550418 

33 

34 

4.490817 

5.798501 

6.992874 

2.382567 

4.101990 

5.534359 

34 

35 

4.474481 

5.776573 

6.964187 

2.376079 

4.093625 

5.518008 

35 

36 

4.458061 

5.754352 

6.935035 

2.368878 

4.085221 

5.501346 

36 

37 

4.441565 

5.731825 

6.905398 

2.362832 

4.076795 

5.484359 

37 

38 

4.424981 

5.708974 

6.875355 

2.357885 

4.068321 

5.467027 

38 

39 

4.408294 

5.685783 

6.844582 

2.353389 

4.059779 

5.449330 

39 

40 

4.391497 

5.662231 

6.813357 

2.349892 

4.051154 

5.431248 

40 

41 

4.374575 

5.638300 

6.781554 

2.346198 

4.042427 

5.412760 

41 

42 

4.357528 

5.613969 

6.749148 

2.344526 

4.033597 

5.393841 

42 

48 

4.340328 

5.589213 

6.716110 

2.342574 

4.024618 

5.374468 

43 

44 

4.322971 

5.564011 

6.682410 

2.341926 

4.015492 

5.354616 

44 

45 

4.305434 

5.538336 

6.648017 

2.341962 

4.006183 

5.334255 

45 

46 

4.287706 

5.512159 

6.612898 

2.342611 

3.996672 

5.313356 

46 

47 

4.269761 

5.485453 

6.577017 

2.344284 

3.986931 

5.291888 

47 

48 

4.251582 

5.458185 

6.540337 

2.346408 

3.976928 

5.269817 

48 

49 

4.233143 

5.430321 

6.502816 

2.349365 

3.966638 

5.247109 

49 

50 

4.214422 

5.401826 

6.464416 

2.353049 

3.956026 

5.223723 

50 

51 

4.195383 

5.372659 

6.425086 

2.357360 

3.945054 

5.199619 

51 

52 

4.176002 

5.342781 

6.384782 

2.362203 

3.933684 

5.174753 

52 

1 

53 

4.156242 

5.312144 

6.343450 

2.367488 

3.921875 

5.149080 

53 

54 

4.136069 

5.280702 

! 

6.301037 

2.373134 

3.909586 

! 

5.122548 

54 

TABLE    XXXIII. 

LOGARITHMS  OF  COMMUTATION  COLUMNS,        3  PER  CENT. 


*X7 


AGE. 

55 

Wx. 

^^x. 

ASic. 

ACa,. 

AM^. 

AEa;. 

AGE. 
55 

4.115439 

5.248403 

6.257481 

2.379759 

3.896771 

5.095102 

56 

4.094302 

5.215188 

6.212720 

2.386212 

3.883360 

5.066684 

56 

57 

4.072616 

5.181000 

6.166688 

2.393428 

3.869311 

5.037233 

57 

58 

4.050312 

5.145771 

6.119311 

2.400363 

3.854545 

5.006680 

58 

59 

4.027342 

5.109432 

6.070511 

2.407303 

3.839009 

4.974955 

59 

60 

4.003641 

5.071906 

6.020205 

2.414486 

3.822632 

4.941976 

60 

61 

3.979127 

5.033113 

5.968304 

2.421576 

3.805323 

4.907662 

61 

62 

3.953720 

4.992959 

5.914710 

2.428044 

3.786993 

4.871918 

62 

63 

3.927341 

4.951351 

5.859320 

2.434413 

3.767561 

4.834648 

63 

64 

3.899882 

4.908181 

5.802021 

2.440200 

3.746910 

4.795743 

64 

65 

3.871238 

4.863336 

5.742691 

2.445442 

3.724931 

4.755087 

65 

66 

3.841287 

4.816692 

5.681200 

2.449536 

3.701491 

4.712555 

66 

67 

3.809911 

4.768113 

5.617405 

2.452995 

3.676471 

4.668009 

67 

68 

3.776948 

4.717453 

5.551154 

2.454676 

3.649703 

4.621301 

68 

69 

3.742273 

4.664552 

5.482278 

2.455695 

3,621061 

4.572270 

69 

70 

3.705674 

4.609234 

5.410597 

2.454C06 

3.590321 

4.520737 

70 

71 

3.666990 

4.551309 

5.335912 

2.451932 

3.557326 

4.466513 

71 

72 

3.625996 

4.490568 

5.258010 

2.447057 

3.521843 

4.409384 

72 

73 

3.582474 

4.426784 

5.176655 

2.439743 

3.483653 

4.349125 

73 

74 

3.536178 

4.359706 

5.091590 

2.430257 

3.442511 

4.285483 

74 

75 

3.486794 

4.289057 

5.002533 

2.417419 

3.398094 

4.218181 

75 

76 

3.434051 

4.214542 

4.909175 

2.401231 

3.350135 

4.146922 

76 

77 

3.377621 

4.135827 

4.811174 

2.381793 

3.298311 

4.071373 

77 

78 

3.317094 

4.052544 

4.708152 

2.358035 

3.242203 

3.991167 

78 

79 

3.252091 

3.964295 

4.599690 

2.329813 

3.181440 

3.905906 

79 

80 

3.182162 

3.870631 

4.485317 

2.296645 

3.115572 

3.815142 

80 

81 

3.106809 

3.771056 

4.364506 

2.257828 

3.044105 

3.718382 

81 

82 

3.025515 

3.665013 

4.236659 

2.213264 

2.966531 

3.615073 

82 

83 

2.937626 

3.551869 

4.101090 

2.161473 

2.882198 

3.504585 

83 

84 

2.842579 

3.430916 

3.957006 

2.102795 

2.790560 

3.386216 

84 

85 

2.739553 

3.301306 

3.803473 

2.035563 

2.690804 

3.259121 

85 

86 

2.627829 

3.162055 

3.639382 

1.959073 

2.582237 

3.122326 

86 

87 

2.506618 

3.011926 

3.463394 

1.873785 

2.464111 

2.974596 

87 

88 

2.374659 

2.849271 

3.273885 

1.776042 

2.335189 

2.814272 

88 

89 

2.231318 

2.671920 

3.068950 

1.684756 

2.194950 

2.639158 

89 

90 

2.068146 

2.476349 

2.846493 

1.571385 

2.034496 

2.445625 

90 

91 

1.882579 

2.261210 

2.605074 

1.424280 

1.851228 

2.232352 

91 

92 

1.676910 

2.025995 

2.343028 

1.254844 

1.647691 

1.998920 

92 

93 

1.449591 

1.768228 

2.057433 

1.065143 

1.422413 

1.742883 

93 

94 

1.196422 

1.484119 

1.744248 

0.848650 

1.171168 

1.460461 

94 

95 

0.914003 

1.169334 

1.398060 

0.600135 

0.890611 

1.147368 

95 

96 

0.600135 

0.817223 

1.010237 

0.334573 

0.578765 

0.797033 

96 

97 

0.231910 

0.412043 

0.565103 

1.997225 

0.212324 

0.393667 

97 

98 

1.821133 

1.942898 

0.037892 

1.632205 

1.804059 

1.926863 

98 

99 

1.331175 

1.331175 

1.331175 

1.318338 

1.318338 

1.318338' 

99 

♦18 


TABLE    XXXIY. 

C50MMUTATI0N  COLUMNS.         3^  PER  CENT. 


— 

AGE.    Da;. 

Na.. 

S.. 

Cx. 

M^. 

Ra>. 

AOE. 

10  1  70,892.0 

1,601,484.9 

31,058,393.9 

443.845 

16,735.405 

551,200.709 

10 

11  68,050.8 

1,530,592.9 

29,456,909.0 

427.512 

16,291.560 

534,465.304 

11 

12  65,332.1 

1,462,542.1 

27,926,316.1 

411.138 

15,864.048 

518,173.744 

12 

13  1  62,701.9 

1,397,220.0 

26,463,774.0 

395.998 

15,452.910 

502,309.696 

13 

14  60,185.5 

1,334,518.1 

25,066,554.0 

382.010 

15,056.912 

486,856.786 

14 

15  1  57,768.4 

1,274,332.6 

23,732,035.9 

367.938 

14,674.902 

471,799.874 

15 

16 

55,446.7 

1,216,564.2 

22,457,703.3 

354.382 

14,306.964 

457,124.972 

16 

17 

53,217.4 

1,161,117.5 

21,241,139.1 

341.859 

13,952.582 

442,818.008 

17 

18 

51,076.0 

1,107,900.1 

20,080,021.6  ' 

329.779 

13,610.723  428,865.426 

18 

19 

49,019.0 

1,056,824.1 

18,972,121.5  ; 

318.124 

13,280.944  i  415,254.703 

19 

20 

47,043.2 

1,007,805.1 

17,915,297.4 

307.366 

12,962.820  401,973.759 

20 

21 

45,145.0 

960,761.9 

16,907,492.3  i  296.972 

12,655.454  |  389,010.939 

21 

22 

43,321.3 

915,616.9 

15,946,730.4  !  286.930 

12,358.482  :  376,355.485 

22 

23 

41,569.4 

872,295.6 

15,031,113.5 

277.665 

12,071.552  i  363,997.003 

23 

24 

39,886.1 

830,726.2 

14,158,817.9 

268.698 

11,793.887  1  351,925.451 

24 

25 

38,268.6 

790,840.1 

13,328,091.7 

260.021 

11,525.189  i  340,131.564 

25 

26 

36,714.5 

752,571.5 

12,537,251.6 

252.413 

11,265.168  328,606.375 

26 

27 

35,220.5 

715.857.0 

11,784,680.1  1 

244.640 

11,012.755  !  317,341.207  |  27 

28 

33,784.8 

680,636.5 

11,068,823.1  : 

237.474 

10,768.115  306,328.452  1  28 

29 

32,404.8 

646,851.7 

10,388,186.6 

231.225 

10,530.641  295,560.337  j  29 

30 

31,077.8 

614,446.9 

9,741,334.9 

224.782 

10,299.416  285,029.696 

30 

31 

29,802.1 

583.369.1 

9,126,888.0 

218.844 

10,074.634'  274,730.280 

31 

32  ;  28,575.4 

553,567.0 

8,543,518.9 

213.372 

9,855.790  ;  264,655.646  i  32  1 

33  !  27,395.8 

524,991.6 

7,989,951.9 

208.330 

9,642.418  i  254,799.856  i  33  | 

34 

26,261.0 

497,595.8 

7,464,960.3  , 

203.684 

9,434.088 

245,157.438  34 

35 

25,169.3 

471,334.8 

6,967,364.5 

199.695 

9,230.404 

235,723.350  j  35 

36 

24,118.4 

446,165.5 

6,496,029.7 

195.462 

9,030.709  1  226,492.946  i  36 

37  !  23,107.3 

422,047.1 

6,049,864.2 

191.828 

8,835.247  i  217,462.237  i  37 

38 

22,134.2 

398,939.8 

5,627,817.1 

188.740 

8,643.419  :  208,626.990  38 

39 

21,196.9 

376,805.6 

5,228,877.3 

185.893 

8,454.679 

199,983.^71  39 

40 

20,294.2 

355,608.7 

4,852,071.7 

183.512 

8,268.786 

191,528.892  40 

41 

19,424.4 

335,314.5 

4,496,463.0 

181.078 

8,085.274 

183,260.106  i  41 

42 

18,586.5 

315,890.1 

4,161,148.5 

179.511 

7,904.19C  i  175,174.832  42  | 

43  !  17,778.4 

297,303.6 

3,845,258.4 

177.843 

7,724.685 

167,270.636  :  43 

44 

16,999.4 

279,525.2 

3,547,954.8 

176.720 

7,546.842 

159,545.951  44 

45 

16,247.8 

262,525.8 

3,268,429.6 

175.881 

7,370.122 

151,999.109  1  45 

46 

15,522.5 

246,278.0 

3,005,903.8 

175.293 

7,194.241 

144,628.987  ^  46 

47 

14,822.3 

230,755.5 

2,759,625.8 

175.119 

7,018.948 

137,434.746  :  47 

48 

14,145.9 

215,933.2 

2,528,870.3 

175.128 

6,843.829 

130,415.798  i  48 

49 

13,492.4 

201,787.3 

2,312,937.1 

175.473 

6,668.701 

'  123,571.969  1  49 

50 

12,860.7 

188,294.9 

2,111,149.8 

176.112 

6,493.228 

116,903.268  !  50 

51 

12,249.7 

175,434.2 

1,922,854.9 

177.010 

6,317.116 

110,410.040  '  51 

52 

11,658.4 

163,184.5 

1,747,420.7 

178.130 

6.140.106 

104,092.924  52 

53 

11,086.1 

151,526.1 

1,584,236.2 

179.440 

5,961.976 

97,952.818  53 

54 

10,531.7 

140,440.0 

1,432.710.1 

180.910 

5,782.536 

91,990.842  54 

1 

'19 


TABLE  XXXIY. 

C50MMUTATI0N  COLUMNS.    3^  PER  CENT. 

AQB. 

D,, 

N:.. 

Sx. 

Cx 

Mx. 

^ 

65 

55 

9,994.66 

129,908.28 

1,292,270.07 

182.803 

5,601.626 

86,208.306  ' 

56 

9,473.86 

119,913.62 

1,162,361.79 

184.644 

5,418,823 

80,606.680 

56 

57 

8,968.85 

110,439.70 

1,042,448.17 

186.830 

5,234.179 

75,187.857 

57 

58 

8,478.73 

101,470.91 

932,008.41 

188.920 

5,047.349 

69,953.678 

58 

59 

8,803.10 

92,992.18 

830,537.50 

191.036 

4,858.429 

64,906.329 

59 

60 

7,541.42 

84.989.08 

737,545.32 

193.284 

4,667.393 

60,047.900 

60 

61 

7,093.12 

77,447.66 

652,556.24 

195.516 

4,474.109 

55,380.507 

61 

62 

6,657.73 

70,354.54 

575,108.58 

197.491 

4,278.593 

50,906.398 

62 

63 

6,235.11 

63,696.81 

504,754.04 

199.440 

4,081.102 

46,627.805 

63 

64 

5,824.80 

57,461.70 

441,057.23 

201.139 

3,881.662 

42,546.703 

64 

65 

5,426.69 

51,636.90 

383,595.53 

202.598 

3,680.523 

38,665.041 

65 

66 

5,040.59 

46,210.21 

331,958.63 

203.529 

3,477.925 

34,984.518 

66 

67 

4,666.62 

41,169.62 

285,748.42 

204.165 

3,274.396 

31,506.593 

67 

68 

4,304.63 

36,503.00 

244,578.80 

203.967 

3,070.231 

28,232.197 

68 

69 

3,955.10 

32,198.37 

208,075.80 

1  203.459 

1 

2,866.264 

25,161.966 

69 

70 

3.617.90 

28,243.27 

175,877.43 

!  201.969 

2,662.805 

22,295.702 

70 

71  13,293.58 

24,625.37 

147,634.16 

i  199.759 

2,460.836 

19,632.897 

71 

72 

2,982.44 

21,331.79 

123,008.79 

196.575 

2,261.077 

17,172.061 

72 

73 

2,685.02 

18,349.35 

101,677.00 

i  192.359 

2,064.502 

14,910.984 

73 

74 

2,401.86 

15, 664.  .33 

83,327.65 

i  187.293 

1,872.143 

12,846.482 

74 

75 

2,133.34 

13,262.47 

67,663.32 

!  180.960 

1,684.850 

10,974.339 

75 

76 

1,880.24 

11,129.13 

54,400.85 

1  173.496 

1,503.890 

9,289.489 

76 

77 

1,643.16 

9,248.89 

43,271.72 

165.101 

1,330.394 

7,785.599 

77 

78 

1,422.49 

7,605.73 

34,022.83 

155.556 

1,165.293 

6,455.205 

78 

79 

1,218.832 

6,183.245 

26,417.108 

!  145.065 

! 

1,009.737 

5,289.912 

79 

80 

1,032.552 

4,964.413 

20,233.863 

'  133.749 

864.672 

4,280.175 

80 

81 

863.885 

3.931.861 

15,269.450 

121.723 

730.923 

3,415.503 

81 

82 

712.948 

3,067.976 

11,337.589 

109.321 

609.200 

2,684.580 

82 

83 

579.518 

2,355.028 

8,269.613 

96.5629 

499.8792 

2,075.3797 

83 

84 

463.358 

1,775.510 

5,914.585 

83.9517 

403.3163 

1,575.5005 

84 

85 

363.737 

1,312.152 

4,139.075 

1  71.5639 

319.3646 

1,172.1842 

85 

86 

279.872 

948.415 

2,826.923 

59.7175 

247.8007 

852.8196 

86 

87 

210.691 

668.543 

1,878.508 

48.8326 

188.0832 

605.0189 

87 

88 

154.733 

457.852 

1,209.965 

38.8028 

139.2506 

416.9357 

88 

89 

110.698 

303.119 

752.113 

31.2950 

100.4478 

277.6851 

89 

90 

75.6598 

192.4206 

448.9945 

23.9884 

.69.1528 

177.2373 

90 

91 

49.1127 

116.7608 

256.5739 

17.0135 

45.1644 

108.0845 

91 

92 

30.4385 

67.6481 

139.8131 

1  11.4618 

28.1509 

62.9201 

92 

93 

17.9474 

37.2096 

72.1650 

!   7.36969 

16.68907 

34.76921 

93 

94 

9.97075 

19.26219 

34.95535 

1   4.45506 

9.31938 

18.08014 

94 

95 

5.17852 

9.29144 

15.69316 

'     2.50170 

4.86432 

8.76076 

95 

96 

2.50170 

4.11292 

6.40172 

i  1.35074 

2.36262 

3.89644 

96 

97 

1.06637 

1.61122 

2.28880 

\       .618184 

1.011883 

1.533823 

97 

1  98  \   .413123 

.544852 

.677581 

!   .265458 

.393699 

.521940 

98 

1  aft-  '   .132729 

.132729 

.132729 

.128241 

.128241 

.128241 

99 

*ao 


TABLE    XXXIY. 

LOGARITHMS  OF  COMMUTATION  COLUMNS.         3|-  PER  CENT. 


AQE. 
10 

ADa;. 

ANa,. 

ASa,. 

AC^. 

AMa:. 

AR-c. 

AGE. 
10 

4.850597 

6.204523 

7.492179 

2.647231 

4.223636 

5.741310 

11 

4.832833 

6.184860 

7.469187 

2.630948 

4.211963 

5.727919 

11 

12 

4.815060 

6.165108 

7.446014 

2.6L3987 

4.200414 

5.714475 

12 

13 

4.797281 

6.145265 

7.422652 

2.597693 

4.189010 

5.700972 

13 

14 

4.779492 

6.125324 

7.399095 

2.582075 

4.177736 

5.687401 

14 

15 

4.761690 

6.105283 

7.375335 

2.565775 

4.166575 

5.673758 

15 

16 

4.743876 

6.085135 

7.351365 

2.549471 

4.155547 

5.660035 

16 

17 

4.726054 

6.064876 

7.327178 

2.533847 

4.144655 

5.646225 

17 

18 

4.708217 

6.044501 

7.302764 

2.518223 

4.133881 

5.632321 

18 

19 

4.690364 

6.024002 

7.278116 

2.502597 

4.123229 

5.618315 

19 

20 

4.672497 

6.003376 

7.253224 

2.487656 

4.112700 

5.604198 

20 

21 

4.654610 

5.982616 

7.228079 

2.472716 

4.102278 

5.589962 

21 

22 

4.636702 

5.961714 

7.202672 

2.457776 

4.091966 

5.575598 

22 

23 

4.618774 

5.940664 

7.176991 

2.443521 

4.081763 

5.561097 

23 

24 

4.600822 

5.919458 

7.151027 

2.429265 

4.071658 

5.546451 

24 

25 

4.582842 

5.898089 

7.124768 

2.415008 

4.061648 

5.531647 

25 

26 

4.564837 

5.876548 

7.098202 

2.402111 

4.051738 

5.516676 

26 

27 

4.546796 

5.854826 

7.071318 

2.388528 

4.041896 

5.501527 

27 

28 

4.528721 

5.832915 

7.044101 

2.375616 

4.032140 

5.486188 

28 

29 

4.510609 

5.810805 

7.016540 

2.364034 

4.022454 

5.470646 

29 

30 

4.492450 

5.788484 

6.988618 

2.351762 

4.012812 

5.454891 

30 

31 

4.474247 

5.765943 

6.960323 

2.340135 

4.003229 

5.438906 

31 

32 

4.455993 

5.743170 

6.931637 

2.329137 

3.993692 

5.422681 

32 

33 

4.437684 

5.720152 

6.902544 

2.318750 

3.984186 

5.406199 

33 

34 

4.419311 

5.696877 

6.873028 

2.308958 

3.974700 

5.389445 

34 

35 

4.400871 

5.673330 

6.843068 

2.300367 

3.965221 

5.372402 

35 

36 

4.382349 

5.649496 

6.812648 

2.291063 

3.955722 

5.355055 

36 

37 

4.363750 

5.625361 

6.781746 

2.282913 

3.946219 

5.337383 

37 

38 

4.345063 

5.600907 

6.750340 

2.275864 

3.936686 

5.319371 

38 

39 

4.326272 

5.576117 

6.718409 

2.269264 

3.927097 

5.300994 

39 

40 

4.307372 

5.550972 

6.685927 

2.263664 

3.917442 

5.282234 

40 

41 

4.288348 

5.525452 

6.652871 

2.257866 

3.907695 

5.263068 

41 

42 

4.269197 

5.499536 

6.619213 

2.254091 

3.897858 

5.243472 

42 

43 

4.249893 

5.473200 

6.584925 

•  2.250036 

3.887881 

5.223420 

43 

44 

4.230434 

5.446421 

6.549978 

2.247285 

3.877765 

5.202886 

44 

45 

4.210794 

5.419172 

6.514339 

2.245218 

3.867475 

5.181841 

45 

46 

4.190961 

5.391426 

6.477975 

2.243764 

3.856985 

5.160255 

46 

47 

4.170915 

5.363152 

6.440850 

2.243334 

3.846272 

5.138097 

47 

48 

4.150631 

5.334319 

6.402927 

2.243355 

3.835299 

5.115330 

48 

49 

4.130090 

5.304894 

6.364164 

2.244209 

3.824041 

5.091920 

49 

50 

4.109265 

5.274839 

6.324519 

2.245790 

3.812461 

5.067827 

50 

51 

4.088124 

6.244114 

6.283946 

2.247998 

3.800519 

5.043008 

51 

52 

4.066640 

5.212679 

6.242398 

2.250737 

3.788176 

5.017421 

52 

53 

4.044777 

5.180487 

6.199820 

2.253919 

3.775391 

4.991017 

53 

54 

4.022499 

6.147491 

6.156158 

2.257462 

3-.  762119 

4.963744 

54 

*21 


TABLE    XXXIY. 

LOGARITHMS  OP  COMMUTATION  COLUMNS.         3|-  PER  CENT. 


A&E. 

ADa,. 

ANa,. 

XSx 

AOa;. 

AM«,. 

AR^. 

1 
AGE. 

55 

55 

3.999768 

5.113637 

6.111353 

2.261984 

3.748314 

4.935550 

56 

3.976527 

5.078868 

6.065341 

2.266334 

3.733905 

4.906371 

56 

57 

3.952737 

5.043126 

6.018055 

2.271446 

3.718849 

4.876148 

57 

58 

3.928331 

5.006342 

5.969420 

2.276278 

3.703063 

4.844811 

58 

59 

3.903258 

4.968446 

5.919359 

2.281116 

3.686496 

4.812287 

59 

60 

3.877453 

4.929363 

5.867789 

2.286195 

3.669074 

4.778498 

60 

61 

3.850837 

4.889008 

5.814618 

2.291182 

3.650707 

4.743357 

61 

62 

3.823326 

4.847292 

5.759750 

2.295547 

?.  631301 

4.706773 

62 

63 

3.794844 

4.804118 

5.703080 

2.299813 

3.610777 

4.668645 

63 

64 

3.765281 

4.759379 

5.644495 

2.303497 

3.589018 

4.628866 

64 

65 

3.734535 

4.712960 

5.583873 

2.306636 

3.565909 

4.587318 

65 

66 

3.702481 

4.664738 

5.521084 

2.308627 

3.541321 

4.543876 

66 

67 

3.669002 

4.614577 

5.455984 

2.309982 

3.515132 

4.498401 

67 

68 

3.633936 

4.562329 

5.388419 

2.309560 

3.487171 

4.450745 

68 

69 

3.597157 

4.507834 

5.318222 

2.308476 

3.457316 

4.400744 

69 

70 

3.558456 

4.450915 

5.245210 

2.305284 

3.425340 

4.348221 

70 

71 

3.517668 

4.391383 

5.169187 

2.300507 

3.391083 

4.292985 

71 

72 

3.474572 

4.329027 

5.089936 

2.293529 

3.354316 

4.234823 

72 

73 

3.428947 

4.263620 

5.007223 

2.284112 

3.314815 

4.173506 

73 

74 

3.380547 

4.194912 

4.920789 

2.272522 

3.272338 

4.108784 

74 

75 

3.329060 

4.122625 

4.830353 

2.257582 

3.226561 

4.040379 

75 

76 

3.274213 

4.046461 

4.735606 

2.239291 

3.177216 

3.967992 

76 

77 

3.215680 

3.966090 

4.636204 

2.217750 

3.123979 

3.891292 

77 

78 

3.153050 

3.881141 

4.531770 

2.191888 

3.066434 

3.809910 

78 

79 

3.085944 

3.791316 

4.421885 

2.161563 

3.004208 

3.733448 

79 

80 

3.013912 

3.695868 

4.306079 

2.126291 

2.936850 

3.631462 

80 

81 

2.936456 

3.594598 

4.183823 

2.085372 

2.863872 

3.533454 

81 

82 

2.853058 

3.486852 

4.054521 

2.038705 

2.784760 

3.428877 

82 

83 

2.763067 

3.371996 

3.917485 

1.984810 

2.698865 

3.317098 

83 

84 

2.665917 

3.249323 

3.771924 

1.924029 

2.605646 

3.197418 

84 

85 

2.560787 

3.117984 

3.616903 

1.854694 

2.504287 

3.068996 

85 

86 

2.446960 

2.976999 

3.451314 

1.776101 

2.394103 

2.930857 

86 

87 

2.323646 

2.825129 

3.273813 

1.688710 

2.274350 

2.781769 

87 

88 

2.189584 

2.660725 

3.082773 

1.588863 

2.143798 

2.630069 

88 

89 

2.044140 

2.481613 

2.876283 

1.495475 

2.001940 

2.443553 

89 

90 

1.878865 

2.284251 

2.652241 

1.380000 

1.839811 

2.248555 

90 

91 

1.691194 

2.067297 

2.409213 

1.230793 

1.654796 

2.033763 

91 

92 

1.483423 

1.830256 

2.145548 

1.059254 

1.449492 

1.798790 

92 

93 

1.254001 

1.570655 

1.858327 

0.867449 

1.222433 

1.541195 

93 

94 

0.998728 

1.284706 

1.543513 

0.648853 

0.969388 

1.257201 

94 

95 

0.714206 

0.968083 

1.195710 

0.398235 

0.687022 

0.942542 

95 

96 

0.398235 

0.614150 

0.806297 

0.130570 

0.373394 

0.590668 

96 

97 

0.027907 

0.207154 

0.359608 

1.791118 

0.005129 

0.185775 

97 

98 

1.615027 

1.736279 

1.830961 

1.423995 

1.595164 

1.717621 

98 

99 

1.122965 

1.122965 

1.122965 

1.108025 

1.108025 

1.108025 

99 

*22 


TABLE    XXXY. 

COMMUTATION  COLUMNS.         4  PER  CENT. 


A&E. 

D.. 

N^. 

S.. 

Co.. 

M^. 

K.. 

AQE. 

10 

10 

67,556.5 

1,400,554.9 

25,570,207.5 

420.929 

13,688.944 

417,085.094 

11 

64,537.2 

1,332,998.4 

24,169,652.6 

403.490 

13,268.015 

403,396.150 

11 

12 

61,651.5 

1,268,461.2 

22,836,654.2 

386.169 

12,864.525 

390,128.135 

12 

13 

58,894.1 

1,206,809.7 

21,568,193.0 

370.161 

12,478.356 

377,263.610 

13 

14 

56,258.7 

1,147,915.6 

20,361,383.3 

355.369 

12,108.195 

364,785.254 

14 

15 

53,739.7 

1,091,656.9 

19,213,467.7 

340.634 

11,752.826 

352,677.059 

15 

16 

51,332.1 

1,037,917.2 

18,121,810.8 

;  326.505 

11,412.192 

340.924.233 

16 

17 

49,031.3 

986,585.1 

17,083,893.6 

313.454 

11,085.687 

329,512.041 

17 

18 

46,832.0 

937,553.8 

16,097,308.5 

300.923 

10,772.233 

318,426.354 

18 

19 

44,729.9 

890,721.8 

15,159,754.6 

288.893 

10,471.310 

307,654.121 

19 

20 

42,720.6 

845,991.9 

14,269,032.8 

277.782 

10,182.417 

297,182.811 

20 

21 

40,799.7 

803,271.3 

13,423,040.9 

267.098 

9,904.635 

287,000.394 

21 

22 

38,963.4 

762,471.6 

12,619,769.6 

256.825 

9,637.537 

277,095.759 

22 

23 

37,207.9 

723,508.2 

11,857,298.0 

247.337 

9,380.712 

267,458.222 

23 

24 

35,529.6 

686,300.3 

11,133,789.8 

238.199 

9,133.375 

258,077.510 

24 

25 

33,924.9 

650,770.7 

10,447,489.5 

229.398 

8,895.176 

248,944,135 

25 

26 

32,390.6 

616,845.8 

9,796,718.8 

221.616 

8,665.778 

240,048.959 

26 

27 

30,923.2 

584,455.2 

9,179,873.0 

213.759 

8,444.162 

231,383.181 

27 

28 

29,520.1 

553,533.0 

8,595,417.8 

206.499 

8,230.403 

222,939.019 

28 

29 

28,178.2 

524,011.9 

8,041,885.8 

200.099 

8,023.904 

214,708.616 

29 

30 

26,894.3 

495,833.7 

7,517,873.9 

193.589 

7,823.805 

206,684.712 

30 

31 

25,666.4 

468,939.4 

7,022,040.2 

187.568 

7,630.216 

198,860.907 

31 

32 

24,491.6 

443,273.0 

6,553,100.8 

181.999 

7,442.648 

191,2.30.691 

32 

33 

23,367.6 

418,781.4 

6,109,827.8 

176.843 

7,260.649 

183,788.043 

33 

34 

22,292.1 

395,413.8 

5,691,046.4 

172.069 

7,083.806 

176,527.394 

34 

35 

21,262.6 

373,121.7 

5,295,632.6 

167.888 

6,911.737 

169,443.588 

35 

36 

20,276.9 

351,859.1 

4,922,510.9 

163.539 

6,743.849 

162,531.851 

36 

37 

19,333.4 

331,582.2 

4,570,651.8 

159.727 

6,580.310 

155,788.002 

37 

38 

18,430.2 

312,248.8 

4,239,069.6 

156.400 

6,420.583 

149,207.692 

38 

39 

17,564.9 

293,818.6 

3,926,820.8 

153.301 

6,264.183 

142,787.109 

39 

40 

16,736.0 

276,253.7 

3,633,002.2 

150.609 

6,110.882 

136,522.926 

40 

41 

15,941.7 

259,517.7 

3,356,748.5 

147.898 

5,960.273 

130,412.044 

41 

42 

15,180.7 

243,576.0 

3,097,230.8 

145.913 

5,812.375 

124,451.771 

42 

43 

14,450.9 

228,395.3 

2,853,654.8 

143.862 

5,666.462 

118,639.396 

43 

44 

13,751.2 

213,944.4 

2,625,259.5 

142.266 

5,522.600 

112,972.934 

44 

45 

13,080.1 

200,193.2 

2,411,315.1 

140.909 

5,380.334 

107,450.334 

45 

46 

12,4.36.1 

187,113.1 

2,211,121.9 

139.764 

5,239.425 

102,070.000 

46 

47 

11,818.0 

174,677.0 

2,024,008.8 

138.954 

5,099.661 

96,830.575 

47 

48 

11,224.5 

162,859.0 

1,849,331.8 

138.292 

4,960.707 

91,730.914 

48 

49 

10,654.5 

151,634.5 

1,686,472.8 

137.898 

4,822.415 

86,770.207 

49 

50 

10,106.8 

140,979.99 

1,534,838.27 

137.736 

4,684.517 

81,947.792 

50 

51 

9,580.36 

130,873.19 

1,393,858.28 

137.773 

4,546.781 

77,263.275 

51 

52 

9,074.11 

121.292.83 

1,262,985.09 

137.978 

4,409.008 

72,716.494 

52 

53 

8,587.13 

112,218.72 

1,141,-692.26 

138.324 

4,271.030 

68,307.486 

53 

54 

8,118.54 

103,631.59 

1,029,473.541 

138.787 

4,132.706 

64,036.456 

54 

•   1 

TABLE    XXXY. 

COMMUTATION  COLUMNS.         4  PER  CENT. 


♦23 


AGE. 

55 

Do, 

N.. 

Sa.. 

0^. 

Ma,. 

K«. 

AGE. 

7,667.49 

95,513.05 

925,841.95 

139.565 

3,993.919 

59,903.750 

55 

56 

7,233.03 

87,845.56 

830,328.90 

140.292 

3,854.354 

55,909.831 

56 

57 

6,814.55 

80,612.53 

'  742,483.34 

141.271 

3,714.062 

52,055.477 

57 

58 

6,411.17 

73,797.98 

661,870.81 

142.165 

3,572.791 

48,341.415 

58 

59 

6,022.43 

67,386.81 

588,072.83 

143.066 

3,430.626 

44,768.624 

59 

60 

5,647.73 

61,364.38 

520,686.02 

144.053 

3,287.560 

41,337.998 

60 

61 

5,286.45 

55,716.65 

459,321.64 

145.016 

3,143.507 

38,050.438 

61 

62 

4,938.11 

50,430.20 

403,604.99 

145.777 

2,998.491 

34,906.931 

62 

63 

4,602.42 

45,492.09 

353,174.79 

146.508 

2,852.714 

31,908.440 

63 

64 

4,278.88 

40,889.67 

307,682.70 

147.046 

2,706.206 

29,055.726 

64 

65 

3,967.26 

36,610.79 

266,793.03 

147.400 

2,559.160 

26,349.520 

65 

66 

3,667.28 

32,643.53 

230,182.24 

147.366 

2,411.760 

23,790.360 

66 

67 

3,378.87 

28,976.25 

197,538.71 

147.116 

2,264.394 

21,378.600 

67 

68 

3,101.79 

25,597.38 

168,562.46 

146.266 

2,117.278 

19,114.206 

68 

69 

2,836.23 

22,495.59. 

142,965.08 

145.200 

1,971.012 

16,996.928 

69 

70 

2,581.94 

19,659.36 

120,469.49 

143.444 

1,825.812 

15,025.916 

70 

71 

2,339.19 

17,077.42 

100,810.13 

141.193 

1,682.368 

13,200.104 

71 

72 

2,108.03 

14,738.23 

83,732.71 

138.274 

1,541.175 

11,517.736 

72 

73 

1,888.68 

12,630.20 

68,994.48 

134.657 

1,402.901 

9,976.561 

73 

74 

1,681.38 

10,741.52 

56,364.28 

130.481 

1,268.244 

8,573.660 

74 

75 

1,486.23 

9,060.14 

45,622,76 

125.463 

1,137.763 

7,305.416 

75 

76 

1,303.60 

7,573.91 

36,562.62 

119.710 

1,012.300 

6,167.653 

76 

77 

1,133.76 

6,270.31 

28,988.71 

113.369 

892.590 

5,155.353 

77 

78 

976.78 

5,136.55 

22,718.40 

106.302 

779.221 

4,262.763 

78 

79 

832.910 

4,159.77 

17,581.85 

98.6560 

672.9185 

3,483.5424 

79 

80 

702.220 

3,326.861 

13,422.083 

90.5231 

574.2625 

2,810.6239 

80 

81 

584.688 

2,624.641 

10,095.222 

81.9874 

483.7394 

2,236.3614 

81 

82 

480.212 

2,039.953 

7,470.581 

73.2802 

401.7520 

1,752.6220 

82 

83 

388.462 

1,559.741 

5,430.628 

64.4168 

328.4718 

1,350.8700 

83 

84 

309.105 

1,171.279 

3,870.887 

55.7346 

264.0550 

1,022.3982 

84 

85 

241.481 

862.174 

2,690.608 

47.2821 

208.3204 

758.3432 

85 

86 

184.911 

620.693 

1,837.434 

39.2655 

161.0383 

550.0228 

86 

87 

138.534 

435.782 

1,216.741 

31.9541 

121.7728 

388.9845 

87 

88 

101.251 

297.248 

780.959 

25.2689 

89.8187 

267.2117 

88 

89 

72.088 

195.997 

483.711 

20.2818 

64.5498 

177.3930 

89 

90 

49.0339 

123.9092 

287.7138 

15.4717 

44.2680 

112.8432 

90 

91 

31.6761 

74.8754 

163.8046 

10.9204 

28.7963 

68.5752 

91  1 

92 

19.5375 

43.1993 

88.9292 

7.32159 

17.87594 

39.77885 

92 

93 

11.4644 

23.6618 

45.7299 

4.68498 

10.55435 

21.90291 

93 

94 

6.3385 

12.1974 

22.0681 

2.81850 

5.86937 

11.34856 

94 

95 

3.27621 

5.85884 

9.87072 

1.57510 

3.05087 

5.47919 

95 

96 

1.57510 

2.58263 

4.01188 

.846350 

1.475769 

2.428324 

96 

97 

.668170 

1.00753 

1.42925 

.385483 

.629419 

.952555 

97 

98 

.256988 

.339356 

.421724 

.164736 

.243936 

.323136 

98 

99 

.082368 

.082368 

.082368 

.079200 

.079200 

.079200 

99 

*24 


TABLE     XXXY 


LOGARITHMS  OF  COMMUTATION  COLUMNS.        4  PER  CENT. 


AGE. 

AD„. 

ANo,. 

ASa,- 

aLix- 

AM». 

AEa, 

AGE. 

10 

4.829667 

6.146300 

7.407734 

i  2.624208 

4.136370 

5.620225 

10 

11 

4.809810 

6.124829 

7.383270 

2.605832 

4.122806 

5.605732 

11 

12 

4.789944 

6.103277 

7.358632 

2.586777 

4.109394 

5.591207 

12 

13 

4.770072 

6.081639 

7.333814 

2.568391 

4.096158 

5.576645 

13 

14 

4.750190 

6.059910 

7.308807 

2.550679 

4.083080 

5.562037 

14 

15 

4.730295 

6.038086 

7.283606 

2.532287 

4.070142 

5.547377 

15 

16 

4.710389 

6.016162 

7.258202 

2.513890 

4.057369 

5.532658 

16 

17 

4.690473 

5.994135 

7.232587 

2.496174 

4.044763 

5.517871 

17 

18 

4.670543 

5.971996 

7.206756 

2.478456 

4.032306 

5.503009 

18 

19 

4.650598 

5.949742 

7.180692 

2.460737 

4.020001 

5.488063 

19 

20 

4.630637 

5.927366 

7.154394 

2.443704 

4.007850 

5.473024 

20 

21 

4.610657 

5.904862 

7.127851 

2.426670 

3.995839 

5.457883 

21 

22 

4.590657 

5.882224 

7.101051 

2.409637 

3.983966 

5.442630 

22 

23 

4.570635 

5.859443 

7.073985 

2.393289 

3.972236 

5.427256 

23 

24 

4.550590 

5.836514 

7.046643 

2.376940 

3.960632 

5.411750 

24 

25 

4.530518 

5.813428 

7.019012 

2.360590 

3.949155 

5.396102 

25 

26 

4.510419 

5.790177 

6.991081 

2.345601 

3.937808 

5.380300 

26 

27 

4.490285 

5.766751 

6.962837 

2.329925 

3.926557 

5.364332 

27 

28 

4.470118 

5.743143 

6.934267 

2.314919 

3.915421 

5.348186 

28 

29 

4.449913 

5.719341 

6.905358 

2.301245 

3.904386 

5.331849 

29 

30 

4.429661 

5.695336 

6.876095 

2.286880 

3.893418 

5.315308 

30 

31 

4.409365 

5.671117 

6.846463 

2.273159 

3.882537 

5.298549 

31 

32 

4.389017 

5.646671 

6.816447 

2.260068 

3.871728 

5.281558 

32 

33 

4.368615 

5.621987 

6.786029 

2.247589 

3.860976 

5.264317 

33 

34 

4.348150 

5.597052 

6.755192 

2.235703 

3.850267 

5.246812 

34 

35 

4.327616 

5.571850 

6.723918 

2.225019 

3.839587' 

5.229025 

35 

36 

4.307002 

5.546369 

6.692187 

2.213622 

3.828908 

5.210938 

36 

37 

4.286309 

5.520591 

6.659978 

2.203379 

3.818246 

5.192534 

37 

38 

4.265529 

5.494501 

6.627271 

2.194237 

3.807574 

5.173791 

38 

39 

4.244646 

5.468079 

6.594041 

2.185544 

3.796864 

5.154689 

39 

40 

4.223652 

5.441308 

6.560266 

2.177851 

3.786104 

5.135206 

40 

41 

4.202535 

5..414167 

6.525919 

2.169961 

3.775266 

5.115321 

41 

42 

4.181292 

5.386634 

6.490974 

2.164093 

3.764354 

5.095001 

42 

43 

4.159894 

5:358687 

6.455401 

2.157945 

3.753312 

5.074229 

43 

44 

4.138342 

5.330301 

6.419172 

2.153101 

3.742144 

5.052974 

44 

45 

4.116610 

5.301449 

6.382254 

2.148940 

3.730809 

5.031208 

45 

46 

4.094683 

5.272104 

6.344613 

2.145394 

3.719284 

5.008898 

46 

47 

4.072544 

5.242236 

6.306212 

2.142871 

3.707541 

4.986013 

47 

48 

4.050168 

5.211812 

6.267015  • 

2.140798 

3.695544 

4.962516 

48 

49 

4.027533 

5.180798 

6.226979 

2.139559 

3.683265 

4.938371 

49 

50 

4.004615 

5.149157 

6.186062 

2.139048 

3.670665 

4.913537 

50 

51 

3.981382 

5.116851 

6.144219 

2.139162 

3.657704 

4.887973 

51 

52 

3.957804 

5.083835 

6.101398 

2.139809 

3.644341 

4.861633 

52 

53 

3.933848 

5.050065 

6.057549 

2.140898 

3.630533 

4.834468 

53 

54 

3.909478 

5.015492 

6.012615 

2.142348 

3.616235 

4.806427 

54 

TABLE     XXXY. 

LOGARITHMS  OF  COMMUTATION  COLUMNS.        4  PER  CENT. 


*25 


AGE. 

55 

ADa,. 

AN«,. 

Ahx' 

AUa)' 

AM«,- 

A  Raj- 

AGE. 

3.884653 

4.980063 

5.966537 

2.144777 

3.601399 

4.777454 

55 

56 

3.859320 

4.943720 

5.919250 

2.147034 

3.585951 

4.747488 

56 

57 

3.833437 

4.906403 

5.870687 

2.150053 

3.569849 

4.716466 

57 

58 

3.806937 

4.868044 

5.820773 

2.152792 

3.553008 

4.684319 

58 

59 

3.779772 

4.828575 

5.769431 

2.155536 

3.535374 

4.650974 

59 

60 

3.751874 

4.787916 

5.716576 

2.158523 

3.516874 

4.616349 

60 

61 

3.723164 

4.745985 

5.662117 

2.161417 

3.497415 

4.580360 

61 

62 

3.693561 

4.702691 

5.605956 

2.163689 

3.476903 

4.542912 

62 

63 

3.662986 

4.657936 

5.547990 

2.165862 

3.455258. 

4.503906 

63 

64 

3.631330 

4.611614 

5.488103 

2.167453 

3.432362 

4.463232 

64 

65 

3.598491 

4.563609 

5.426174 

2.168499 

3.408097 

4.420773 

65 

66 

3. 534344 

4.513797 

5.362072 

2.168397 

3.382334 

4.376401 

66 

67 

3.528771 

4.462042 

5.295651 

2.167659 

3.354951 

4.329979 

67 

68 

3.491613 

4.408196 

5.226761 

2.165144 

3.325778 

4.281356 

68 

69 

3.452741 

4.352097 

5.155230 

2.161967 

3.294689 

4.230371 

69 

70 

3.411946 

4.293569 

5.080877 

2.156682  • 

3.261456 

4.176841 

70 

71 

3.369066 

4.232422 

5.003504 

2.149812 

3.225922 

4.120577 

71 

72 

3.323877 

4.168445 

4.922895 

2.140740 

3.187853 

4.061367 

72 

73 

3.276158 

4.101410 

4.838814 

2.129230 

3.147027 

3.998981 

73 

74 

3.225666 

4.031066 

4.751004 

2.115548 

3.103203 

3.933166 

74 

75 

3.172086 

3.957135 

4.659182 

2.098515 

3.056051 

3.863645 

75 

76 

3.115146 

3.879320 

4.563037 

2.078130 

3.005309 

3.790120 

76 

77 

3.054520 

3.797289 

4.462229 

2.054496 

2.950652 

3.712258 

77 

78 

2.989797 

3.710672 

4.356378 

2.026542 

2.891660 

3.629691 

78 

79 

2.920598 

3.61906& 

4.245065 

1.994123 

2.827963 

3.542021 

79 

80 

2.846473 

3.522035 

4.127820 

1.956759 

2.759111 

3.448803 

80 

81 

2.766924 

3.419070 

4.004116 

1.913747 

2. 6846] 1 

3.349542 

81 

82 

2.681433 

3.309620 

3.873354 

1.864986 

2.603958 

3.243688 

82 

83 

2.589349 

3.193052 

3.734850 

1.808999 

2.516498 

3.130614 

83 

84 

2.490106 

3.068660 

3.587811 

1.746125 

2.421694 

3.009620 

84 

85 

2.382883 

2.935595 

3.429850 

1.674697 

2.318731 

2.879866 

85 

86 

2.266963 

2.792877 

3.264212 

1.594011 

2.206928 

2.740381 

86 

87 

2.141556 

2.639269 

3.085198 

1.504527 

2.085551 

2.589932 

87 

88 

2.005401 

2.473119 

2.892628 

1.402587 

1.953368 

2.426855 

88 

89 

1.857863 

2.292249 

2.684587 

1.307105 

1.809896 

2.248936 

89 

90 

1.690496 

2.093104 

2.458961 

1.189538 

1.646090 

2.052475 

90 

91 

1.500732 

1.874339 

2.214326 

1.038238 

1.459332 

1.836167 

91 

92 

1.290868 

1.635477 

1.949044 

0.864606 

1.252269 

1.599652 

92 

93 

1.059352 

1.374048 

1.660200 

0.670708 

1.023431 

1.340502 

93 

94 

0.801987 

1.086267 

1.343765 

0.450019 

0.768591 

1.054941 

94 

95 

0.515372 

0.767812 

0.994349 

0.197308 

0.484424 

0.738716 

95 

96 

0.197308 

0.412062 

0.603348 

1.927550 

0.169018 

0.385307 

96 

97 

1.824887 

0.003258 

0.155108 

1.586005 

1.798940 

1.978890 

97 

98 

1.409913 

1.530656 

1.625028 

1.216789 

1.387276 

1.509385 

98 

99 

2.915759 

2.915759 

2.915759 

2.898726 

2.898726 

2.898726 

99 

♦36 


TABLE    XXXYI. 

COMMUTATION  COLUMNS.  4^  PER  CENT. 


A&E. 

D.. 

N«,. 

s.. 

a. 

M„. 

Ra;. 

AGE. 

10 

64,392.8 

1,232,047.6 

21,206,324.6 

399.297 

11,338.107 

318,856.514 

10 

11 

61,320.7 

1,167,654.8 

19,974,277.0 

380.923 

10,938.810 

307,518.407 

11 

12 

58,203.5 

1,106,434.1 

18,806,622.2 

362.827 

10,557.887 

296,579.597 

12 

13 

55,334.1 

1,048,230.6 

17,700,188.1 

346.123 

10,195.060 

286,021.710 

13 

14 

52,605.2 

992,896.5 

16,651,957.5 

330.701 

9,848.937 

275,826.650 

14 

15 

50,009.3 

940,291.3 

15,659,061.0 

315.471 

9,518.236 

265,977.713 

15 

16 

47,540.2 

890,282.0 

14,718,769.7 

300.940 

9,202.765 

256,459.477 

16 

17 

45,192.2 

842,741.8 

13,828,487.7 

287.528 

8,901.825 

247,256.712 

17 

18 

42,958.6 

797,549.6 

12,985,745.9 

274.714 

8,614.297 

238,354.887 

18 

19 

40,833.9 

754,591.0 

12,188,196.3 

262.469 

8,339.583 

229,740.590 

19 

20 

38,813.1 

713,757.1 

11,433,605.3 

251.166 

8,077.114 

221,401.007 

20 

21 

36,890.5 

674,944.0 

10,719,848.2 

240.351 

7,825.948 

213,323.893 

21 

22 

35,061.5 

638,053.5 

10,044,904.2 

230.001 

7,585.597 

205,497.945 

22 

23 

33,321.7 

602,992.0 

9,406,850.7 

220.444 

7,355.596 

197,912.348 

23 

24 

31,666.4 

569,670.3 

8,803,858.7 

211.284. 

7,135.152 

190,556.752 

24 

25 

30,091.5 

538,003.9 

8,234,188.4 

202.504 

6,923.868 

183,421.600 

25 

26 

28,593.2 

507,912.4 

7,696,184.5 

194.698 

6,721.364 

176,497.732 

26 

27 

27,167.2 

479,319.2 

7,188,272.1 

186.897 

6,526,666 

169,776.368 

27 

28 

25,810.4 

452,152.0 

6,708,952.9 

179.686 

6,339.769 

163,249.702 

28 

29 

24,519.3 

426,341.6 

6,256,800.9 

173.283 

6,160.083 

156,909.933 

29 

30 

23,290.1 

401,82^.3 

5,830,459.3 

166.843 

5,986.800 

150,749.850 

30 

31 

22,120.4 

378,532.2 

5,428,637.0 

160.881 

5,819.957 

144,763.050 

31 

32 

21,007.0 

356,411.8 

5,050,104.8 

155.357 

5,659.076 

138,943.093 

32 

33 

19,947.0 

335,404.8 

4,693,693.0 

150.234 

5,503.719 

133,284.017 

33 

34 

18,937.8 

315,457.8 

4,358,288.2 

145.479 

5,353.485 

127,780.298 

34 

35 

17,976.8 

296,520.0 

4,042,830.4 

141.264 

5,208.006 

122,426.813 

35 

36 

17,061.5 

278,543.2 

3,746,310.4 

136.947 

5,066.742 

117,218.807 

36 

37 

16,189.7 

261,481.7 

3,467,767.2 

133.115 

4,929.795 

112,152.065 

37 

38 

15,359.5 

245,292.0 

3,206,285.5 

129.719 

4,796.680 

107,222.270 

38 

39 

14,568.4 

229,932.5 

2,960,993.5 

126.539 

4,666.961 

102,425.590 

39 

40 

13,814.5 

215,364.1 

2,731,061.0 

123.723 

4,540.422 

97,758.629 

40 

41 

13,095.9 

201.,  549. 6 

2,515,696.9 

120.914 

4,416.699 

93.218.207 

41 

42 

12,411.0 

188,453.7 

2,314,147.3 

118.721 

4,295.785 

88,801.508 

42 

43 

11,757.9 

176,042.7 

2,125,693.6 

116.492 

4,177.064 

84,505.723 

43 

44 

11,135.0 

164,284.8 

1,949,650.9 

114.648 

4,060.572 

80,328.659 

44 

45 

10,540.9 

153,149.8 

1,785,366.1 

113.012 

3,945.924 

76,268.087 

45 

46 

9,973.97 

142,608.93 

1,632,216.26 

111.555 

3,832.912 

72,322.163 

46 

47 

9,432.90 

132,634.96 

1,489,607.33 

110.380 

3,721.357 

68,489.251 

47 

48 

8,916.33 

123,202.06 

1,356,972.37 

109.329 

3,610.977 

64,767.894 

48 

49 

8,423.02 

114,285.73 

1,233,770.31 

108.496 

3,501.648 

61,156.917 

49 

50 

7,951.85 

105,862.71 

1,119,484.58 

107.849 

3,393.152 

57,655.269 

50 

51 

7,501.55 

97,910.86 

1,013,621.87 

107.362 

3,285.303 

54,262.117 

51 

52 

7,071.17 

90,409.31 

915,711.01 

107.007 

3,177.941 

50,976.814 

52 

53 

6,659.66 

83,338.14 

825,301.70 

106.762 

3,070.934 

47,798.873 

53 

54 

6,266.11 

76,678.48 

741,963.56 

106.607 

2,964.172 

44,727.939 

54 

TABLE    XXXYI. 


■^7 


COMMUTATION  COLUMNS. 

4J  PER  CENT. 

AGE.     Da,. 

N^. 

s^. 

Cx- 

Mo,. 

Ra;- 

AGE. 
55 

55  i5,889.67 

70,412.37 

665,285.08 

106.692 

2,857.565 

41,763.767 

56  15,529.36 

64,522.70 

594,872.71 

106.735 

2,750.873 

38,906.202 

56 

57 

5,184.51 

58,993.34 

530,350.01 

106.965 

2,644.138 

36,155.329 

57 

58 

4,854.29 

53,808.83 

471,356.67 

107.127 

2,537.173 

33,511.191 

58 

59 

4,538.14 

48,954.54 

417,547.84 

107.290 

2,430.046 

30,974.018 

59 

60 

4,235.43 

44,416.40 

368,593.30 

107.513 

2,322.756 

28,543.972 

60 

61 

3,945.52 

40,180.97 

324,176.90. 

107.715 

2,215.243 

26,221.216 

61 

62 

3,667.90 

36,235.45 

283,995.93 

107.761 

2,107.528 

24,005.973 

62 

63 

3,402.20 

32,567.55 

247,760.48 

107.784 

1,999.767 

21,898.445 

63 

64 

3,147.90 

29,165.35 

215,192.93 

107.662 

1,891.983 

19,898.678 

64 

65 

2,904.68 

26,017.45 

186,027.58 

107.405 

1,784.321 

18,006.695 

65 

66 

2,672.'20 

23,112.77 

160,010.13 

106.866 

1,676.916 

16,222.374 

66 

67 

2,450.27 

20,440.57 

136,897.36 

106.174 

1,570.050 

14.545.458 

67 

68 

2,238.58 

17,990.30 

116,456.79 

105.056 

1,463.876 

12,975.408 

68 

69 

2,037.12 

15,751.72 

98,466.49 

103.791 

1,358.820 

11,511.532 

69 

70 

1,845.61 

13,714.60 

82,714.77 

102.045 

1,255.029 

10,152.712 

70 

71 

1.664.09 

11,868.99 

69,000.17 

99.9629 

1,152.9835 

8,897.6832 

71 

72 

1,492.47 

10,204.90 

57,131.18 

97.4282 

1,053.0206 

7,744.6997 

72 

73 

1,330.77 

8,712.43 

46,926.28 

94.4261 

955.5924 

6,691.6791 

73 

74 

1,179.04 

7,381.66 

38,213.85 

91.0598 

861.1663 

5,736.0867 

74 

75 

1,037.20 

6,202.62 

30,832.19 

87.1385 

770.1065 

•4,874.9204 

75 

76 

905.403 

5,165.420 

24,629.570 

82.7453 

682.9680 

4,104.8139 

76 

77 

783.670 

4,260.017 

19,464.150 

77.9877 

600.2227 

3,421.8459  77 

78 

671.933 

3,476.347 

15,204.133 

72.7760 

522.2350 

2,821.6232  78 

79 

570.223 

2,804.414 

11,727.786 

67.2183 

449.4590 

2,299.3882 

79 

80 

478.451 

2,234.191 

8,923.372 

61.3819 

382.2407 

1,849.9292 

80 

81 

396.465 

1,755.740 

6,689.181 

55.3280 

320.8588 

1,467.6885 

81 

82 

324.064 

1,359.275 

4,933.441 

49.2155 

265.5308 

1,146.8297 

82 

83 

260.894 

1,035.211 

3,574.166 

43.0558 

216.3153 

881.2989 

83 

84 

206.604  . 

774.317 

2,538.955 

37.0744 

173.2595 

664.9836 

84 

85 

160.632 

567.713 

1,764.638 

31.3014 

136.1851 

491.7241 

85 

86 

122.413 

407.081 

1,196.925 

25.8699 

104.88371 

355.5390 

86 

87 

91.2723 

284.6678 

789.8437 

20.9521 

79.0138 

250.6553 

87 

88 

66.3897 

193.3955 

505.1759 

16.4894 

58.0617 

171.6415 

88 

89 

47.0415 

127.0058 

311.7804 

13.1716 

41.5723 

113.5798 

89 

90 

31.8442 

79.9643 

184.7746 

9.99977 

28.40072 

72.00746 

90  i 

91 

20.4731 

48.1201 

104.8103 

7.02435 

18.40095 

43.60674 

91 

92 

12.5671 

27.6470 

56.6902 

4.68696 

11.37660 

25.20579 

92 

93 

7.33902 

15.07986 

29.04321 

2.98476 

6.68964 

13.82919 

93 

94 

4.03822 

7.74084 

13.96335 

1.78706 

3.70488 

7.13955 

94 

95 

2.07726 

3.70262 

6.22251  i 

.993905 

1.917819 

3.434666 

95 

96 

.993905 

1.62536 

2.51989 

.531500 

.923914 

1.516847 

96 

97 

.419605 

.631453 

.894534 

.240922 

.392414 

.592933 

97 

98 

.160615 

.211848 

.263081 

.102465 

.151492 

.200519 

98 

99 

.051233j 

.051233 

.051233 

.049027 

.049027 

.049027 

99 

-I 

*28 


TABLE    XXXYI. 


LOGARITHMS  OF  COMMUTATION  COLUMNS.         4|^  PER  CENT. 


AGE. 

10 

ADo,. 

ANa;. 

ASo,. 

AC^. 

AMa;. 

AB«. 

AGE. 

4.808837 

6.090628 

7.336465 

3.601396 

4.054541 

5.503595 

10 

11 

4.786898 

6.067315 

-  7.300471 

3.580837 

4.038970 

5.487871 

11 

12 

4.764949 

6.043936 

7.374311 

2.559699 

4.033576 

5.472141 

12 

13 

4.742993 

6.030457 

7.347978 

2.539230 

4.008390 

5.456399 

13 

14 

4.731029 

5.996904 

7.331465 

2.519436 

3.993390 

5.440636 

14 

15 

4.699051 

5.973362 

7.194766 

2.498960 

3.978557 

5.424845 

15 

16 

4.677061 

5.949528 

7.167871 

2.478480 

3.963919 

5.409019 

16 

17 

4.655063 

5.925695 

7.140775 

2.458681 

3.949479 

5.393148 

17 

18 

4.633050 

5.901758 

7.113467 

2.438880 

3.935220 

5.377224 

18 

19 

4.611021 

5.877712 

7.085939 

2.419078 

3.921144 

5.361238 

19 

20 

4.588978 

5.853551 

7.058183 

2.399962 

3.907256 

5.345180 

20 

21 

4.566915 

5.829268 

7.030189 

3.380845 

3.893537 

5.329040 

21 

22 

4.544831 

5.804857 

7.001946 

3.361739 

3.879990 

5.312808 

22 

23 

4.522727 

5.780312 

6.973444 

3.343398 

3.866618 

5.296473 

23 

24 

4.500599 

5.755624 

6.944673 

2.324866 

3.853403 

5.280024 

24 

25 

4.478444 

5.730785 

6.915631 

2.306433 

3.840349 

5.263451 

25 

26 

4.456262 

5.705789 

6.886375 

2.289361 

3.827457 

5.246739 

26 

27 

4.434045 

5.680625 

6.856634 

2.271602 

3.814693 

5.329878 

27 

28 

4.411795 

5.655284 

6.836655 

2.254514 

3.802074 

5.212852 

28 

29 

4.389508 

5.629758 

6.796353 

2.338756 

3.789586 

5.195651 

29 

30 

4.367172 

5.604034 

6.765703 

3.333308 

3.777195 

5.178257 

30 

31 

4.344793 

5.578103 

6.734691 

2.206505 

3.764920 

5.160658 

31 

32 

4.322363 

5.551952 

6.703300 

2.191330 

3.752746 

5.142837 

32 

33 

4.299877 

5.525569 

6.671515 

3.176769 

3.740656 

5.134778 

33 

34 

4.277329 

5.498941 

6.639316 

3.163800 

3.728637 

5.106464 

34 

35 

4.254713 

5.473054 

6.606686 

2.150033 

3.716672 

5.087876 

35 

36 

4.232016 

5.444893 

6.573604 

2.136553 

3.704729 

5.068998 

36 

37 

4.209240 

5.417441 

6.540050 

2.124227 

3.693829 

5.049807 

37 

38 

4.186377 

5.389686 

6.506003 

2.113002 

3.680941 

5.030385 

38 

39 

4.163411 

5.361600 

6.471437 

2.102226 

3.669034 

5.010408 

39 

40 

4.140334 

5.333173 

6.436331 

2.092450 

3.657096 

4.990155 

40 

41 

4.117134 

5.304383 

6.400658 

2.082477 

3.645098 

4.969501 

41 

42 

4.093808 

5.375305 

6.364391 

3.074536 

3.633043 

4.948431 

42 

43 

4.070328 

5.345618 

6.327501 

2.066295 

3.620871 

4.936886 

43 

44 

4.046692 

5.315597 

6.289957 

2.059368 

3.608587 

4.904870 

44 

45 

4.022877 

5.185117 

6.351727 

2.053124 

3.596148 

4.883343 

45 

46 

3.998868 

5.154147 

6.313778 

2.047495 

3.583529 

4.859271 

46 

47, 

3.974645 

5.122658 

6.173073 

2.042889 

3.570702  , 

4.835623 

47 

48 

3.950186 

5.090618 

6.133571 

2.038734 

3.557625 

4.811359 

48 

49 

3.925468 

5.057992 

6.091334 

2.035413 

3.544273 

4.786445 

49 

50 

3.900468 

5.024743 

6.049018 

3.033817 

3.530603 

4.760839 

50 

51 

3.875151 

4.990834 

6.005876 

3.030849 

3.516575 

4.734497 

51 

52 

3.849491 

4.956314 

5.961759 

3.039413 

3.502146 

4.707372 

52 

53 

3.823453 

4.920844 

5.916613 

3.028418 

3.487270 

4.679418 

53 

54 

3.796998 

4.884674 

5.870383 

3.037785 

3.471903 

4.650578 

54 

*29 


TABLE    XXXTl. 

LOGARITHMS  OF  COMMUTATION  COLUMNS.         4|^  PER  CENT. 


A^E. 

ADa:. 

ANo, 

ASa,. 

AOor. 

AMa, 

ARa;. 

AGE. 

55 

3.770091 

4.847649 

5.823008 

2.028131 

3.455997 

4.620800 

55 

56 

3.742675 

4.809712 

5.774424 

2.028305 

3.439470 

4.590019 

56 

57 

3.714708 

4.770803 

5.724563 

2.029242 

3.422285 

4.558172 

57 

58 

3.686126 

4.730854 

5.673350 

2.029898 

3.404350 

4.525189 

58 

59 

3.656878 

4.689793 

5.620706 

2.030559 

3.385615 

4.490997 

59 

60 

3.626897 

4.647543 

5.566547 

2.031463 

3.366004 

4.455515 

60 

61 

3.596104 

4.604020 

5.510782 

2.032274 

3.345421 

4.418653 

61 

62 

3.564418 

4.559134 

5.453312 

2.032463 

3.323774 

4.380319 

62 

63 

3.531760 

4.512785 

5.394032 

2.032553 

3.300980 

4.340413 

63 

64 

3.498021 

4.464867 

5.332828 

2.032061 

3.276917 

4.298824 

64 

65 

3.463099 

4.415265 

5.269577 

2.031024 

3.251473 

4.255434 

65 

66 

3.426869 

4.363852 

5.204148 

2.028839 

3.224512 

4.210114 

66 

67 

3.389214 

4.310493 

5.136395 

2.026018 

3.195914 

4.162728 

67 

68 

3.349972 

4.255038 

5.066165 

2.021420 

3.165504 

4.113121 

68 

69 

3.309017 

4.197328 

4.993288 

2.016160 

3.133162 

4.061133 

69 

70 

3.266139 

4.137183 

4.917583 

2.008793 

3.098654 

4.006582 

70 

71 

3.221176 

4.074414 

4.838850 

1.999839 

3.061823 

3.949277 

71 

72 

3.173904 

4.008809 

4.756873 

1.988685 

3.022437 

3.889005 

72 

73 

3.124103 

3.940139 

4.671416 

1.975092 

2.980273 

3.825535 

73 

74 

3.071528 

3.868154 

4.582221 

1.959327 

2.935087 
^886551 

3.758616 

74 

75 

3.015864 

3.792575 

4.489004 

1.940210 

3.687968 

75 

76 

2.956842 

3.713106 

4.391457 

1.917743 

2.834400 

3.613293 

76 

77 

2.894133 

3.629412 

4.289235 

1.892026 

2.778313 

3.534260 

77 

78 

2.827326 

3.541123 

4.181962 

1.861988 

2.717866 

3.450499 

78 

79 

2.756045 

3.447842 

4.069216 

1.827487 

2.652690 

3.361612 

79 

80 

2.679837 

3.349120 

3.950529 

1.788040 

2.582337 

3.267155 

80 

81 

2.598205 

3.244460 

3.825373 

1.742945 

2.506314 

3.166634 

81 

82 

2.510631 

3.133307 

3.693150 

1.692102 

2.424115 

3.059499 

82 

83 

2.416464 

3.015029 

3.553175 

1.634031 

2.335087 

2.945123 

83 

84 

2.315138 

2.888918 

3.404655 

1.569074 

2.238697 

2.822811 

84 

85 

2.205832 

'  2.754129 

3.246656 

1.495563 

2.134129 

2.691722 

85 

86 

2.087829 

2.609681 

3.078067 

1.412794 

2.020708 

2.550887 

86 

87 

1.960339 

2.454338 

2.897541 

1.321227 

1.897703 

2.399077 

87 

88 

1.822101 

2.286446 

2.703443 

1.217205 

1.763890 

2.234623 

88 

89 

1.672481 

2.103823 

2.493849 

1.119640 

L 618804 

2.055301 

89 

90 

1.503030 

1.902896 

2.266642 

0.999990 

1.453329 

1.857378 

90 

91 

1.311184 

1.682327 

2.020404 

0.846606 

1.264840 

1.639553 

91  1 

92 

1.099236 

1.441648 

1.753508 

0.670891 

1.056013 

1.401500 

92 

93 

0.865638 

1.178398 

1.463045 

0.474910 

0.825403 

1.140797 

93 

94 

0.606190 

0.888788 

1.144990 

0.252138 

0.568774 

0.853671 

94 

95 

0.317491 

0.568509 

0.793966 

T.  997345 

0.282808 

0.535885 

95 

96 

1.997345 

0.210950 

0.401382 

1.725503 

1.965632 

0.180942 

96 

97 

1.622841 

1.800341 

1.951597 

1.381876 

1.593744 

1.773005 

97 

98 

1.205785 

1.326024 

1.420089 

1.010577 

1.180390 

1.302156 

98 

99 

"2.709547 

2. 709547 

2.709547 

2.690431 

2.690431 

2.690431 

99 

♦30 


TABLE    XXXVII. 


COMMUTATION    COLUMNS.         5  PER  CENT. 


Aa£. 

J>x- 

N^. 

s^. 

C.:. 

M^. 

E«. 

1 

1  AQE. 

10 

61,391.3 

1,089,674.9 

17,710,636.6 

378.872 

9,502.066 

246,311.154 

1 

10 

11 

58,089.1 

1,028,283.6 

16,620,961.7 

359.717 

9,123.194 

236,809.088 

11 

12 

54,963.2 

970,194.5 

15,592,678.1 

340.997 

8,763.477 

227,685.894 

12 

13 

52,004.9 

915,231.3 

14,622,483.6 

323.749 

8,422.480 

218,922.417 

13 

14 

49,204.8 

863,226.4 

13,707,252.3 

307.851 

8,098.731 

210,499.937 

14 

15 

46,553.9 

814,021.6 

12,844,025.9 

292.275 

7,790.880 

202,401.206 

15 

16 

44,044.6 

767,467.7 

12,030,004.3 

277.485 

7,498.605 

194,610.326 

16 

17 

41,669.8 

723,423.1  [11,262,536.6 

263.856 

7,221.120 

187,111.721 

17 

18 

39,421.7 

681,753.3 

10,539,113.5 

250.895 

6,957.264 

179,890.601 

18 

19 

37,293.6 

642,331.6 

9,857,360.2 

238.571 

6,706.369 

172,933.337 

19 

20 

35,279.2 

605,038.0 

9,215,028.6 

227.210 

6,467.798 

166,226.968 

20 

21 

33,372.0 

569,758.8 

8,609,990.6 

216.391 

6,240.588 

159,759.170 

21 

22 

31,566.4 

536,386.8 

8,040,231.8 

206.087 

6,024.197 

153,518.582 

22 

23 

29,857.1 

504,820.4 

7,503,845.0 

196.583 

5,818.110 

147,494.385 

23 

24 

28,238.9 

474,963.3 

6,999,024.6 

187.517 

5,621.527 

141,676.275 

24 

25 

26,706.6 

446,724.4 

6,524,061.3 

178.869 

5,434.010 

136,054.748 

25 

26 

25,256.0 

420,017.8 

6,077,336.9 

171.155 

5,255.141 

130,620.738 

26 

27 

23,882.2 

394,761.8 

5,657,319.1 

163.515 

5,083.986 

125,365.597 

27 

28 

22,581.4 

370,879.6 

5,262,557.3 

156.457 

4,920.471 

120,281.611 

28 

29 

21,349.6 

348,298.2 

4,891,677.7 

150.164 

4,764.014 

115,361.140 

29 

30 

20,182.8 

326,948.6 

4,543,379.5 

143.895 

4,613.850 

110,597.126 

30 

31 

19,077.9 

306,765.8 

4,216,430.9 

138.092 

4,469.955 

105,983.276 

31 

32 

18,031.3 

287,687.9 

3,909,665.1 

i  132.715 

4,331.863 

101,513.321 

32 

33 

17,039.9 

269,656.6 

3,621,977.2 

i  127.728 

4,199.148 

97,181.458 

33 

34 

16,100.8 

252,616.7 

3,352,320.6 

123.096 

4,071.420 

92,982.310 

34 

35 

15,211.0 

236,515.9 

3,099,703.9 

118.961 

3,948.324 

88,910.890 

35 

36 

14,367.7 

221,304.9 

2,863,188.0 

114.776 

3,829.363 

84,962.566 

36 

37 

13,568.7 

206,937.2 

2,641,883.1 

i  111.033 

3,714.587 

81,133.203 

37 

38 

12,811.6 

193,368.5 

2,434,945.9 

i  107.685 

3,603.554 

77,418.616 

38 

39 

12,093.8 

180,556.9 

2,241,577.4 

104.546 

3,495.869 

73,815.062 

39 

40 

11,413.4 

168,463.1 

2,061,020.5 

101.732 

3,391.323 

70,319.193 

40 

41 

10,768.2 

157,049.7 

1,892,557.4 

'  98.9489 

3,289.591 

66,927.870 

41 

42 

10,156.4 

146,281.46 

1,735,507.74 

96.6911 

3,190.6419 

63,638.2786 

42 

43 

9,576.08 

136,125.06 

1,589,226.28 

94.4239 

3,093.9508 

60,447.6367 

43 

44 

9,025.68 

126,548.98 

1,453,101.22 

92.4874 

2,999.5269 

57,353.6859 

44 

45 

8,503.39 

117,523.30 

1,326,552.24 

90.7332 

2,907.0395 

54,354.1590 

45 

46 

8,007.72 

109,019.91 

1,209,028.94 

89.1382 

2,816.3063 

51,447.1195 

46 

47 

7,537.27 

101,012.19 

1,100,009.03 

87.7777 

2,727.1681 

48,630.8132 

47 

48 

7,090.58 

93,474.92 

998,996.84 

86.5279 

2,639.3904 

45,903.6451 

48 

49 

6,666.40 

86,384.34 

905,521.92 

85.4596 

2,552.8625 

43,264.2547 

49 

50 

6,263.50 

79,717.94 

819,137.58 

84.5461 

2,467.4029 

40,711.3922 

50 

51 

5,880.69 

73,454.44 

739,419.64 

83.7630 

2,382.8568 

38,243.9893 

51 

52 

5,516.89 

67,573.75 

665,965.20 

83.0888 

2,299.0938 

35,861.1325 

52 

53 

5,171.09 

62,056.86 

598,391.45 

82.5041 

2,216.0050 

33,562.0387 

53 

54 

4,842.34 

56,885.77 

536,334.59 

81.9917 

2,133.5009 

31,346.0337 

1 

54 

TABLE    XXXVII. 

COMMUTATION  COLUMNS.         5  PER  CENT. 


*tt-< 


AQE. 

Dec. 

Na.. 

fear* 

Ca,. 

Ma,. 

Rs. 

AQE. 

1 

55 

65 

4,529.77 

52,043.43 

479,448.82 

81.6663 

2,051.5092 

29,212.5328 

56 

4,232.39 

47,513.66 

427,405.39 

81.3100 

1,969.8429 

27,161.0236 

56 

57 

3,949.55 

43,281.27 

379,891.73   ! 

81.0975 

1,888.5329 

25,191.1807 

57 

58 

3,680.37 

39,331.72 

336,610.46   i 

80.8333 

1,807.4354 

23,302.6478 

58 

59 

3,424.28 

35,651.35 

297,278.74 

80.5710 

1,726.6021 

21,495.2124 

59 

60  13,180.65 

32,227.07 

261,627.39 

80.3543 

1,646.0311 

19,768.6103 

60 

61  3,948.84 

29,046.42 

229,400.32 

80.1212 

1,565.6768 

18,122.5792 

61 

6?  2,728.30 

26,097.58 

200,353.90 

79.7744 

1,485.5556 

16,556.9024 

62 

63 

2,518.61 

23,369.28 

174,256.32 

79.4110 

1,405.7812 

15,071.3468 

63 

64 

2,319.26 

20,850.67 

150,887.04 

78.9433 

1,326.3702 

13,665.5656 

64 

65 

2,129.88 

18,531.41 

130,036.37 

78.3800 

1,247.4269 

12,339.1954 

65 

66 

1,950.07 

16,401.53 

111,504.96 

77.6153 

1,169.0469 

11,091.7685 

66 

67 

1,779.60 

14,451.46 

95,103.43 

76.7456 

1,091.4316 

9,922.7216 

67 

68 

1,618.11 

12,671.86 

80,651.97 

75.5758 

1,014.6860 

8,831.2900 

68 

69 

1,465.48 

11,053.75 

67,980.11 

74.3104 

939.1102 

7,816.6041 

69 

70 

1,321.38 

9,588.27 

56,926.36 

72.7125 

864.7998 

6,877.4939 

70 

71 

1,185.75 

8,266.89 

47,338.09 

70.8896 

792.0873 

6,012.6941 

71 

72 

1,058.39 

7,081.14 

39,071.20 

68.7631 

721.1977 

5,220.6068 

72 

73 

939.232 

6,022.748 

31,990.065 

66.3269 

652.4346 

4,499.4091 

73 

74 

§28.180 

5,083.516 

25,967.317 

63.6577 

586.1077 

3,846.9745 

74 

75 

725.085 

4,255.336 

20,883.801 

60.6264 

522.4500 

3.260.8668 

75 

76 

629.931 

3,530.251 

16,628.465 

57.2956 

461.8236 

2,738.4168 

76 

77 

542.639 

2,900.320 

13,098.214 

53.7442 

404.5280 

2,276.5932 

77 

78 

463.054 

2,357.681 

10,197.894 

49.9138^ 

350.7838 

1,872.0652 

78 

79 

391.090 

1,894.627 

7,840.213 

45.8824 

300.8700 

1,521.2814 

79 

80 

326.585 

1,503.537 

5,945.586 

41.6991 

254.9876 

1,220.4114 

80 

81 

269.334 

1,176.952 

4,442.049 

37.4075 

213.2885 

965.4238 

81 

82 

219.102 

907.618 

3,265.097 

33.1163 

175.8810 

752.1353 

82 

,83 

175.551 

688.516 

2,357.479 

28.8336 

142.7647 

576.2543 

83 

84 

138.358 

512.965 

1,668.963 

24.7098 

113.9311 

433.4896 

84 

85 

107.0600 

374.6070 

1,155.9980 

20.7627 

89.2213 

319.5585 

85 

86 

81.1989 

267.5473 

781.3912 

17.0782 

68.4586 

230.3372 

86 

87 

60.2541 

186.3484 

513.8439 

13.7658 

51.3804 

161.8786 

87 

88 

43.6191 

126.0943 

327.4955 

10.7822 

37.6146 

110.4982 

88 

89 

30.7598 

82.4752 

201.4012 

8.57174 

26.8324 

72.88355 

89 

90 

20.7233 

51.7154 

118.9260 

6.47659 

18.26065 

46.05116 

90 

91 

13.2599 

30.9921 

67.2106 

4.52782 

11.78406 

*27. 79151 

91 

92 

8.10065 

17.73217 

36.21852 

3.00676 

7.25624 

16.00745 

92 

93 

4.70813 

9.63152 

18.48635 

1.90567 

4.24948 

8.75121 

93 

94 

2.57826 

4.92339 

8.85483 

1.13554 

2.34381 

4.50173 

94 

95 

1.31995 

2.34513 

3.93144 

.628545 

1.208272 

2.157920 

95 

96 

.628544 

1.02518 

1.58631 

.334520 

.579727 

.949648 

96 

97 

.264094 

.396640 

.561125 

.150911 

.245207 

.369921 

97 

98 

.100607 

.132546 

.164485 

.063878 

.094296 

.124714 

98 

99 

.031939 

.031939 

.031939 

.030418 

.030418 

.030418 

99 

*32 


TABLE     XXXVII. 

LOGARITHMS  OF  COMMUTATION  COLUMNS.         5  PER  CENT. 


A0£. 

ADa,. 

ANa,. 

ASas. 

AUa;, 

AM,. 

ARa,. 

AGE. 

10 

4.788107 

6.037297 

7.248234 

2.578493 

3.977818 

5.391484 

10 

11 

4.764095 

6.012113 

7.220656 

2.555961 

3.960147 

5.374398 

11 

12 

4.740073 

5.986859 

7.192921 

2.532750 

3.942677 

5.357336 

12 

13 

4.716044 

5.961531 

7.165021 

2.510208 

3.925440 

5.340290 

13 

14 

4.692007 

5.936125 

7.136950 

2.488341 

3.908417 

5.323252 

14 

15 

4.667956 

5.910636 

7.108701 

2.465792 

3.891587 

5.306214 

15 

18 

4.643893 

5.885060 

7.080266 

2.443230 

3.874981 

5.289166 

16 

17 

4.619822 

5.859393 

7.051636 

2.421366 

3.858605 

5.272101 

17 

18 

4.595736 

5.833627 

7.022804 

2.399493 

3.842438 

5.255008 

18 

19 

4.571634 

5.807759 

6.993760 

2.377618 

3.826488 

5.237878 

19 

20 

4.547518 

5.781783 

6.964496 

2.356428 

3.810757 

5.220701 

20 

21 

4.523382 

5.755691 

6.935003 

2.335239 

3.795226 

5.203466 

21 

22 

4.499225 

5.729478 

6.905269 

2.314050 

3.779899 

5.186161 

22 

23 

4.475048 

5.703137 

6.875284 

2.293546 

3.764782 

5.168775 

23 

24 

4.450847 

5.676660 

6.845037 

2.273041 

3.749855 

5.151297 

24 

25 

4.426619 

5.650039 

6.814518 

2.252535 

3.735120 

5.133713 

25 

26 

4.402364 

5.623268 

6.783714 

2.233390 

3.720584 

5.116012 

26 

27 

4.378074 

5.596335 

6.752611 

2.213558 

3.706205 

5.098178 

27 

28 

4.353751 

5.569232 

6.721197 

2.194396 

3.692007 

5.080199 

28 

29 

4.329390 

5.541951 

6.689458 

2.176566 

3.677973 

5.062059 

29 

30 

4.304982 

5.514479 

6.657379 

2.158045 

3.664064 

5.043744 

30 

31 

4.280530' 

5.486807 

6.624945 

2.140168 

3.650304 

5.025237 

31 

32 

4.256026 

5.458922 

6.592139 

2.122921 

3.636674 

5.006523 

32 

33 

4.231468 

5.430811 

6.558945 

2.106286 

3.623161 

4.987583 

33 

34 

4.206847 

5.402462 

6.525346 

2.090244 

3.609746 

4.968401 

34 

35 

4.182158 

5.373861 

6.491321 

2.075404 

.3.596412 

4.948955 

35 

36 

4.157387 

5.344991 

6.456850 

2.059851 

3.583126 

4.929228 

36 

37 

4.132539 

5.315838 

6.421913 

2.045453 

3.569911 

4.909199 

37 

38 

4.107603 

5.286386 

6.386489 

2.032155 

3.556731 

4.888846 

38 

39 

4.082563 

5.256614 

6.350554 

2.019306 

3.543555 

4.868145 

39 

40 

4.057414 

5.226505 

6.314082 

2.007457 

3.530369 

4.847074 

40 

41 

4.032141 

5.196037 

6.277049 

1.995411 

3.517142 

4.825607 

41 

42 

4.006741 

5.165189 

6.239427 

1.985386 

3.503878 

4.803718 

42 

43 

3.981188 

5.133938 

6.201186 

1.975082 

3.490513 

4.781379 

43 

44 

3.955480 

5.102258 

6.162296 

1.966083 

3.477053 

4.758561  ■ 

44 

45 

3.929592 

5.070124 

6.122724 

1.957766 

3.463451 

4.735233 

45 

46 

3.9035(39 

5.037506 

6.082436 

1.950064 

3.449680 

4.711361 

46 

47 

3.877214 

5.004373 

6.041397 

1.943384 

3.435712  1 

4.686911 

47 

48 

3.850682 

4.970694 

5.999564 

1.937156 

3.421504 

4.661847 

48 

49 

3.823891 

4.936435 

5.956899 

1.931761 

3.407027 

4.636130 

49 

50 

3.796817 

4.901556 

5.913357 

1.927093 

3.392240 

4.609716 

50 

51 

3.769428 

4.866018 

5.868891 

1.923052 

3.377098 

4.582563 

51 

52 

3.741694 

4.829778 

5.823452 

1.919543 

3.361557 

4.554624 

52 

53 

3.713582 

4.792790 

5.776985 

1.916476 

3.345571 

4.525848 

53 

54 

3.685056 

4.755003 

5.729436 

1.913770 

3.329093 

4.496183 

54 

TABLE    XXXYII. 

LOGARITHMS  OF  COMMUTATION  COLUMNS.         5  PER  CENT. 


"33 


AGE. 

AD^. 

ANa,. 

ASx- 

.AC«,. 

AMa;. 

AKa;. 

AGE. 
55 

55 

3.656076 

4.716366 

5.680742 

1.912043 

3.312073 

4.465569 

56 

3.626586 

4.676818 

5.630840 

1.910144 

3.294432 

4.433946 

56 

57 

3.596547 

4.636300 

5.579660 

1.909007 

3.276125 

4.401248 

57 

58 

3.565892 

4.594743 

5.527128 

1.907590 

3.257063 

4.367405 

58 

59 

3.534570 

4.552076 

5.473164 

1.906179 

3.237192 

4.332341 

59 

60 

3.502516 

4.508221 

5.417684 

1.905009 

3.216438 

4.295976 

60 

61 

3.469651 

4.463092 

5.360594 

1.903747 

3.194702 

4.258220 

61 

62 

3.435892 

4.416600 

5.301798 

1.901863 

3.171889 

4.218979 

62 

63 

3.401160 

4.368645 

5.241189 

1.899881 

3.147918 

4.178152 

63 

64 

3.365349 

4.319120 

5.178652 

1.897315 

3.122665 

4.135627 

64 

65 

3.328354 

4.267908 

5.114065 

1.894205 

3.096015 

4.091287 

65 

66 

3.290050 

4.214884 

5.047294 

1.889947 

3.067832 

4.045001 

66 

67 

3.250322 

4.159912 

4.978196 

1.885054 

3.037997 

3.996631 

67 

68 

3.209008 

4.102840 

4.906615 

1.878383 

3.006332 

3.946025 

68 

69 

3.165979 

4.043509 

4.832382 

1.871050 

2.972717 

3.893018 

69 

70 

3.121029 

3.981740 

4.755314 

1.861609 

2.936916 

3.837430 

70 

71 

3.073992 

3.917342 

4.675211 

1.850582 

2.898773 

3.779069 

71 

72 

3.024648 

3.850103 

4.591857 

1.837355 

2.858055 

3.717721 

72 

73 

2.972773 

3.779794 

4.505015 

1.821689 

2.814537 

3.653156 

73 

74 

2.918125 

3.706164 

4.414427 

1.803851 

2.767978 

3.585119 

74 

75 

2.860389 

3.628933 

4.319810 

1.782662 

2.718045 

3.513332 

75 

76 

2.799293 

3.547806 

4.220852 

1.758122 

2.664476 

3.437499 

76 

77 

2.734511 

3.462446 

4.117212 

1.730332 

2.606948 

3.357286 

77 

78 

2.665632 

3.372485 

4.049136 

1.698221 

2.545040 

3.272321 

78 

79 

2.592277 

3.277524 

3.894328 

1.661647 

2.478379 

3.182209 

79 

80 

2.513996 

3.177114 

3.774195 

1.620127 

2.406519 

3.086506 

80 

81 

2.430291 

3.070759 

3.647583 

1.572958 

2.328967 

2.984718 

81 

82 

2.340645 

2.957903 

3.513896 

1.520042 

2.245219 

2.876296 

82 

83 

2.244404 

2.837914 

3.372448 

1.459899 

2.154621 

2.760614 

83 

84 

2.141005 

2.710088 

3.222446 

1.392869 

2.056642 

2.636979 

84 

85 

2.029627 

2.573576 

3.062957 

1.317285 

1.950468 

2.504550 

85 

86 

1.909550 

2.427401 

2.892869 

1.232443 

1.835428 

2.362364 

86 

87 

1.779987 

2.270325 

2.710831 

1.138802 

1.710797 

2.209189 

87 

88 

1.639677 

2.100695 

2.515205 

1.032707 

1.575356 

2.043355 

88 

89 

1.487983 

1.916323 

2.304062 

0.933069 

1.428659 

1.862629 

89 

90 

1.316459 

1.713619 

2.075277 

0.811346 

1.261516 

1.663240 

90 

91 

1.122540 

1.491251 

1.827438 

0.655890 

1.071295 

1.443912 

91 

92 

0.908520 

1.248762 

1.558930 

0.478101 

0.860712 

1.204322 

92 

93 

0.672848 

0.983695 

1.266851 

0.280048 

0.628336 

0.942069 

93 

94 

0.411327 

0.692264 

0.947181 

0.055202 

0.369922 

0.653380 

94 

95 

0.120556 

0.370167 

0.594551 

1.798336 

0.082165 

0.334035 

95 

96 

1.798336 

0.010800 

0.200388 

1.524422 

1.763223 

1.977563 

96 

97 

1.421759 

1.598397 

1.749060 

1.178721 

1.389533 

1.568109 

97 

98 

1.002630 

1.122367 

1.216127 

2.805349 

2.974493 

1.095915 

98 

99 

2.504319 

2.504319 

2.504319 

2.483130 

2.483130 

2.483130 

99 

*34 


TABLE     XXXYIII. 

COMMUTATION  COLUMNS.         6  PER  CENT. 


AGE. 

D^. 

Na,. 

Sa;. 

C.,. 

Ma,. 

R^. 

AOE. 
10 

10 

55,839.4 

864,777.4 

12,598.316.8 

341.358 

6,889.834 

151,664.904 

11 

52,337.5 

808,938.0 

11,733,539.4 

321.042 

6,548.476 

144,775.070 

11 

12 

49,054.0 

756,600.5 

10,924,601.4  i 

301.464 

6,227.434 

138,226.594 

12 

13 

45,975.8 

.707,546.5 

10,168,000.9  i 

283.515 

5,925.970 

131,999.160 

13 

14 

43,089.8 

661,570.7 

9,460,454.4 

267.050 

6,642.455 

126,073.190 

14 

15 

40,383.8 

618,480.9 

8,798,883.7 

251.146 

5,375.405 

120,430.735 

15 

16 

37,846.7 

578,097.1 

8,180,402.8  : 

236.188 

5,124.259 

115,055.330 

16 

17 

35,468.3 

540,250.4 

7,602,305.7 

222.468 

4,888.071 

109,931.071 

17 

18 

33,238.2 

504,782.1 

7,062,055.3 

209.545 

4,665.603 

105,043.000 

18 

19 

31,147.3 

471,543.9 

6,557,273.2 

197.372 

4,456.058 

100,377.397 

19 

20 

29,186.8 

440,396.6 

6,085,729.3 

186.200 

4,258.686 

95,921.339 

20 

21 

27,348.5 

411,209.8 

5,645,332.7 

175.661 

4,072.486 

91,662.653 

21 

22 

25,624.8 

383,861..  3 

5,234,122.9 

165.718 

3,896.825 

87,590.167 

22 

23 

24,008.6 

358,236.5 

4,850,261.6 

156.584 

3,731.107 

83,693.342 

23 

24 

22,493.1 

334,227.9 

4,492,025.1 

147.954 

3,574.523 

79,962.235 

24 

25 

21,071.9 

311,734.8 

4,157,797.2 

139.799 

3,426.569 

76,387.712 

25 

26 

19,739.4 

290,662.9 

3,846,062.4 

132.508 

3,286.770 

72,961.143 

26 

27 

18,489.6 

270,923.5 

3,555,399.5 

125.399 

3,154.262 

69,674.373 

27 

28 

17,317.6 

252,433.9 

3,284,476.0 

118.855 

3,028.863 

66,520.111 

28 

29 

16,218.4 

235,116.3 

3,032,042.1 

112.998 

2,910.008 

63,491.248 

29 

30 

15,187.5 

218,897.9 

2,796,925.8 

107.258 

2,797.010 

60,581.240 

30 

31 

14,220.5 

203,710.4 

2,578,027.9 

101.962 

2,689.752 

57,784.230 

31 

32 

13,313.6 

189,489.9 

2,374,317.5 

97.0677 

2,587.7904 

55,094.4779 

32 

33 

12,463.0 

176,176.3 

2,184,827.6 

92.5386 

2,490.7227 

52,506.6875 

33 

34 

11,665.0 

163,713.3- 

2,008,651.3 

88.3414 

2,398.1841 

50,015.9648 

34 

35 

10,916.4 

152,048.3 

1,844,938.0 

84.5684 

2,309.8427 

47,617.7807 

35 

36 

10,213.9 

141,131.9 

1,692,889.7 

80.8236 

2,225.2743 

45,307.9380 

36 

37 

9,554.90 

130,918.01 

1,551,757.77 

77.4503 

2,144.4507 

43,082.6637 

37 

38 

8,936.61 

121,363.11 

1,420,839.76 

74.4061 

2,067.0004 

40,938.2130 

38 

39 

8,356.36 

112,426.50 

1,299,476.65 

71.5555 

1,992.5943 

38,871.2126 

39 

40 

7,811.80 

104,070.14 

1,187,050.15 

68.9727 

1,921.0388 

36,878.6183 

40 

41 

7,300.66 

96,258.34 

1,082,980.01 

66.4531 

1,852.0661 

34,957.5795 

41 

42 

6,820.97 

88,957.68 

986,721.67 

64.3241 

1,785.6130 

33,105.6134 

42 

43 

6,370.54 

82,136.71 

897,763.99 

62.2233 

1,721.2889 

31,319.9004 

43 

44 

5,947.73 

75,766.17 

815,627.28 

60.3722 

1,659.0656 

29,598.6115 

44 

45 

5,550.68 

69,818.44 

739,861.11 

58.6684 

1,598.6934 

27,939.5459 

45 

46 

5,177.82 

64,267.76 

670,042.67 

57.0933 

1,540.0250 

26,340.8525 

46 

47 

4,827.64 

59,089.94 

605,774.91 

55.6915 

1,482.9317 

24,800.8275 

47 

48 

4,498.69 

54,262.30 

546,684.97 

54.3806 

1,427.2402 

23,317.8968 

48 

49 

4,189.66 

49,763.61 

492,422.67 

53.2026 

1,372.8596 

21,890.6656 

49 

50 

3,899.32 

45,573.95 

442,659.06 

52.1373 

1,319.6570 

20,517.7960 

50 

51 

3,626.46 

41,674.63 

397,085.11 

51.1671 

1,267.5197 

19,198.1390 

51 

52 

3,370.02 

38,048.17 

355,410.48 

50.2765 

1,216.3526 

17,930.6193 

52 

53 

3,128.99 

34,678.15 

317,362.31 

49.4517 

1,166.0761 

16,714.2667 

53 

54 

2,902.42 

31,549.16 

282,684.16 

48.6809 

1,116.6244 

15,548.1906 

54 

TABLE    XXXYIII. 

COMMUTATION    COLUMNS.         6    PER    CENT. 


*35 


AGE. 

Do,. 

Na> 

Sx' 

Cx. 

Ma,. 

Hr. 

AQiE. 
55 

55 

2,689.45 

28,646.74 

251,135.00 

48.0303 

1,067.9435 

14,431.5662 

56 

2,489.19 

25,957.29 

222,488.26 

47.3696 

1,019.9132 

13,363.6227 

56 

57 

2,300.93 

23,468.10 

196,530.97 

46.8001 

972.5436 

12,343.7095 

57 

58 

2,123.88 

21,167.17 

173,062.87 

46.2075 

925.7435 

11,371.1659 

58 

59 

1,957.46 

19,043.29 

151,895.70 

45.6231 

879.5360 

10,445.4224 

59 

60 

1,801.03 

17,085.83 

132,852.41 

45.0711 

833.9129 

9,565.8864 

60 

61 

1,654.02 

15,284.80 

115,766.58 

44.5164 

788.8418 

8,731.9735 

61 

62 

1,515.88 

13,630.78 

100,481.78 

43.9056 

744.3254 

7,943.1317 

62 

63 

1,386.17 

12,114.90 

86,851.00 

43.2933 

700.4198 

7,198.8063 

63 

64 

1,264.41 

10,728.73 

74,736.10 

42.6323 

657.1265 

6,498.3865 

64 

65 

1,150.21 

9,464.32 

64,007.37 

41.9288 

614.4942 

5,841.2600 

65 

66 

1,043.18 

8,314.11 

54,543.05 

41.1279 

572.5654 

5,226.7658 

66 

67 

943.001 

7,270.934 

46,228.937 

40.2835 

531.4375 

4,654.2004 

67 

68 

849.339 

6,327.933 

38,958.003 

39.2952 

491.1540 

4,122.7629 

68 

69 

761.967 

5,478.594 

32,630.070 

38.2728 

451.8588 

3,631.6089 

69 

70 

680.564 

4,716.627 

27,151.476 

37.0965 

413.5860 

3,179.7501 

70 

71 

604.947 

4,036.063 

22,434.849 

35.8253 

376.4895 

2,766.1641 

71 

72 

534.878 

3,431.116 

18,398.786 

34.4228 

340.6642 

2,389.6746 

72 

73 

470.180 

2,896.238 

14,967.670 

32.8900 

306.2414 

2,049.0104 

73 

74 

410.676 

2,426.058 

12,071.432 

31.2686 

273.3514 

1,742.7690 

74 

75 

356.161 

2,015.382 

9,645.374 

29.4987 

242.0828 

1,469.4176 

75 

76 

306.503 

1,659.221 

7,629.992 

27.6150 

212.5841 

1,227.3348 

76 

77 

261.538 

1,352.718 

5,970.771 

25.6589 

184.9691 

1,014.7507 

77 

78 

221.075 

1,091.180 

4,618.053 

23.6054 

159.3102 

829.7816 

78 

79 

184.956 

870.105 

3,526.873 

21.4942 

135.7048 

670.4714 

79 

80 

152.993 

685.149 

2,656.768 

19.3502 

114.2106 

534.7666 

80 

81 

124.982 

532.156 

1,971.619 

17.1949 

94.8604 

420.5560 

81 

82 

100.713 

407.174 

1,439.463 

15.0788 

77.6655 

325.6956 

82 

83 

79.9335 

306.4614 

1,032.2888  ; 

13.0049 

62.5867 

248.0301 

83 

84 

62.4041 

226.5279 

725.8274 

11.0398 

49.5818 

185.4434 

84 

85 

47.8320 

164.1238 

499.2995 

9.18883 

38.54196 

135.86156 

85 

86 

35.9357 

116.2918 

335.1757 

7.48689 

29.35313 

97.31960 

86 

87 

26.4147 

80.3561 

218.8839 

5.97784 

21.86624 

67.96647 

87 

88 

18.9417 

53.9414 

138.5278 

4.63802 

15.88840 

46.10023 

88 

89 

13.2315 

34.9997 

84.5864 

3.65240 

11.25038 

30.21183 

89 

90 

8.83015 

21.76824 

49.58671 

2.73362 

7.59798 

18.96145 

90 

91 

5.59670 

12.93809 

27.81847 

1.89306 

4.86436 

11.36347 

91 

92 

3.38684 

7.34139 

14.88038 

1.24526 

2.97130 

6.49911 

92 

93 

1.94988 

3.95455 

7.53899 

.781790 

1.726036 

'  3.527809 

93 

94 

1.05772 

2.00467 

3.58444 

.461455 

.944246 

1.801773 

94 

95 

.536392 

.946947 

1.579772 

.253015 

.482791 

.857527 

95 

96 

.253015 

.410555 

.632825 

.133387 

.229776 

.374736 

96 

97 

.105306 

.157540 

.222270 

.059607 

.096389 

.144960 

97 

98 

.039738 

.052234 

.064730 

.024993 

.036782 

.048571 

98 

99 

.012496 

.012496 

.012496 

.011789 

.011789 

.011789 

99 

*36 


TABLE    XXXYIII. 


LOGABITHMS  OP  COMMUTATION  COLUMNS.         6  PER  CENT. 


AGE. 
10 

AD,. 

ANa,. 

Aba?. 

ACa,. 

AMa,. 

ARai. 

AGE. 

4.746941 

5.936905 

7.100313 

2.533211 

3.838209 

5.180885 

10 

11 

4.718813 

5.907915 

7.069429 

:  2.506562 

3.816140 

5.160694 

11 

12 

4.690674 

5.878866 

7.038405 

■    2.479235 

3.794309 

5.140591 

12 

13 

4.662529 

5.849755 

7.007236 

2.452576 

3.772759 

5.120571 

13 

14 

4.634375 

5.820576 

6.975912 

2.426592. 

3.751468 

5.100623 

14 

15 

4.606207 

5.791327 

6.944427 

^  2.399927 

3.730411 

5.080738 

15 

16 

4.578028 

5.762000 

6.912775 

2.373257 

3.709631 

5.060907 

16 

17 

4.549840 

5.732595 

6.880945 

2.347268 

3.689138 

5.041120 

17 

18 

4.521637 

5.703104 

6.848931 

2.321278 

3.668908 

5.021367 

18 

19 

4.493420 

5.673522 

6.816723 

2.295286 

3.648951 

5.001636 

19 

20 

4.465187 

5.643844 

6.784313 

2.2699,81 

3.629276 

4.981915 

20 

21 

4.436934 

5.614064 

6.751690 

2.244675 

3.609860 

4.962192 

21 

22 

4.408661 

5.584174 

6.718844 

2.219369 

3.590711 

4.942456 

22 

23 

4.380367 

5.554170 

6.685766 

2.194749 

3.571838 

4.922691 

23 

24 

4.352049 

5.524042 

6.652442 

2.170127 

3.553218 

4.902885 

24 

25 

4.323704 

5.493786 

6.618864 

2.145505 

3.534859 

4.883023 

25 

26 

4.295334 

5.463389 

6.585016 

2.122242 

3.516769 

4.863092 

26 

27 

4.266927 

5.432847 

6.550888 

2.098294 

3.498898 

4.843073 

27 

28 

4.238487 

5.402148 

6.516466 

2.075016 

3.481280 

4.822953 

28 

29 

4.210009 

5.371283 

6.481735 

2.053069 

3.463894 

4.802714 

29 

30 

4.181485 

5.340242 

6.446681 

2.030431 

3.446694 

4.782338 

30 

31 

4.152916 

5.309013 

6.411288 

2.008438 

3.429712 

4.761810 

31 

32 

4.124296 

5.277586 

6.375539 

1.987075 

3.412929 

4.741108 

32 

33 

4.095621 

5.245948 

6.339418 

1.966323 

3.396325 

4.720214 

33 

34 

4.066884 

5.214084 

6.302904 

1.946164 

3.379883 

4.699109 

34 

35 

4.038078 

5.181981 

6.265982 

1.927208 

3.363583 

4.677769 

35 

36 

4.009191 

5.149625 

6.228628  | 

1.907538 

3.347384 

4.656174 

36 

37 

3.980226 

5.116999 

6.190824 

1.889023 

3.331316 

4.634303 

37 

38 

3.951173 

5.084087 

6.152545 

1.871609 

3.315341 

4.612129 

38 

39 

3.922017 

5.050869 

6.113768 

1.854643 

3.299419 

4.589628 

39 

40 

3.892751 

5.017327 

6.074469 

1.838677 

3.283536 

4.566774 

40 

41 

3.863362 

4.983438 

6.034620 

1.822515 

3.267656 

4.543541 

41 

42 

3.833846 

4.949183 

5.994195 

1.808374 

3.251787 

4.519901 

42 

43 

3.804176 

4.914537 

5.953162 

1.793953 

3.235854 

4.495821 

43 

44 

3.774351 

4.879475 

5.911492 

1.780837 

3.219864 

4.471271 

44 

45 

3.744346 

4.843970 

5.869151 

1.768404 

3.203765 

4.446219 

45 

46 

3.714147 

4.807993 

5.826103 

1.756585 

3.187528 

4.420630 

46 

47 

3.683735 

4.771513 

5.782311 

1.745789 

3.171121 

4.394466 

47 

48 

3.653086 

4.734498 

5.737737 

1.735444 

3.154497 

4.367689 

48 

49 

3.622179 

4.696912 

5.692338 

1.725933 

3.137626 

4.340259 

49 

50 

3.590989 

4.658717 

5.646069 

1.717149 

3.120461 

4.312131 

50 

51 

3.559483 

4.619872 

5.598884 

1.708991 

3.102955 

4.283259 

51 

52 

3.527633 

4.580334 

5.550731 

1.701365 

3.085060 

4.253595 

52 

53 

3.495404 

4.540056 

5.501555 

1.694181 

3.066727 

4.223087 

53 

54 

3.462761 

4.498988 

5.451301 

1.687359 

3.047907 

4.191680 

54  i 

TABLE    XXXYIII. 


LOGARITHMS  OF  COMMUTATION  COLUMNS.        6  PER  CENT. 


*37 


AQrB. 

W„. 

AN«. 

Aba). 

AOa,. 

AMa,. 

AE«,. 

AGE, 

55 

55 

3.429664 

4.457075 

5.399907 

1.681515 

3.028548 

4.159313 

56 

3.396059 

4.414259 

5.347307 

1.675499 

3.008563 

4.125924 

56 

57 

3.361903 

4.370478 

5.293431 

1.670247 

2.987909 

4.091446 

57 

58 

3.337131 

4.325663 

5.238204 

1.664713 

2.966491 

4.055805 

58 

59 

3.291693 

4.279742 

5.181546 

1.659185 

2.944254 

4.018926 

59 

60 

3.255522 

4.232636 

5.123370 

1.653898 

2.921121 

3.980725 

60 

61 

3.218540 

4.184259 

5.063583 

1.648520 

2.896990 

3.941113 

61  . 

62 

3.180664 

4.134521 

5.002088 

1.642520 

2.871763 

3.899992 

62  i 

63 

3.141817 

4.083319 

4.938775 

1.636420 

2.845358 

3.857260 

63 

64 

3.101889 

4.030548 

4.873531 

1.629738 

2.817649 

3.812805 

64 

65 

3.060777 

3.976089 

4.806230 

1.622512 

2.788518 

3.766507 

65 

66 

3.018357 

3.919816 

4.736739 

1.614137 

2.757825 

3.718233 

66 

67 

2.974512 

3.861590 

4.664913 

1.605127 

2.725452 

3.667845 

67 

68 

2.929081 

3.801262 

4.590597 

1.594339 

2.691218 

3.615188 

68 

69 

2.881936 

3.738669 

4.513618 

1.582890 

2.655003 

3.560099 

69 

70 

2.832869 

3.673631 

4.433794 

1.569333 

2.616566 

3.502393 

70 

71 

2.781717 

3.605958 

4.350923 

1.554190 

2.575753 

3.441878 

71 

72 

2.728255 

3.535435 

4.264789 

•  1.536846 

2.532327 

3.378338 

72 

73 

2.672264 

3.461835 

4.175154 

1.517064 

2.486064 

3.311544 

73 

74 

2.613499 

3.384901 

4.081758 

1.495109 

2.436721 

3.241240 

74 

75 

2.551646 

3.304357 

3.984319 

1.469803 

2.383964 

3.167145 

i 
75 

76 

2.486434 

3.219904 

3.882525 

1.441146 

2.327531 

3.088963 

76 

77 

2.417535 

3.131207 

3.776031 

1.409239 

2.267099 

3.006359 

77 

78 

2.344540 

3.037896 

3.664459 

1.373012 

2.202244 

2.918964 

78 

79 

2.267069 

2.939571 

3.547390 

1.332321 

2.132595 

2.826380 

79 

80 

2.184671 

2.835785 

3.424354 

1.286685 

2.057706 

2.728164 

80 

81 

2.096849 

2.726039 

3.294823 

1.235400 

1.977085 

2.623824 

81 

82 

2.003086 

2.609780 

3.158200 

1.178367 

1.890228 

2.512812 

82 

83 

1.902729 

2.486376 

3.013801 

1.114107 

1.796482 

2.394504 

83 

84 

1.795213 

2.355122 

2.860833 

1.042961 

1.695322 

2.268211 

84 

85 

1.679719 

2.215172 

2.698362 

0.963260 

1.585934 

2.133097 

85 

86 

1.555526 

2.065549 

2.525272 

0.874302 

1.467654 

1.988200 

86 

87 

1.421846 

1.905019 

2.340214 

0.776544 

1.339774 

1.832295 

87 

88 

1.277419 

1.731922 

2.141537 

0.666332 

1.201070 

1.663703 

88 

89 

1.121609 

1.544064 

1.927300 

0.562578 

1.051167 

1.480177 

89 

90 

0.945968 

1.337823 

1.695365 

0.436739 

0.880698 

1.277871 

90 

91 

0.747932 

1.111870 

1.444333 

0.277165 

0.687025 

1.055511 

91 

92 

0.529795 

0.865778 

1.172614 

0.095261 

0.472947 

0.812854 

92 

93 

0.290008 

0.597098 

0.877313 

1.893090 

0.237050 

0.547505 

93 

94 

0.024370 

0.302043 

0.554421 

1.664129 

1.975085 

0.255700 

94 

95 

1.729482 

T.  976326 

0.198594 

T.  403146 

T.  683759 

T.  933248 

95 

96 

1.403146 

1.613372 

1.801283 

1.125115 

1.361304 

1.573725 

96 

97 

1.022452 

1.197391 

1.346881 

2.775298 

2.984027 

1.161248 

97 

98 

2.599206 

2.717953 

2.811106 

2.397809 

2.565635 

2.686377 

98 

99 

2.096779 

2.096779 

2.096779 

2.071474 

2.071474 

2.071474 

99 

^38 


TABLE    XXXIX. 

COMMUTATION  COLUMNS.         7  PER  CENT 


Aa£. 

•  Bo-,. 

N«,. 

S«,. 

c«,. 

M„. 

R«,. 

AGE. 

10 

50,834.9 

697,841.8 

9,179,521.1 

307.8601 

5,181.6666  '97,313.2662 

10 

11 

47,201.4 

647,006.9 

8,481,679.3 

286.8318 

4,873.8065  92,131.5996 

11 

12 

43,826.7 

599,805.5 

7,834,672.4 

266.8222 

4,586.9747  87,257.7931 

12 

13 

40,692.6 

555,978.8 

7,234,866.9 

248.5908 

j  4,320.1525  82,670.8184 

13 

14 

37,781.9 

515,286.2 

6,678,888.1 

231.9654 

4,071.6617  78,350.6659 

14 

15 

35,078.3 

477,504.3 

6,163,601.9 

216.1127 

3,839.5963  74,279.1042 

15 

16 

32,567.3 

442,426.0 

5,686,097.6 

201.3413 

3,623.4836  70,439.5079 

16 

17 

30,235.4 

409,858.7 

5,243,671.6 

187.8736 

3,422.1423 

66,816.0243 

17 

18 

28,069.5 

379,623.3 

4,833,812.9 

175.3063 

3,234.2687 

63,393.8820 

18 

19 

26,057.9 

351,553.8 

4,454,189.6 

163.5792 

3,058.9624 

60,159.6133 

19 

20 

24,189.6 

325,495.9 

4,102,635.8 

152.8778 

2,895.3832  '57,100.6509 

20 

21 

22,454.2 

301,306.3 

3,777,139.9 

142.8764 

2,742.5054  [54,205.2677 

21 

22 

20,837.6 

278,852.1 

3,475,833.6 

133.5294 

2,599.6290  51,462.7623 

22 

23 

19,345.3 

258,014.5 

3,196,981.5 

124.9910 

2,466.0996  1 48,863. 1333 

23 

24 

17,954.7 

238,669.2 

2,938,967.0 

116.9982 

2,341.1086  146,397.0337 

24 

25 

16,666.9 

220,714.5 

2,700,297.8 

109.5163 

2,224.1104  44,055.9251 

25 

26 

15,463.5 

204,047.6 

2,479,583.3 

102.8345 

2,114.5941  141,831.8147 

26 

27 

14,349.1 

188,584.1 

2,275,535.7 

96.4078 

2,011.7596  ; 39,717.2206 

27 

28 

13,313.9 

174,235.0 

2,086,951.6 

90.5224 

1,915.3518  37,705.4610 

28 

29 

12,352.4 

160,921.1 

1,912,716.6 

85.2573 

1,824.8294 

35,790.1092 

29 

30 

11,459.0 

148,568.72 

1,751,795.48 

80.1708 

1,739.5721 

33,965.2798 

30 

31 

10,629.2 

137,109.72 

1,603,226.76 

75.4997 

1,659.4013 

32,225.7077 

31 

32 

9,858.32 

126,480.52 

1,466,117.04 

71.2038 

1,583.9016 

30,566.3064 

32 

33 

9.142.19 

116,622.20 

1,339,636.52 

67.2472 

1,512.6978 

28,982.4048 

33 

34 

8,476.86 

107,480.01 

1,223,014.32 

63.5971 

1,445.4506 

27,469.7070 

34 

35 

7,858.71 

99,003.15 

1,115,534.31 

60.3119 

1,381.8535 

26,024.2564 

35 

36 

7,284.27 

91,144.44 

1,016,531.16 

57.1026 

1,321.5416 

24,642.4029 

36 

37 

6,750.61 

83,860.17 

925,386.72 

54.2079 

1,264.4390 

23,320.8613 

37 

38 

6,254.78 

77,109.56 

841,526.55 

51.5905 

1,210.2311 

22,056.4223 

38 

39 

5,794.01 

70,854.78 

764,416.99 

49.1504 

1,158.6406 

20,846.1912 

39 

40 

5,365.81 

65,060.77 

693,562.21 

46.9335 

1,109.4902 

19,687.5506 

40 

41 

4,967.83 

59,694.96 

628,501.44 

44.7964 

1,062.5567 

18,578.0604 

41 

42 

'4,598.04 

54,727.13 

568,806.48 

42.9560 

1,017.7603 

17,515.5037 

42 

43 

4,254.28 

50,129.09 

514,079.35 

41.1647 

974.8043 

16,497.7434 

43 

44 

3,934.80 

45,874.81 

463,950.26 

39.5668 

933.6396 

15,522.9391 

44 

45 

3,637.81 

41,940.01 

418,075.45 

38.0908 

894.0728 

14,589.2995 

45 

46 

3,361.73 

38,302.20 

376,135.44 

36.7217 

855.9820 

13,695.2267 

46 

47 

3,105.08 

34,940.47 

337,833.24 

35.4854 

819.2603 

12,839.2447 

47 

48 

2,866.47 

31,835.39 

302,892.77 

34.3263 

783.7749 

12,019.9844 

48 

49 

2,644.61 

28,968.92 

271,057.38 

33.2688 

749.4486 

11,236.2095 

49 

50 

2,438.33 

26,324.31 

242,088.46 

32.2979 

716.1798 

10,486.7609 

50 

51 

2,246.51 

23,885.98 

215,764.15 

31.4007j  683.8819 

9,770.5811 

51 

52 

2,068.15 

21,639.47 

191,878.17 

30.56581  652.4812 

•9,086.6992 

52 

53 

1,902.28 

19,571.32 

170,238.70 

29.7834{  621.9154 

8,434.2180 

53 

54 

1,748.05 

17,669.04 

150,667.38 

29.0451   592.1320 

7,812.3026 

54 

TABLE    XXXIX. 

COMMUTATION  COLUMNS.         7  PER  CENT. 


♦39 


AGE. 

D«,. 

N«,. 

Si. 

c„. 

M„. 

Ka,. 

AGR 

55 

1,604.65 

15,920.99 

132,998.34 

28.3891 

563.0869 

7,220.1706 

55 

56 

1,471.38 

14,316.34 

117,077.35 

27.7369 

534.6978 

6,657.0837 

56 

57 

1,347.29 

12,845.06 

102,761.01 

27.1474 

506.9609 

6,122.3859 

57 

58 

1,232.00 

11,497.77 

89,915.95 

26.5532 

479.8135 

5,615.4250 

58 

59 

1,124.85 

10,265.77 

78,418.18 

25.9723 

453.2603 

5,135.6115 

59 

60 

1,025.29 

9,140.916 

68,152.409 

25.4183 

427.2880 

4,682.3512 

60 

61 

932.797 

8,115.626 

59,011.493 

24.8708 

401.8697 

4,255.0632 

61 

62 

846.904 

7,182.829 

50,895.867 

24.3003 

376.9989 

3,853.1935 

62 

63 

767.199 

6,335.925 

43,713.038 

23.7374 

352.6986 

3,476.1946 

63 

64 

693.269 

5,568.726 

37,377.113 

23.1566 

328.9612 

3,123.4960 

64 

65 

624.758 

4,875.457 

31,808.387 

22.5616 

305.8046 

2,794.5348 

65 

66 

561.326 

4,250.699 

26,932.930 

21.9239 

283.2430 

2,488.7302 

66 

67 

502.680 

3,689.373 

22,682.231 

21.2730 

261.3191 

2,205.4872 

67 

68 

448.521 

3,186.693 

18,992.858 

20.5572 

240.0461 

1,944.1681 

68 

69 

398.621 

2,738.172 

15,806.165 

19.8352 

219.4889 

1,704.1220 

69 

70 

352.709 

2,339.551 

13,067.993 

19.0459 

199.6537 

1,484.6331 

70 

71 

310.588 

1,986.842 

10,728.442 

18.2213 

180.6078 

1,284.9794 

71 

72 

272.048 

1,676.254 

8,741.600 

17.3443 

162.3865 

1,104.3716 

72 

73 

236.906 

1,404.206 

7,065.346 

16.4172 

145.0422 

941.9851 

73 

74 

204.991 

1,167.300 

5,661.140 

15.4620 

128.6250 

796.9429 

74 

75 

176.118 

962.309 

4,493.840 

14.4504 

113.1630 

668.3179 

75 

76 

150.146 

786.191 

3,531.531 

13.4013 

98.71266 

555.15498 

76 

77 

126.922 

636.045 

2,745.340 

12.3357 

85.31136 

456.44232 

77 

78 

106.283 

509.123 

2,109.295 

11.2423 

72.97566 

371.13096 

78 

79 

88.0874 

402.8396 

1,600.1718 

10.1412 

61.73336 

298.16530 

79 

80 

72.1835 

314.7522 

1,197.3322 

9.04428 

51.59216 

236.42194 

80 

81 

58.4168 

242.5687 

882.5800 

7.96179 

42.54788 

184.82978 

81 

82 

46.6334 

184.1519 

640.0113 

6.91672 

34.58609 

142.28190 

82 

83 

36.6660 

137.5185 

455.8594 

5.90966 

27.66937 

107.69581 

83 

84 

28.3576 

100.8525 

318.3409 

4.96979 

21.75971 

80.02644 

84 

85 

21.5326 

72.4949 

217.4884 

4.09788 

16.78992 

58.26673 

85 

86 

16.0260 

50.9623 

144.9935 

3.30768 

12.69204 

41.47681 

86 

87 

11.6699 

34.9363 

94.0312 

2.61630 

9.38436 

28.78477 

87 

88 

8.29016 

23.26642 

59.09493 

2.01094 

6.76806 

19.40041 

88 

89 

5.73687 

14.97626 

35:82851 

1.56879 

4.75712 

12.63235 

89 

90 

3.79277 

9.23939 

20.85225 

.16319 

3.18833 

7.87523 

90 

91 

2.38145 

5.44662 

11.61286 

.797990 

2.025136 

4.686905 

91 

92 

1.42767 

3.06517 

6.16624 

.520014 

1.227146 

2.661769 

92 

93 

.814258 

1.637496 

3.101066 

.323420 

.707132 

1.434623 

93 

94 

.437568 

.823238 

1.463570 

.189116 

.383712 

.727491 

94 

95 

.219827 

.385670 

.640332 

.102723 

.194596 

.343779 

95 

96 

.102723 

.165843 

.254662 

.053648 

.091873 

.149183 

96 

97 

.042354 

.063120 

.088819 

.023750 

.038225 

.057310 

97 

98 

.015833 

.020766 

.025699 

.009865 

.014475 

.019085 

98 

99 

.004933 

.004933 

.004933 

.004610 

.004610 

.004610 

99 

*40 


TABLE     XXXIX. 

LOGARITHMS  OF  COMMUTATION  COLUMNS.        7  PER   CENT. 


AOE. 

10 

ADa,. 

AN«. 

Aba;. 

ACa,. 

AMa,. 

AEa,. 

AGE. 

4.706162 

5.843757 

6.962820 

2.488353 

3.714470 

4.988172 

10 

11 

4.673955 

5.810909 

6.928482 

2.457627 

3.687868 

4.964409 

11 

12 

4.641739 

5.778010 

6.894021 

2.426222 

3.661526 

4.940804 

12 

13 

4.609516 

5.745058 

6.859431 

2.395485 

3.635499 

4.917352 

13 

14 

4.577284 

5.712049 

6.824704 

2.365423 

3.609761 

4.894043 

14 

15 

4.545038 

5.678977 

6.789834 

2.334680 

3.584286 

4.870867 

15 

16 

4.512782 

5.645841 

6.754814 

2.303933 

3.559126 

4.847816 

16 

17 

4.480516 

5.612635 

6.719636 

2.273866 

3.534298 

4.824881 

17 

18 

4.448235 

5.579353 

6.684290 

2.243798 

3.509776 

4.802047 

18 

119 

4.415939 

5.545992 

6.648769 

2.213728 

3.485574 

4.779305 

19 

20 

4.383628 

5.512545 

6.613063 

2.184344 

3.461706 

4.756641 

20 

21 

4.351298 

5.479008 

6.577163 

2.154961 

3.438147 

4.734041 

21 

22 

4.318847 

5.445374 

6.541059 

2.125577 

3.414911 

4.711493 

22 

23 

4.286575 

5.411644 

6.504740 

2.096879 

3.392011 

4.688981 

23 

24 

4.254179 

5.377796 

6.468195 

2.068179 

3.369422 

4.666490 

24 

25 

4.221856 

5.343831 

6.431412 

2.039479 

3.347156 

4.644004 

25 

26 

4.189308 

5.309732 

6.394379 

2.012139 

3.325227 

4.621507 

26 

27 

4.156823 

5.275505 

6.357084 

1.984112 

3.303576 

4.598979 

27 

28 

4.124305 

5.241135 

6.319512 

1.956756 

3.282249 

4.576404 

28 

29 

4.091750 

5.206613 

6.281651 

1.930731 

3.261222 

4.553763 

29 

30 

4.059148 

5.171927 

6.243484 

1.904016 

3.240442 

4.531035 

30 

31 

4.026501 

5.137068 

6.204995 

1.877945 

3.219951 

4.508202 

31 

32 

3.993803 

5.102024 

6.166169 

1.852503 

3.199728 

4.485243 

32 

33 

3.961050 

5.066781 

6.126987 

1.827674 

3.179752 

4.462134 

33 

34 

3.928235 

5.031328 

6.087431 

1.803438 

3.160004 

4.438854 

34 

35 

3.895351 

4.995649 

6.047483 

1.780403 

3.140462 

4.415378 

35 

36 

3.862386 

4.959730 

6.007120 

1.756656 

3.121081 

4.391683 

36 

37 

3.829343 

4.923556 

5.96G323 

1.734062 

3.101898 

4.367745 

37 

38 

3.796212 

4.887108 

5.925068 

1.712570 

3.082868 

4.343535 

38 

39 

3.762979 

4.850369 

5.883330 

1.691527 

3.063949 

4.319027 

39 

40 

3.729635 

4.813319 

5.841085 

1.671483 

3.045123 

4.294192 

40 

41 

3.696167 

4.775938 

5.798306 

1.651243 

3.026352 

4.269000 

41 

42 

3.662573 

4.738203 

5.754964 

1.633024 

3.007645 

4.243423 

42 

43 

'3.628826 

4.700090 

5.711030 

1.614525 

2.988917 

4.217425 

43 

44 

3.594923 

4.661574 

5.666471 

1.597331 

2.970179 

4.190974 

44 

45 

3.560840 

4.622628 

5.621254 

1.580820 

2.951373 

4.164034 

45 

46 

3.526563 

4.588224 

5.575344  : 

1.564923 

2.932465 

4.136569 

46 

47 

3.492073 

4.543329 

5.528702 

1.550050 

2.913422 

4.108539 

47 

48 

3.457347 

4.502910 

5.481289 

1.535627 

2.894191 

4.079904 

48 

49 

3.422362 

4.461933 

5.433061 

1.522037 

2.874742 

4.050620 

49 

50 

3.387093 

4.420357 

5.383974 

1.509175 

2.855022 

4.020641 

50 

51 

3.351509 

4.378143 

5.333979 

1.496940 

2.834981 

3.989920 

51 

52 

3.315582 

4.335247 

5.283026 

1.485235 

2.814568 

3.958406 

52 

53 

3.279275 

4.291620 

5.231059 

1.473974 

2.793731 

3.926045 

53 

54 

3.242554 

4.247213 

5.178019 

1 

1.463073 

2.772419 

3.892779 

54 

TABLE    XXXIX. 

LOGARITHMS  OP  COMMUTATION  COLUMNS.         7  PER  CENT. 


HX 


kQB. 

55 

XD^. 

AN:,. 

ASa;. 

aC^. 

AMa,. 

ARa,. 

AGE. 

55 

3.205379 

4.201970 

5.123846 

1.453152 

2.750575 

3.858547 

56 

3.167695 

4.155832 

5.068473 

1.443058 

2.728108 

3.823284 

56 

57 

3.129462 

4.108736 

5.011828 

1.433728 

2.704975 

3.786920 

57 

58 

3.090612 

4.060614 

4.953837 

1.424116 

2.681073 

3.749383 

58 

59 

3.051096 

4.011391 

4.894417 

1.414510 

2.656348 

3.710592 

59 

60 

3.010847 

3.960990 

4.833481 

1.405146 

2.630721 

3.670464 

60 

61 

2.969787 

3.909322 

4.770936 

1.395690 

2.604085 

3.628906 

61 

62 

2.927834 

3.856295 

-  4.706683 

1.385611 

2.576340 

3.585821 

62 

63 

2.884908 

3.801810 

4.640611 

1.375434 

2.547404 

3.541104 

63 

64 

2.840902 

3.745756 

4.572605 

1.364674 

2.517145 

3.494641 

64 

65 

2.795712 

3.688015 

4.502541 

1.353370 

2.485444 

3.446310 

65 

66 

2.749215 

3.628460 

4.430284 

1.340917 

2.452159 

3.395976 

66 

67 

2.701292 

3.566953 

4.355685 

1.327829 

2.417171 

3.343505 

67 

68 

2.651783 

3.503340 

4.278591 

1.312963 

2.380295 

3.288734 

68 

69 

2.600560 

3.437461 

4.198826 

1.297436 

2.341413 

3.231501 

69 

70 

2.547416 

3.369133 

4.116209 

1.279801 

2.300277 

3.171019 

70 

71 

2.492185 

3.298163 

4.030537 

1.260580 

2.256737 

3.108896 

71 

72 

2.434645 

3.224340 

3.941591 

1.239158 

2.210550 

3.043115 

72 

73 

2.374576 

3.147431 

3.849134 

1.215298 

2.161494 

2.974044 

73 

74 

2.311734 

3.067183 

3.752904 

1.189265 

2.109326 

2.901427 

74 

75 

2.245803 

2.983314 

3.052618 

1.159881 

2.053705 

2.824983 

75 

76 

2.176513 

2.895528 

3.547963 

1.127147 

1.994373 

2.744414 

76 

77 

2.103536 

2.803488 

3.438596 

1.091162 

1.931007 

2.659386 

77 

78 

2.026462 

2.706823 

3.324137 

1.050857 

1.S63178 

2.569527 

78 

79 

1.944914 

2.605132 

3.204166 

1.006088 

1.790520 

2.474442 

79 

80 

1.858438 

2.497969 

3.078215 

0.956374 

1.712584 

2.373688 

80 

'  81 

1.766538 

2.384835 

2.945754 

0.901011 

1.628878 

2.266772 

81 

82 

1.668697 

2.265176 

2.806188 

0.839900 

1.538901 

2.153150 

82 

83 

1.564263 

2.138361 

2.658830 

0.771562 

1.441999 

2.032199 

83 

84 

•  1.452669 

2.003687 

2.502892 

0.696338 

1.337653 

1.903233 

84 

85 

1.333096 

1.860307 

2.337436 

0.612559 

1.225049 

1.765421 

85 

86 

1.204825 

1.707249 

2.161349 

0.519523 

1.103531 

1.617805 

86 

87 

1.067067 

1.543277 

1.973272 

0.417688 

0.972405 

1.459163 

87 

88 

0.918563 

1.366730 

1.771550 

0.303398 

0.830464 

1.287811 

88 

89 

0.758675 

1.175403 

1.554229 

0.195566 

0.677344 

1.101484 

89 

90 

0.578956 

0.965644 

1.319153 

0.065649 

0.503563 

0.896263 

90 

91 

0.376842 

0.736127 

1.064939 

1.901997 

0.306454 

0.670886 

91 

92 

0.154628 

0.486455 

0.790021 

1.716015 

0.088896 

0.425170 

92 

93 

1.910762 

0.214181 

0.491511 

1.509767 

1.849510 

0.156738 

93 

94 

1.641046 

1.915525 

0.165413 

1.276727 

1.584005 

1.861828 

94 

95 

1.342080 

T.  586216 

1.806405 

1.011666 

1.289134 

1.536279 

95 

96 

1.011666 

1.219697 

1.405964 

2.729557 

2".  963188 

1.173719 

96 

97 

2.626895 

2.800167 

2.948506 

2.375662- 

2.582347 

2.758230 

97 

98 

2.199571 

2.317353 

2.409916 

3.994096 

2.160619 

2.280692 

98 

99 

3.693066 

3.693066 

3.693066 

3.663682 

3.663682 

3.663682 

99 

*42 


TABLE    XL. 


COMMUTATION  COLUMNS,        8  PER  CENT. 


AOE. 

10 

J)x- 

N^. 

i^x- 

Co,. 

Mo,. 

Rx. 

AGE. 

46,319.3 

571,113.6 

6,833,398.9 

277.916 

4,014.670 

64,935.891 

10 

11 

42,610.4 

524,794.3 

6,262,285.3 

256.536 

3,736.754 

60,921.221 

11 

12 

39,197.6 

482,183.9 

5,737,491.0 

236.430 

3,480.218 

57,184.467 

12 

13 

36,057.5 

442,986.3 

5,255,307.1 

218.235 

3,243.788 

53,704.249 

13 

14 

33,168.4 

406,928.8 

4,812,320.8 

201.755 

3,025.553 

50,460.461 

14 

15 

30,509.8 

373,760.4 

4,405,392.0 

186.226 

2,823.798 

47,434.908 

15 

16 

28,063.5 

343,250.6 

4,031,631.6 

171.891 

2,637.572 

44,611.110 

16 

17 

25,812.9 

315,187.1 

3,688,381.0 

158.908 

2,465.681 

41,973.538 

17 

18 

23,741.9 

289,374.3 

3,373,193.9 

146.906 

2,^06.773 

39,507.857 

18 

19 

21,836.4 

265,632.3 

3,083,819.7 

135.809 

2,159.867 

37,201.084 

19 

20 

20,083.0 

243,795.9 

2,818,187.4 

125.749 

2,024.058 

35,041.217 

20 

21 

18,469.6 

223,712.9 

2,574,391.5 

116.434 

1,898.309 

33,017.159 

21 

22 

16,985.1 

205,243.3 

2,350,678.6 

107.810 

1,781.875 

31,118.850 

22 

23 

15,619.1 

188,258.2 

2,145,435.3 

99.9814 

1,674.0644 

29,336.9753 

23 

24 

14,362.2 

172,639.1 

1,^57,177.1 

92.7214 

1,574.0830 

27,662.9109 

24 

25 

13,205.6 

158,276.9 

1,784,538.0 

85.9883 

1,481.3616 

26,088.8279 

25 

26 

12,141.4 

145,071.3 

1,626,261.1 

79.9944 

1,395.3733  '  24,607.4663 

26 

27 

11,162.1 

132,929.9 

1,481,189.8 

74.3007 

1,315.3789  I  23,212.0930 

27 

28 

10,260.9 

121,767.8 

1,348,259.9 

69.1189 

1,241.0782  :  21,896.7141 

28 

29 

9,431.72 

111,506.91 

1,226,492.13 

64.4959 

1,171.9593 

20,655.6359 

29 

30 

8,668.58 

102,075.19 

1,114,985.22 

60.0865 

1,107.4634 

19,483.6766' 

30 

31 

7,966.40 

93,406.61 

1,012,910.03 

56.0616 

1,047.3769 

18,376.2132 

31 

32 

7,320.22 

85,440.21 

919,503.42 

52.3823 

991.3153 

17,328.8363 

32 

33 

6,725.60 

78,119.99 

834,063.21 

49.0134 

938.9330 

16,337.5210 

33 

34 

6,178.39 

71,394.39 

755,943.22 

45.9239 

889.9196 

16,398.5880 

34 

35 

5,674.82 

65,216.00 

684,548.83 

43.1483 

843.9957 

14,508.6684 

35 

36 

5,211.31 

59,541.18 

619,332.83 

40.4740 

800.8474 

13,664.6727 

36 

37 

4,784.80 

54,329.87 

559,791.65 

38.0666 

760.3734 

12,863.8253 

37 

38 

4,392.31 

49,545.07 

505,461.78 

35.8931 

722.3068 

12,103.4519. 

38 

39 

4,031.07 

45,152.76 

455,916.71 

33.8788 

686. 4137* 

11,381.1451 

39 

40 

3,698.59 

41,121.69 

410,763.95 

32.0512 

652.5349 

10,694.7314 

40 

41 

3,392.56 

37,423.10 

369,642.26 

30.3084 

620.4837 

10,042.1965 

41 

42 

3,110.96 

34,030.54 

332,219.16 

28.7942 

590.1753 

9,421.7128 

42 

43 

2,851.72 

30,919.58 

298,188.62 

27.3380 

561.3811 

8,831.5375 

43 

44 

2,613.15 

28,067.86 

267,269.04 

26.0335 

534.0431 

8,270.1564 

44 

45 

2,393.54 

25,454.71 

239,201.18 

24.8303 

508.0096 

7,736,1133 

45 

46 

2,191.41 

23,061.17 

213,746.47 

23.7162 

483.1793 

7,228.1037 

46 

47 

2,005.37 

20,869.76 

190,685.30 

22.7055 

459.4631 

6,744.9244 

47 

48 

1,834.12 

18,864.39 

169,815.54 

21.7604 

436.7576 

6,285.4613 

48 

49 

1,676.50 

17,030.27 

150,951.15 

20.8948 

414.9972 

5,848.7037 

49 

50 

1,531.42 

15,353.77 

133,920.88 

20.0972 

394.1024 

5,433.7065 

50 

51 

1,397.88 

13,822.35 

118,567.11 

19.3580 

374.0052 

5,039.6041 

51 

52 

1,274.98 

12,424.47 

104,744.76 

18.6688 

354.6472 

4,665.5989 

52 

53 

1,161.87 

11,149.49 

92,320.29 

18.0225 

335.9784 

4,310.9517 

53 

54 

1,057.78 

9,987.62 

81,170.80 

17.4130 

317.9559 

3,974.9733 

54 

TABLE     XL. 


COMMUTATION  COLUMNS.        8  PER  CENT. 


H3 


AGE. 

Do,. 

N.. 

bfl)' 

0^ 

M«,. 

RfB- 

AGE. 

55 

962.011 

8,929.843 

71,183.180 

16.8622 

300.5429 

3,657.0174 

55 

56 

873.891 

7,967.832 

62,253.337 

16.3222 

283.6807 

3,356.4745 

56 

57 

792.835 

7,093.941 

54,285.505 

15.8274 

267.3-585 

3,072.7938 

57 

58 

718.279 

6,301.106 

47,191.564 

15.3376 

251.5311 

2,805.4353 

58 

59 

649.736 

5,582.827 

40,890.458 

14.8632 

236.1935 

2,553.9042 

59 

60 

586.745 

4,933.091 

35,307.631 

14.4114 

221.3303 

2,317.7107 

60 

61 

528.870 

4,346.346 

30,374.540 

13.9705 

206.9189 

2,096.3804 

61 

62 

475.724 

3,817.476 

26,028.194 

13.5236 

192.9484 

1,889.4615 

62 

63 

426.962 

3,341.752 

22,210.718 

13.0881 

179.4248 

3,696.5131 

63 

64 

382.247 

2,914.790 

18,868.966 

1 12.6496 

166.3367 

1,517.0883 

64 

65 

341.283 

2,532.543 

15,954.176 

12.2104 

153.6871 

1,350.7516 

65 

66 

303.792 

2,191.260 

13,421.633 

11.7554 

141.4767 

1,197.0645 

66 

67 

269.534 

1,887.468 

11,230.373 

11.3008 

129.7213 

1,055.5878 

67 

68 

238.268 

1,617.934 

9,342.905 

10.8195 

118.4205 

925.8665 

68 

69 

209.798 

1,379.666 

7,724.971 

10.3428 

107.6010 

807.4460 

69 

70 

183.916 

1,169.868 

6,345.305 

9.83926 

97.25822 

699.84498 

70 

71 

160.452 

985.952 

5,175.437 

9.32613 

87.41896 

602.58676 

71 

72 

139.241 

825.500 

4,189.485 

8.79508 

78.09283 

515.16780 

72 

73 

120.132 

686.259 

3,363.985 

8.24783 

69.29775 

437.07497 

73 

74 

102.985 

566.127 

2,677.726 

7.69603 

61.04992 

367.77722 

74 

75 

87.6605 

463.1417 

2,111.5992 

7.12596 

53.35389 

306.72730 

75 

76 

74.0413 

375.4812 

1,648.4575 

6.54739 

46.22793 

253.37341 

76 

77 

62.0095 

301.4399 

1,272.9763 

5.97096 

39.68054 

207.14548 

77 

78 

51.4451 

239.4304 

971.5364 

5.39136 

33.70958 

167.46494 

78 

79 

42.2430 

187.9853 

732.1060 

4.81826 

28.31822 

133.75536 

79 

80 

34.2957 

145.7423 

544.1207 

4.25731 

23.49996 

105.43714 

80 

81 

27.4979 

111.4466 

398.3784 

3.71307 

19.24265 

81.93718 

81 

82 

21.7480 

83.9487 

286.9318 

3.19582 

15.52958 

62.69453 

82 

83 

16;  9412 

62.2007 

202.9831 

2.70523 

12.33376 

47.16495 

83 

84 

12.9811 

45.2595 

140.7824 

2.25393 

9.62853 

34.83119 

Si 

85 

9.76558 

32.27839 

95.52286 

1.84129 

7.37460 

25.20266 

85 

86 

7.20090 

22.51281 

63.24447 

1.47247 

5.53331 

17.82806 

86 

87 

5.19504 

15.31191 

40.73166 

1.15391 

4.06084 

12.29475 

87 

88 

3.65633 

10.11687 

25.41975 

.878699 

2.906926 

8.233909 

88 

89 

2.50679 

6.46054 

15.30288 

.679154 

2.028227 

5.326983 

89 

j  90 

1.64194 

3.95375 

8.84234 

.498897 

1.349073 

3.298756 

90 

!  91 

1.02142 

2.31181 

4.88859 

.339094 

.850176 

1.949683 

91 

92 

.606667 

1.290385 

2.57678 

.218926 

.511082 

1.099507 

92 

93 

.342803 

.683718 

1.286398 

.134899 

.292156 

.588425 

93 

94 

.182511 

.340915 

.602680 

.078150 

.157257 

.296269 

94 

95 

.090841 

.158404 

.261765 

.04^056 

.079107 

.139012 

95 

96 

.042056 

.067563 

.103361 i 

.021761 

.037051 

.059905 

96 

97 

.017180 

.025507 

.035798 

.009544 

.015290 

.022854 

97 

98 

.006363 

.008327 

.010291 

.003928 

.005746 

.007564 

98 

99 

.001964 

.001964 

.001964 

.001818 

.001818 

.001818 

99 

♦44 


TABLE    XLI. 

COMMUTATION  COLUMNS.        9  PER  CENT. 


AQtE. 

^x 

^x- 

Saf. 

G^. 

Ma;. 

Ba,. 

AGE. 

10 

42,241.1 

473,006.5 

5,184,561.6 

251.121 

i 

;  3,185.523 

44,923.415 

10 

11 

38,502.2 

430,765.4 

4,711,555.1 

1  229.675 

2,934.402 

41,737.892 

11 

12 

35,093.4 

392,263.2 

4,280,789.7 

1  209.733 

:  2,704.727 

38,803.490 

12 

13 

31,986.0 

357,169.8 

3,888,526.5 

i  191.817 

2,494.994 

36,098.763 

13 

14 

29,153.2 

325,183.8 

3,531,356.7 

j  175.704 

2,303.177 

j  33,603.769 

14 

15 

26,570.4 

296,030.6 

3,206,172.9 

160.693 

2,127.473 

31,300.592 

15 

16 

24,215.8 

269,460.2 

2,910,142.3 

146.963 

i  1,966.780 

29,173.119 

16 

17 

22,069.4 

245,244.4 

2,640,682.1 

134.616 

1,819.817 

27,206.339 

17 

18 

20,112.5 

223,175.0 

2,395,437.7 

123.306 

1,685.201 

25,386.522 

18 

19 

18,328.6 

203,062.5 

2,172,262.7 

!  112.947 

1,561.895 

j  23,701.321 

19 

20 

16,702.2 

184,733.9 

1,969,200.2 

'  103.621 

1.448.948 

22.139.426 

20 

21 

15,219.5 

168,031.7 

1,784,466.3 

95.0650 

1,345.3274 

1  20,690.4780 

1  21 

22 

13,867.8 

152,812.2 

1,616,434.6 

^  87.2156 

1,250.2624 

■  19,345.1506  22 

23 

12,635.5 

138,944.4 

1,463,622.4 

I    80.1407 

1,163.0468 

18,094.8882 

23 

24 

11,512.1 

126,308.9 

1,324,678.0 

73.6396 

1,082.9061 

16,931.8414 

24 

25 

10,487.9 

114,796.8 

1,198,369.1 

1  67.6656 

1,009.2665 

15,848.9353  !  25 

26 

9,554.26 

104,308.94 

1,083,572.28 

i  62.3714 

941.6009 

14,839.6688  ^  26 

27 

8,703.02 

94,754.68 

979,263.34 

1  57.4006 

879.2295 

13,898.0679  '.   27 

28 

7,927.00 

86,051.66 

884,508.66 

i  52.9075 

821.8289 

13,018.8384  28 

29 

7,219.58 

78,124.66 

798,457.00 

48.9159 

768.9214 

12,197.0095 

29 

30 

6,574.55 

70,905.08 

720,332.34 

45.1535 

720.0055 

11,428.0881 

30 

31 

5,986.56 

64,330.53 

649,427.26 

41.7425 

674.8520 

10,708.0826 

31 

32 

5,450.50 

58,343.97 

585,096.73 

38.6450 

633.1095 

10,033.2306  32  | 

33 

4,961.82 

52,893.47 

526,752.76 

j  35.8279 

594.4645 

9,400.1211 

33 

34 

4,516.29 

47,931.65 

473,859.29 

33.2615 

558.6366 

8,805.6566 

34 

35 

4,110.13 

43,415.36 

425,927.64 

30.96,46 

525.3751 

8,247.0200 

35 

36 

3,739.80 

39,305.23 

382,512.28 

28.7789 

494.4105 

7,721.6449 

36 

37 

3,402.23 

35,565.43 

343,207.05 

26.8188 

465.6316 

7.227.2344 

37 

38 

3,094.49 

32,163.20 

307,641.62 

25.0555 

438.8128 

6,761.6028 

38 

39 

2,813.93 

•29,068.71 

275,478.42 

23.4325 

413.7573 

6,322.7900 

39 

40 

2,558.15 

26,254.78 

246,409.71 

21.9650 

390.3248 

5,909.0327 

40 

41 

2,324.96 

23,696.63 

220,154.93 

20.5801 

368.3598  ! 

5,518.7079 

41 

42 

2,112.41 

21,371.67 

196,458.30 

19.3726 

347.7797  : 

5,150.3481 

42 

43 

1,918.62 

19,259.26 

175,086.63 

18.2241 

328.4071  i 

4,802.5684 

43 

44 

1,741.98 

17,340.64 

155,827.37 

17.1952 

310.1830 

4,474.1613 

44 

45 

1,580.95 

15,598.66 

138,486.73 

16.2501 

292.9878 

4,163.9783 

45 

46 

1,434.16 

14,017.71 

122,888.07 

15.3786 

276.7377 

3,870.9905 

46 

47 

1,300.37 

12,583.55 

108,870.36 

14.5881  ! 

261.3591 

3,594.2528 

47 

48 

1,178.41 

11,283.18 

96,286.81 

13.8527  i 

246.7710 

3,332.8937 

48 

49 

1,067.26 

10,104.77 

85,003.63 

13.1796 

232.9183 

3,086.1227 

49 

50 

965.955 

9,037.511 

74,898.859 

12.5602 

219.7387 

2,853.2044 

50 

51 

873.636 

8,071.556 

65,861.348 

11.9872 

207.1785  j 

2,633.4657 

51 

52 

789.514 

7,197.920 

57,789.792 

11.4544 

195.1913  : 

2,4^6.2872 

52 

53 

712.871 

6,408.406 

50,591.872 

10.9564 

183.7369 

2,231.0959 

53 

54 

643.053 

5,695.535 

44,183.466 

10.4888 

172.7805 

2,047.3590 

54 

TABLE     XLI. 

COMMUTATION  COLUMNS.  9  PER  CENT. 


♦45 


A&E. 

D.. 

N.. 

s.. 

c„. 

M.. 

R«. 

AaE. 
55 

55 

579.469 

5,052.482 

38,487.931 

10.06385 

162.2917 

1,874.5785 

56 

521.559 

4,473.013 

33,435.449 

9.65214 

152.22788 

1,712.28676 

56 

57 

468.843 

3,951.454 

28,962.436 

9.27363 

142.57574 

1,560.05888 

57 

58 

420.857 

3,482.611 

25,010.982 

8.90421 

133.30211 

1,417.48314 

58 

59 

377.204 

3,061.754 

21,528.371 

8.54962 

124.39790 

1,284.18103 

59 

60 

337.508 

2,684.550 

18,466.617 

8.21372 

115.84828 

1,159.78313 

60 

61 

301.427 

2,347.042 

15,782.067 

7.88935 

107.63456 

1,043.93485 

61 

62 

268.649 

2,045.615 

13,435.025 

7.56693 

99.74521 

936.30029 

62 

63 

238.901 

1,776.966 

11,389.410 

7.25604 

92.17828 

836.55508 

63 

64 

211.918 

1,538.065 

9,612.444 

6.94860 

84.92224 

744.37680 

64 

65 

187.472 

1,326.147 

8,074.379 

6.64584 

77.97364 

659.45456 

65 

66 

165.347 

1,138.675 

6,748.232 

6.33950 

71.32780 

581.48092 

66 

67 

145.355 

973.328 

5,609.557 

6.03843 

64.98830 

510.15312 

67 

68 

127.315 

827.973 

4,636.229 

5.72817 

58.94987 

445.16482 

68 

69 

111.074 

700.658 

3,808.256 

5.42557 

53.22170 

386.21495 

69 

70 

96.4773 

589.5838 

3,107.5975 

5.11408 

47.79613 

332.99325 

70 

71 

83.3973 

493.1065 

2,518.0137 

4.80291 

42.68205 

285.19712 

71 

72 

71.7082 

409.7092 

2,024.9072 

4.48787 

37.87914 

242.51507 

72 

73 

61.2997 

338.0*010 

1,615.1980 

4.17001 

33.39127 

204.63593 

73 

74 

52.0681 

276.7013 

1,277.1970 

3.85533 

29.22126 

171.24466 

74 

75 

43.9136 

224.6332 

1,000.4957 

3.53700 

25.36593 

142.02340 

75 

76 

36.7507 

180.7196 

775.8625 

3.22001 

21.82893 

116.65747 

76 

77 

30.4963 

143.9689 

595.1429 

2.90958 

18.60892 

94.82854 

77 

78 

25.0686 

113.4726 

451.1740 

2.60305 

15.69934 

76.21962 

78 

79 

20.3957 

88.4040 

337.7014 

2.30500 

13.09629 

60.52028 

79 

80 

16.4067 

68.0083 

249.2974 

2.01796 

10.79129 

47.42399 

80 

81 

13.0340 

51.6016 

181.2891 

1.74385 

8.77333 

36.63270 

81 

82 

10.2140 

38.5676 

129.6875 

1.48715 

7.02948 

27.85937 

82 

83 

7.88346 

28.35357 

91.11993 

1.24731 

5.54233 

20.82989 

83 

84 

5.98522 

20.47011 

62.76636 

1.02969 

4.29502 

15.28756 

84 

85 

4.46134 

14.48489 

42.29625 

.833461 

3.265334 

10.992535 

85 

86 

3.25950 

10.02355 

27.81136 

.660399 

2.431873 

7.727201 

86 

87 

2.32997 

6.76405 

17.78781 

.512777 

1.771474 

5.295328 

87 

88 

1.62481 

4.43408 

11.02376  i 

.386898 

1.258697 

3.523854 

88 

89 

1.10376 

2.80927 

6.58968 

.296293 

.871799 

2.265157 

89 

90 

.716326 

1.705505 

3.780411 

.215656 

.575506 

1.393358 

90 

91 

.441525 

.989179 

2.074906 

.145234 

.359850 

.817852 

91 

92 

.259835 

.547654 

1.085727 

.092906 

.214616 

.458002 

92 

93 

. 145475 

.287819 

.538073 

.056722 

.121710 

.243386 

93 

94 

.076742 

.142344 

.250254 

.032559 

.064988 

.121676 

94 

95 

.037846 

.065602 

.107910 

.017361 

.032429 

.056688 

95 

96 

.017361 

.027756 

.042308 

.008900 

.015068 

.024259 

96 

97 

.007027 

.010395 

.014552 

.003868 

.006168 

.009191 

97 

98 

.002579 

.003368 

.004157 

.001577 

.002300 

.003023 

98 

99 

.000789 

.000789 

.000789 

.000723 

.000723 

.000723 

99 

*46 


TABLE     XLII. 

COMMUTATION  COLUMNS.        10  PER  CENT. 


AGE. 

J)x. 

^x- 

Sa.. 

C;.. 

Mo,. 

Kx- 

AGE. 

10 

38,554.3 

395,760.5 

4,000,286.2 

227.120 

2,576.107 

32,098.169 

10 

11 

34,822.3 

357,206.2 

3,604,525.7 

205.836 

2,348.987 

29,522.062 

11 

12 

31,450.8 

322,383.9 

3,247,319.5 

186.254 

2,143.151 

27,173.075 

12 

13 

28,405.3  1 

290,933.1 

2,924,935.6 

168.795 

1,956.897 

25,029.924 

13 

14 

25,654.2 

262,527.8 

2,634,002.5 

153.211 

1,788.102 

23,073.027 

14 

15 

23,168.9 

236,873.6 

2,371,474.7 

138.847 

1,634.891 

21,284.925 

15 

16 

20,923.7 

213,704.7 

2,134,601.1 

125.829 

1,496.044 

19,650.034 

16 

17 

18,895.8 

192,781.0 

1,920,896.4 

114.210 

1,370.215 

18,153.990 

17 

18 

17,063.8 

173,885.2 

1,728,115.4 

103.664 

1,256.005 

16,783.775 

18 

19 

15,408.8 

156,821.4 

1,554,230.2 

94.0914 

1,152.3412 

15,527.7698 

19 

20 

13,913.9 

141,412.6 

1,397,408.8 

85.5376 

1,058.2498 

14,375.4286 

20 

21 

12,563.5 

127,498.7 

1,255,996.2 

77.7615 

972.7122 

13,317.1788 

21 

22 

11,343.6 

114,935.2 

1,128,497.5 

70.6923 

894.9507 

12,344.4666 

22 

23 

10,241.7 

103,591.6 

1,013,562.3 

64.3673 

824.2584 

11,449.5159 

23 

24 

9,246.26 

93,349.9 

909,970.7 

58.6080 

759.8911 

10,625.2575 

24 

25 

8,347.07 

84,103.61 

816,620.82 

53.3639 

701.2831 

9,865.3664 

25 

26 

7,534.87 

75,756.54 

732,517.21 

48.7414 

647.9192 

9,164.0833 

26 

27 

6,801.16 

68,221.67 

656,760.67 

44.4491 

599.1778 

8,516.1641  1  27  1 

28 

•6,138.41 

61,420.51 

588,539.00 

40.5974 

554.7287 

7,916.9863  28 

29 

5,539.77 

55,282.10 

527,118.49 

37.1933 

514.1313 

7,362.2576 

29 

30 

4,998.96 

49,742.33 

471,836.39 

34.0205 

476.9380 

6,848.1263 

30 

31 

4,510.50 

44,743.37 

422,094.06 

31.1645 

442.9175 

6,371.1883 

31 

32 

4,069.28 

40,232.87 

377,350.69 

28.5897 

411.7530 

5,928.2708 

32 

33 

3,670.76 

36,163.59 

337,117.82 

26.2646 

383.1633 

5,516.5178 

33 

34 

3,310.79 

32,492.83 

300,954.23 

24.1616 

356.8987 

5,133.3545 

34 

35 

2,985.64 

29,182.04 

268,461.40 

22.2886 

332.7371 

4,776.4558 

35 

36 

2,691.94 

26,196.40 

239,279.36 

20.5270 

310.4485 

4,443.7187 

36 

37 

2,426.69 

23,504.46 

213,082.96 

18.9550 

289.9215 

4,133.2702 

37 

38 

2,187.13 

21,077.77 

189,578.50 

17.5478 

270.9665 

3,843.3487 

38 

39 

1,970.75 

18,890.64 

168,500.73 

16.2619 

253.4187 

3,572.3822 

39 

40 

1,775.33 

16,919.89 

149,610.09 

15.1049 

237.1568 

3,318.9635 

40 

41 

1,598.83 

15,144.56 

132,690.20 

14.0239 

222.0519 

3,081.8067 

41 

42 

1,439.46 

13,545.73 

117,545.64 

13.0810 

208.0280 

2,859.7548 

42 

43 

1,295.52 

12,106.27 

103,999.91 

12.1936 

194.9470 

2,651.7268 

43 

44 

1,165.55 

10,810.75 

91,893.64 

11.4007 

182.7534 

2,456.7798 

44 

45 

1,048.19 

9,645.20 

81,082.89 

10.6761 

171.3527 

2,274.0264 

45 

46 

942.224 

8,597.01 

71,437.69 

10.0116 

160.6766 

2,102.6737 

46 

47 

846.555 

7,654.785 

62,840.682 

9.41070 

150.66503 

1,941.99711 

47 

48 

760.185 

6,808.230 

55,185.897 

8.85503 

141.25433 

1,791.33208 

48 

49 

682.221 

6,048.045 

48,377.667 

8.34818 

132.39930 

1,650.07775 

49 

50 

611.854 

5,365.824 

42,329.622 

7.88353 

124.05112 

1,517.67845 

50 

51 

548.346 

4,753.970 

36,963.798 

7.45549 

116.16759 

1,393.62733!  51 

52 

491.041 

4,205.624 

32,209.828 

7.05933 

108.71210 

1,277.45974!  52 

53 

439.342 

3,714.583 

,      28,004.204 

6.69103 

101.65277 

1,168.74764  53 

54 

392.711 

3,275.241 

1   24,289.621 

6.34722 

94.96174 

1,067.09487  54 

TABLE     XLII. 


••47 


COMMUTATION  COLUMNS. 

1 

10  PER  CENT. 

AGE. 

55 

D,,. 

No,. 

•  s^. 

Ca,. 

Ma,. 

E^. 

AGE. 

350.662 

2,882.531 

21,014.380 

6.03467 

88.61452 

972.13313 

1  55 

56 

312.750 

2,531.869 

18,131.849 

5.73523 

82.57985 

883.51861 

56 

57 

278.583 

2.219.119 

15,599.980 

5.46023 

76.84462 

:800. 93876 

57 

58 

247.796 

1,940.536 

13,380.861 

5.19506 

71.38439 

724.09414 

58 

59 

220.075 

1,692.740 

11,440.325 

4.94283 

66.18933 

652.70975 

59 

60 

195.125 

1,472.664 

9,747.585 

4.70546 

61.24650 

586.52042 

60 

61 

172.681 

1,277.539 

8,274.921 

4.47855 

56.54104 

525.27392 

61 

62 

152.504 

1,104.858 

6,997.382 

4.25647 

52.06249 

468.73288 

62 

63 

134.384 

952.354 

5,892.524 

4.04449 

47.80602 

416.67039 

63 

64 

118.122 

817.970 

4,940.170 

3.83791 

43.76153 

368.86437 

64 

65 

103.546 

699.848 

4,122.200 

3.63732 

39.92362 

325.10284 

65 

66 

90.4955 

596.3028 

3,422.3523 

3.43811 

36.28630 

285.17922 

66 

67 

78.8306 

505.8073 

2,826.0495 

3.24507 

32.84819 

248.89292 

67 

68 

68.4191 

426.9757 

2,320.2422 

3.05034 

29.60312 

216.04473 

68 

69 

59.1488 

358.5566 

1,893.2665 

2.86294 

26.55278 

186.44161 

69 

70 

50.9087 

299.4078 

1,534.7099 

2.67404 

23.68984 

159.88883 

70 

71 

43.6066 

248.4991 

1,235.3021 

2.48851 

21.01580 

136.19899 

71 

72 

37.1539 

204.8925 

986.8030 

2.30414 

18.52729 

115.18319 

72 

73 

31.4721 

167.7386 

781.9105 

2.12148 

16.22315 

96.65590 

73 

74 

26.4895 

136.2665 

614.1719 

1.94356 

14.10167 

80.43275 

74 

75 

22.1378 

109.7770 

477.9054 

1.76687 

12.15811 

66.33108 

75 

76 

18.3585 

87.6392 

368.1284 

1.59390 

10.39124 

54.17297 

76 

77 

15.0956 

69.2807 

280.4892 

1.42714 

8.79734 

43.78173 

77 

78 

12.2961 

54.1851 

211.2085 

1.26518 

7.37020 

34.98439 

78 

79 

9.91311 

41.88903 

157.02340 

1.11014 

6.10502 

27.61419 

79 

80 

7.90178 

31.97592 

115.13437 

.963058 

4.994877 

21.509173 

80 

81 

6.22038 

24.07414 

83.15845 

.824671 

4.031819 

16.514296 

81 

82 

4.83022 

17.85376 

59.08431 

.696884 

3.207148 

12.482477 

82 

83 

3.69422 

13.02354 

41.23055 

.579181 

2.510264 

9.275329 

83 

84 

2.77920 

9.32932 

28.20701 

.473785 

1.931083 

6.765065 

84 

85 

2.05276 

6.55012 

18.87769 

.380009 

1.457298 

4.833982 

85 

86 

1.48614 

4.49736 

12.32757 

.298365 

1.077289 

3.376684 

86 

87 

1.05267 

3.01122 

7.83021 

.229564 

.778924 

2.299395 

87 

88 

.727410 

1.958552 

4.818985 

.171635 

.549360 

1.520471 

88 

89 

.489646 

1.231142 

2.8f)0433 

.130246 

■  .377725 

.971111 

89 

90 

.314886 

.741496 

1.629291 

.093937 

.247479 

.593386 

90 

91 

.192323 

.426610 

.887795 

.062687 

.153542 

.345907 

91 

92 

.112152 

.234287 

.461185 

.039736 

.090855 

.192365 

92 

93 

.062221 

.122135 

.226898 

.024040 

.051119 

.101510 

93 

94 

.032524 

.059914 

.104763 

.013674 

.027079 

.050391 

94 

95 

.015894 

.027390 

.044849 

.007226 

.013405 

.023312 

95 

96 

.007225 

.011496 

.017459 

.003670 

.006179 

.009907 

96 

97 

.002898 

.004271 

.005963 

.001580 

.002509 

.003728 

97 

98 

.001054 

.001373 

.001692 

.000639 

.000929 

.001219 

98 

99 

.000319 

.000319 

.000319 

.000290 

.000290 

.000290 

99 

♦48 


TA.BLE    XLIII. 

COMMON    LOGARITHMS    FOR   SPECIAL    FORMULAS. 

Yalne  of  A  {i)p^),  of  fXj:,  A  ju^,,  v,  (5,  and  X6. 


AOE, 
X. 

^  (Vi?x). 

l^x- 

A^a;- 

AGE. 

X. 

3 
Per  Cent. 

Per  Cent. 

4 
Per  Cent. 

Per  Cent. 

5 
Per  Cent. 

6 
Per  Cent. 

10 

1.984341 

1.982236 

1.980143  1.978061 

1.975988 

1.971872 

0.006493 

3.81245 

10 

11 

.984329 

.982227 

.980134  .978051 

.975977 

.971861 

.006513 

.81378 

11 

12 

.984325 

.982221 

.980128  .978044 

.975972 

.971855 

.006530 

.81491 

12 

13 

.984313 

.982211 

.980118  .978036 

.975963 

.971846 

.006547 

.81604 

13 

14 

.984302 

.982198 

.980105 

.978022 

.975949 

.971832 

.006572 

.81770 

14 

15 

1.984289 

1.982186 

1.980094 

1.978010 

1.975937 

1.971821 

0.006600 

3.81954 

15 

16 

.984282 

.982178 

.980084 

.978002 

.975929 

.971812 

.006624 

.82112 

16 

17 

.984265 

.982163 

.980070 

.977987'  .975914 

.971797 

.006653 

.82302. 

17 

18 

.984250 

.982147 

.980055 

.977971 

.975898 

.971783 

.006687 

.82523 

18 

19 

.984236 

.982133 

.980039 

.977957 

.975884 

.971767 

.006721 

.82743 

19 

20 

1.984217 

1.982113 

1.980020 

1.977937 

1.975864 

1.971747 

0.006762 

3.83008 

20 

21 

.984195 

.982092 

.980000 

.977916 

.975.843 

.971727 

.006807 

.83296 

21 

22 

.984175 

.982072 

.979978 

.977896 

.975823 

.971706 

.006854 

.83594 

22 

23 

.984150 

.982048 

.979955 

.977872 

.975799 

.971682 

.006906 

.83923 

23 

24 

.984125 

.982020 

.979928 

.977845 

.975772 

.971655 

.006965 

.84292 

24 

25 

f.  984097 

1.981995 

1.979901 

1.977818 

1.975745 

T.971630 

0.007027 

3.84677 

25 

26 

.984062 

.981959 

.979866 

.977783 

.975710 

.971593 

.007098 

.85114 

26 

27 

.984028 

.981925 

.979833 

.977750 

.975677 

.971560 

.007176 

.85588 

27 

28 

.983993 

.981888 

.979795 

.977713 

.975639 

.971522 

.007258 

.86082 

28 

29 

.983943 

.981841 

.979748 

.977664 

.975592 

.971476 

.007354 

.86652 

29 

30 

1.983901 

1.981797 

f.  979704 

1.977621 

1.975548 

1.971431 

0.007460 

3.87274 

30 

31 

.983847 

.981746 

.979652 

.977570 

.975496 

.971380 

.007569 

.87904 

31 

32 

.983795 

.981691 

.979598 

.977514 

.975442 

.971325 

.007692 

.88604 

32 

33 

.983730 

.981627 

.979535 

.977452 

.975379 

.971263 

.007829 

.89371 

33 

34 

.983664 

.981560 

.979466 

.977384 

.975311 

.971194 

.007978 

.90189 

34 

35 

f.  983580 

f.  981 478 

1.979386 

1.977303 

1.975229 

1.971113 

0.008148 

3.91105 

35 

36 

.983504 

.981401 

.979307 

.977224 

.975152 

.971035 

.008330 

.92065 

36 

37 

.983416 

.981313 

.979220 

.977137 

.975064 

.970947 

.008524 

.93064 

37 

38 

.983313 

.981209 

.979117 

.977034 

.974960 

.970844 

.008744 

.94171 

38 

39 

.983203 

.981100 

.979006 

.976923 

.974851 

.970734 

.008987 

.95361 

39 

40 

1.983078 

1.980976 

r.  978883 

1.976800 

1.974727 

1.970611 

0.009254 

3.96633 

40 

41 

.982953 

.980849 

.978757 

.976674 

.974600 

.970484 

.009544 

.97973 

41 

42 

.982800 

.980696 

.978602 

.976520 

.974447 

.970330 

.009866 

.99414 

42 

43 

.982643 

.980541 

.978448 

.976364 

.974292 

.970175 

.010221 

2.00949 

43 

44 

.982463 

.980360 

.978268 

.976185 

.974112 

.969995 

.010606 

.02555 

44 

45 

1.982272 

1.980167 

1.978073 

1.975991 

1.973917 

1.969801 

0.011035 

2.04277 

45 

46 

.982055 

.979954 

.977861 

.975777 

.973705 

.969588 

.011504 

.06085 

46 

47 

.981821 

.979716 

.977624 

.975541 

.973468 

.969351 

.012021 

.07994 

47 

48 

.981561 

.979459 

.977365 

.975282 

.973209 

.969093 

.012589 

.09999 

48 

49 

.981279 

.979175 

.977082 

.975000 

.972926 

.968810 

.013213 

.12100 

49 

50 

1.980961 

1.978859 

1.976767 

1.974683 

1.972611 

1.968494 

0.013901 

2.14305 

50 

51 

.980619 

.978516 

.976422 

.974340 

.972366 

.968150 

.014658 

.16607 

51 

52 

.980240 

.978137 

.976044 

.973961 

.971888 

.967771 

.015488 

.19000 

52  > 

53 

.979827 

.977722 

.975630 

.973546 

.971474 

.967357 

.016402 

.21490 

53  i 

54 

.979370 

.977269 

.975175 

.973093 

.971020 

.966903 

, .017402 

.24060 

54  J 

i 

Vlx  + 


Dx+i 


Formula,  vp^  =  —^ —  =  -^^ —  i^x  =^  — 


dlx 

L  dx 


♦49 


TABLE    XLIII. 

COMMON  LOGARITHMS  FOR  SPECIAL  FORMULAS. 


AGE. 
X. 

A  (?)i?x). 

V-^ 

A^^- 

AGE. 

X. 

3 
Per  Cent. 

Per  Cent. 

4 
Per  Cent. 

Per  Cent. 

5 
Per  Cent. 

1.970510 
.969961 
.969345 
.968678 
.967946 

6 
Per  Cent. 

55 
56 
57 
58 
59 

1.978863 
.978314 
.977696 
.977030 
.976299 

1.976759 
.976210 
.975594 
.974927 
.974195 

1.974667 
.974117 
.973500 
.972835 
.972102 

1.972584 
.972033 
.971418 
.970752 
.970019 

1.966395 

..965844 

.965228 

.964562 

.963829 

0.018508 
.019725 
.021064 
.022541 
.024151 

2.26736 
.29502 
.32354 
.35297 
.38294 

55 
56 
57 
58 
59 

60 
61 
62 
63 
64 

r.  975486 
.974593 
.973621 
.973541 
.971356 

r.  973384 

.972489 
.971518 
.970437 
.969254 

1.971290 
.970397 
.969425 
.968344 
.967161 

1.969207 
.968314 
.967342 
.966261 
.965078 

1.967135 
.966241 

.965268 
.964189 
.963005 

1.963018 
.962124 
.961153 
.960072 

.958888 

0.025921 

.027883 
.030027 
.032385 
.034988 

2.41365 
.44534 
.47751 
.51034 
.54392 

60 
61 
62 
63 
64 

65 
66 
67 
68 
69 

1.970049 
.968624 
.967037 
.965325 
.963401 

1.967946 
.966521 
.964934 
.963221 
.961299 

f.  965853 
.964427 
.962842 
.961128 
.959205 

1.963770 
.962345 
.960758 
.959045 
.957122 

1.961696 
.960272 
.958686 
.956971 
.955050 

1.957580 
.956155 
.954569 
.952855 
.950933 

0.037853 
.040996 
.044457 
.048249 
.052427 

2.57810 
.61274 
.64794 
.68349 
.71956 

65 
66 
67 
68 
69 

70 
71 
72 
73 

74 

1.961316 
.959006 
.956478 
.953704 
.950616 

1.959212 
.956004 
.954375 
.951600 
.948513 

r.  957120 
.954811 
.9.52281 
.949508 
.946420 

1.955037 
.952728 
.950199 
.947425 
.944336 

1.952963 
.950656 
.948125 
.945352 
.942264 

1.948848 
.946538 
.944009 
.941235 
.938147 

0.057039 
.062089 
.067652 
.073746 
.080484 

2.75617 
.79301 

.83028 
.86774 
.90571 

70 

71 
72 
73 

74 

75 
76 

77 
78 
79 

1.947257 
.943570 
.939473 
.934997 
.930071 

1.945153 
.941467 
.937370 
.932894 
.927968 

r.  943060 
.939374 
.935277 
.930801 

.925875 

r.  940978 
.937291 
.933193 
.928719 
.923792 

1.938904 
.935218 
.931121 
.926645 
.921719 

1.934788 
.931101 
.927005 
.922529 
.917602 

0.087902 
.095996 
.104940 
.114801 
.125606 

2.94400 
.98225 

1.02094 
.05995 
.09901 

75 
76 
77 
78 
79 

80 
81 
82 
83 
84 

1.924647 

.918706 
.912111 
.904953 
.896974 

r.  922544 

.916602 
.910009 
.902850 
.894870 

1.920451 
.914509 
.907916 
.900757 

.892777 

1.918368 
.912426 
.905833 
.898674 
.890694 

1.916295 
.910354 
.903759 
.896601 

.888622 

1.912178 
.906237 
.899643 
.892484 

.884500 

0.137506 
.150570 
.164978 
.180795 
.198181 

1.13832 

.17774 
.21743 
.25719 
.29706 

80 
81 
82 
83 
84 

85 
86 
87 
88 
89 

1.888276 
.878789 
.868041 
.856659 
.836828 

1.886173 
.876686 
.865938 
.854556 
.834725 

1.884080 
.874593 
.863845 
.852462 
.832633 

1.881997 
.872510 
.861762 
.850380 
.830549 

r.  879923 
.870437 
.859690 
.848306 

.828476 

1.875807 
.866320 
.855573 
.844190 
.824359 

0.217377 
.238266 
.261501 
.286671 
.321451 

1.33721 
.37706 
.41747 
.45738 
.50711 

85 
86 
87 
88 
89 

90 
91 
92 
93 

94 

1.814433 
.794331 

.772681 
.746831 
.717581 

1.812329 
.792229 

.770578 

.744727 
.715478 

r.  810236 
.790136 
.768484 
.742635 
.713385 

1.808154 
.788052 
.766402 
.740552 
.711301 

1.806081 

.785980 
.764328 
.738479 
.709229 

1.801964 
.781863 
.760213 
.734362 
.705112 

0.371233 
.421033 
.468238 
.522329 
.585986 

1.56965 
.62432 

.67047 
.71794 
.76789 

90 
91 
92 
93 
94 

95 
96 
97 
98 

1.686132 
.631775 
.589223 
.510042 

r.  684029 
.629672 
.587120 
.507938 

1.681936 
.627579 
.585026 
.505846 

1.679854 
.625496 
.582944 
.503762 

1.677780 
.623423 

.580871 
.501689 

1.673664 
.619306  1 
.576754 
.497573 

0.655714 

.748812 
.871770 
.988400 

1.81671 
.87437 
.94040 
.99493 

95 
96 
97 
98 

V 

& 

6 
X6 

0.970874 

.029559 

2.470687 

0.966184  0.961538 

.034401  .039221 

2.536577  2.59.3516 

0.956938 

.044017 

2.643619 

0.952381 

.048790 

2.688332 

0.943396 
.058269 1 
2.765437 

Formula,  8  =  Na'p.  log  (I  +  i)  =  —  Naj}.  log  v. 


*50 


TABLE    XLIY. 


LIFE  AND  TEMPORARY   ANNUITIES.     LOGARITHM  OF  THE    PRESENT    VALUE    OF    fi 
ANNUAL  PAYMENTS    OF  1   AT  THE  BEGINNING  OF  EACH  YEAR. 

The  first  Value  under  the  Age  X  is  a(1  +  ag.)  for  the  whole  Life.  4    PER  CENT. 


Pay- 

a:=:10   11 

12 

13 

14 

15 

16 

17     !  Fay 

ments. 

n. 

ments. 

1.316633 

1.315019'l.313333 

j 

1.311567 

1.309720 

1.307791 

1.305773 

1.303662 

W. 

1 

0.000000 

O.OOOOOolo.  000000 

0.000000  !o. 000000 

0.000000 

0.000000 

0.000000 1  1 

2 

.291215 

.291210 

.291207 

.291203'!  .291196 

.291191 

.291187 

.2^1179 1  2 

3 

.457564 

.457556 

.457549 

.457538  .457527 

.457516 

.457505 

.457491 !  3 

4 

.572834 

.572822 

.572810 

.572794 

.572777 

.572761 

.572743 

.572722 

4 

5 

0.660148 

0.660132 

0.660114 

0.660093 

0.660071 

0.660048'o.  660024 

0.659995 

5 

6 

.729805 

.729785 

.729763 

.729736 

.729707 

.729679!  .729647 

.729610 

6 

7 

.787302 

.787276 

.787248 

.787216 

.787181 

.787145 

.787106 

.787060 

7 

8 

.835915 

.835884 

.835851 

.835813 

.835771 

.835728 

.835681 

.835626 

8 

9 

.877761 

.877725 

.877686 

.877642 

.877593 

.877542 

.877486 

.877423 

9 

10 

0.914284 

0.914242 

0.914198 

0.914146 

0.914090 

0.914032 

0.913967 

0.913893 

10 

11 

.946514 

.946466 

.946415 

.946357 

.946293 

.946226 

.946152 

.946068 

11 

12 

.975210 

.975157 

.975099 

.975033 

.974962 

.974886 

.974802 

.974708 

12 

13 

1.000952 

1.000892 

1.000827 

1.000754  1.000673 

1.000588 

1.000494 

1.000388 

13 

14 

.024186 

,024119 

.024047 

.023966  1  .023877 

] 

.023782 

.023677 

.023560 

14 

15 

1.045269 

1.045196 

1.045116 

1.045026  1 1.044928  1.044822 

1.044707 

1.044576 

15 

16 

.064488 

.064407 

064319 

.064220 

.064112 

.063996 

.063868 

.063725 

16 

17 

.082076 

.081987 

.081891 

.081783 

.081665 

.081537 

.081397 

.081240 

17 

18 

.098228 

.098131 

.098026 

.097908 

.097779 

.097640 

.097486 

.097316 

18 

19 

.113106 

.113001 

.112886 

.112758 

.112618 

.112466 

.112299 

.112113 

19 

20 

1.126848 

1.126733 

1.126610 

1.126470 

1.126318  1.126153'l.l25972 

1.125770 

20 

21 

.139570 

.139446 

.139311 

.1391611 

.138996 

.138818!  .138622 

.138404 

21 

22 

.151373 

.151239 

.151094 

.150932 

.150754 

.150561 

.150349 

.150114 

22 

23 

.162344 

.162201 

.162044 

.161869 

.161678 

.161470 

.161241 

.160988  23 

24 

.172559 

.172405 

.172237 

a  72049, 

.171843 

.171620 

.171374 

.171102  24 

25 

1.182086 

1.181921 

1.181740 

1.181538 

1.181317 

1.181077 

1.180814 

1.180521  25 

26 

.190983 

.190805 

.190610 

.190395 

.190158 

.189901 

.189618 

.189305  26 

27 

.199299 

.199108 

.198901 

.198671 

.198418 

.198142 

.197840 

.1975051  27 

28 

.207084 

.206879 

.206659 

.206412 

.206142 

.205847!  .205524 

.205166:  28 

29 

.214377 

.214160 

.213922 

.213660 

.213371 

.213057!  .212712 

.212330!  29 

30 

1.221216 

1.220984 

1.220731 

1.220451 

1.220144 1.219809*1. 219441 

1.219034  30 

31 

.227633 

.227386 

.227116 

.226818 

.226491^  .2261351  .225743 

.225310 

31 

32 

.233659 

.233396 

.233109 

.232792 

.232444!  .232065  .231648 

.231188 

32 

33 

.239320 

.239041 

.238736 

.238399 

.238029;  .237626  .237183 

.236695 

33 

34 

.244642 

.244345 

.244022 

.243663 

. 243271 r  .242843  .242374 

.241854  34 

35 

1.249645 

1.249332 

1.248988 

1.248607 

1.248192  1.247738!l.247239 

1.246690  35 

36 

.254352 

.254019 

.253655 

.253252 

.2528111  .252331 

.251802 

.251220 

36 

37 

.258780 

.258427 

.258042 

.257616 

.257148  .256640 

.256081 

.255465 

37 

38 

.262948 

.262574 

.262165 

.261715 

.261221  .260682 

.260091 

.259440 

38 

39 

.266868 

.266473 

.266042 

.265565 

.2650431  .264473 

.263848 

.263161 

39 

40 

1.270557 

1.270140 

1.269684 

1.269180 

1.2686271.268027 

1.267367 

1.266642 

40 

41 

.274028 

.273587 

.273105 

.272574 

.271992 

.271357 

.270661 

.269897 

41 

'  42 

.277293 

.276827 

.276318 

.275758 

.275144  .274474 

.273742 

.272936 

42 

43 

.280363 

.279872 

.279335 

.278744 

.278098'  .277391 

.276620 

.275772 

43  ^ 

44 

.283247 

.282730 

.282160 

.281543 

.280862,  .280119 

1 

.279307 

.278415 

44  1 

10 

11 

12 

13 

14     15 

16 

17 

Continued  on  Page  *60. 


Formula,  ^l  +  a^^^)  =  a  ^x-^x^n^x^^3!=L 


D« 


Vpa>-t 


TABLE    XLIY. 


'5i 


LIFE  AND  TEMPORARY  ANNUITIES.      LOGARITHM  OP  THE    PRESENT  VALUE    OF  W 
ANNUAL  PAYMENTS  OF  1   AT  THE  BEGINNING  OF  EACH  YEAR. 


4  PER  CENT. 

Pay- 

18 

19 

20 

21 

22 

23 

24 

25 

Pay- 

ments. 

n. 

1.301453 

ments. 
n. 

1.299144 

1.296729 

1.294205 

1.291567 

1.288808 

1.285924 

1.282910 

1 

0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

1 

2 

.291172 

.291165 

.291155 

.291145 

.291134 

.291123 

.291110 

.291096 

2 

3 

.457477 

.457460 

.457441 

.457421 

.457400 

.457376 

.457349 

.457320 

3 

4 

.572699 

.572674 

.572645 

.572615 

.572581 

.572546 

.572504 

.572459 

4 

5 

0.659963 

0.659929 

0.659890 

0.659848 

0.659803 

0.659753 

0.659698 

0.659636 

5 

6 

.729569 

.729525 

.729476 

.729422 

.729364 

.729300 

.729229 

.729150 

6 

7 

.787011 

.786956 

.786896 

.786830 

.786758 

.786679 

.786591 

.786494 

7 

8 

.835567 

.835502 

.835429 

.835351 

.835265 

.835170 

.835065 

.834949 

8 

9 

.877353 

.877276 

.877193 

.877100 

.876999 

.876888 

.876765 

.876629 

9 

10 

0.913813 

0.913725 

0.913628 

0.913521 

0.913404 

0.913276 

0.913134 

0.912977 

10 

11 

.945977 

.945876 

.945765 

.945644 

.945510 

.945364 

.945202 

.945024 

11 

12 

.974604 

.974491 

.974365 

.974228 

.974078 

.973912 

.973730 

.973528 

12 

13 

1.000273 

1.000145 

1.000005 

.999851 

.999683 

.999498 

.999293 

.999068 

13 

14 

.023431 

.023289 

.023133 

1.022963 

1.022775 

1.022569 

1.022342 

1.022091 

14 

15 

1.044434 

1.044277 

1.044105 

1.043916 

1.043709 

1.043481 

1.043229 

1.042953 

15 

16 

.063569 

.063396 

.063207 

.062999 

.062771 

.062520 

.0622431  .061939 

16 

17 

.081069 

.080880 

.080672 

.080444 

.080194 

.079920 

.0796171  .079283 

17 

18 

.097128 

.096922 

.096695  .096447 

.096174 

.095874 

.095543  .095180 

18 

19 

.111909 

.111685 

.111438  .111168 

.110871 

.110545 

.110185  .109790 

19 

20 

1.125549 

1.125306 

1.125038 

1.124745 

1.124423 

1.124069 

1.1236791.123251 

20 

21 

.138164 

.137901 

.137612 

.137295 

.136946 

.136564 

.136142 

.135678 

21 

22 

.149856 

.149572 

.149159 

.148917 

.148541 

.148128 

.147674 

.147173 

22 

23 

.160710 

.160404 

.160168 

.159699 

.159294 

.158850 

.1583601  .157822 

23 

24 

.170803 

.170474 

.170113 

.169717 

.169282 

.168804 

.168278 

.167700 

24 

25 

1.180200 

1.179848 

1.179460 

1.179035 

1.178569 

1.178056 

1.177492 

1.176873 

25 

26 

.188961 

.188584 

.188169'  .187714 

.187214 

.186665 

.186062 

.185399 

26 

27 

.197137 

.196733 

.196289  .195803 

.195269 

..194682 

.194037 

.193329 

27 

28 

.204773 

.204342 

.203868  .203349 

.202778 

.202152 

.201464 

.200709 

28 

29 

.211911 

.211452 

.210946'  .210392 

.209784 

.209117 

.208384 

.207579 

29 

30 

1.218588 

1.218098 

1.2175591.216970 

1.216322 

1.215612 

1.214832 

1.213976 

30 

31 

.224835 

.224314 

.223741;  .223114 

.222425 

.221670 

.220841 

.219932 

31 

32 

.230683 

.230129 

.2295211  .228854 

.228123 

.227321 

.226441 

.225476 

32 

33 

.236159 

.235571 

.234925;  .234218 

.233442 

.232591 

.231659 

.230636 

33 

34 

.241286 

.240662 

.239978 

.239228 

.238406 

.237506 

.236518 

.235436 

34 

35 

1.246087 

1.245427 

1.244701 

1.243908 

1.243038 

1.242085 

1.241040 

1.239896 

35 

36 

.250583 

.249883 

.249116 

.248276 

.247357 

.246349 

.245246 

.244037 

36 

37 

.254790 

.254051 

.253240!  .252352 

.251381 

.250317 

.249153 

.247879 

37 

38 

.258727 

.257946 

.2570891  .256153 

.255127 

.254006 

.252778 

.251436 

38 

39 

.262408 

.261584 

.260680 

.259692 

.258612 

.257430 

.256138 

.254726 

39 

40 

1.265848 

1.264979 

1.264027 

1.262986 

1.261848 

1.260605 

1.2592461.257762 

40 

41 

.269060 

.268144 

.267141 

.266046 

.264850 

.263543 

.262116!  .260559 

41 

42 

.272055 

.271091 

.270037 

.268886 

.267629 

.266257 

.264760 

.263128 

42 

43 

.274845 

.273832 

.272724 

.271515 

.270196 

.268758 

.267190 

.265481 

43 

1  44 

.277441 

.276377 

.275214 

.273946 

.272564 

.271057 

.269416 

.267631 

44 

18 

19 

20 

21 

22 

23 

24 

25 

Continued  on  Page  *59. 


*53 


TABLE    XLIV. 


LIFE  AND  TEMPORARY  ANNUITIES.     LOGARITHM  OF    THE    PRESENT  VALUE    OF  W 
ANNUAL  PAYMENTS  OF  1  AT  THE  BEGINNING  OF  EACH  YEAR. 

4  PER  CENT. 


Pay- 
ments. 
n. 

x=2Q 

27 

28 

29 

30 

31 

32 

33 

Pay- 
ments 
n. 

1 

1.279758 

1.276466 

1.273025 

1.269428 

1.265675 

1.261752 

1.257654 

1.253372 

1 

0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

2 

.291079 

.291064 

.291045 

.291022 

.291001 

.290975 

.290948 

.290919 

2 

3 

.457288 

.457255 

.457214 

.457170 

.457126 

.457073 

.457019 

.456957 

3 

4 

.572410 

.572357 

.572296 

.572229 

.572159 

.572081 

.571995 

.571899 

4 

5 

0.659568 

0.659496 

0.659413 

0.659322 

0.659227 

0.659119 

0.659000 

0.658868 

5 

6 

.729063 

.728970 

.728864 

.728748 

.728626 

.728486 

.728335 

.728167 

6 

7 

.786388 

.786273 

.786143 

.786001 

.785849 

.785678 

.785492 

.785285 

7 

8 

.834821 

.834684 

.834530 

.834359 

.834177 

.833973 

.833750 

.833503 

8 

9 

.876480 

.876318 

.876137 

.875937 

.875724 

.875485 

.875223 

.874934 

9 

10 

0.912805 

0^.912619 

0.912409 

0.912180 

0.911933 

0.911657 

0.911355 

0.911021 

10 

11 

.944827 

.944614 

.944376 

.944115 

.943833 

.943518 

.943174 

.942794 

11 

12 

.973307 

.973066 

.972798 

.972503 

.972184 

.971830 

.971441 

.971013 

12 

13 

.998820 

.998551 

.998250 

.997921 

.997564 

.997167 

.996732 

.996253 

13 

14 

1.021816 

1.021516 

1.021182 

1.020816 

1.020419 

1.019977 

1.019494 

1.018962 

14 

15 

1.042648 

1.042317 

1.041948 

1.041543 

1.041104 

1.040617 

1.040083 

1.039494 

15 

16 

.061604 

.061239 

.060834 

.060389 

.059906 

.059370 

.058783 

.058136 

16 

17 

.078917 

.078517 

.078073 

.077586 

.077057 

.076471 

.075828 

.075120 

17 

18 

.094780 

.094344 

.093861 

.093329 

.092751 

.092112 

.091411 

.090640 

18 

L9 

.109355 

.108881 

.108355 

.107778 

.107150 

.106455 

.105694  .104856 

19 

20 

1.122779 

1.122265 

1.121695 

1.121070 

1.120389 

1.119637 

1.1188121.117905 

20 

21 

.135169 

.134613 

.133997 

.1333^22 

.132586 

.131773 

.130882  .129903 

21 

22 

.146624 

.146024 

.145361 

.144633 

.143839 

.142963 

.142004  .140949 

22 

23 

.157231 

.156585 

.155872 

.155089 

.154236 

.153294 

.152263 

.151130 

23 

24 

.167066 

.166372 

.165606 

.164766 

.163850 

.162840 

.161734 

.160520 

24 

25 

1.176193 

1.175449 

1.174629 

1.173729 

1.172748 

1.171667 

1.170483 

1.169184 

25 

26 

.184671 

.183876 

.182998  .182037 

.180988 

.179833 

.178568 

.177181 

26 

27 

.192552 

.191702 

.190765 

.189739 

.188620 

.187388 

.186039 

.184561 

27 

28 

.199880 

.198974 

.197976 

.196882 

.195689 

.194377 

.192942 

.191370 

28 

29 

.206696 

.205731 

.204669 

.203506 

.202237 

.200843 

.199318 

.197648 

29 

30 

1.213037 

1.212011 

1.210883 

1.209647 

1.208299 

1.206819 

1.205202 

1.203432 

30 

31 

.218935 

.217846 

.216648 

.215337 

.213908 

.212340 

.210627 

.208753 

31 

32 

.224419 

.223264 

.221995 

.220607 

.219094 

.217434 

.215623 

.213643 

32 

33 

.229516 

.228293 

.226950 

.225482 

.223882 

.222129 

.220217 

.218128 

33 

34 

..234251 

.232957 

.231538 

.229987 

.228298 

.226449 

.224433 

.222234 

34 

35 

1.238644 

1.237278 

1.235780 

1.234144 

1.232364 

1.230416 

1.228294 

1.225982 

35 

36 

.242716 

.241275 

.239697 

.237974 

.236099 

.234051 

.231822 

.229395 

36 

37 

.246486 

.244968 

.243306 

.241494 

.239524 

.237374 

.235035 

.232492 

37 

38 

.249970 

.248373 

.246627 

.244723 

.242656 

.240402  .237953 

.235292 

38 

39 

.253185 

.251507 

.249674 

.247678 

.245512 

.243152  .240592 

.237814 

39 

40 

1.256144 

1.254384 

1.252462 

1.250372 

1.248106 

1.245641  1.242969 

1.240074 

40 

41 

.258862 

.257017 

.255006 

.252821 

.250455 

.247883 

.245100 

.242089 

41 

42 

.261351 

.259421 

.257320 

.255039 

.252571 

.249894 

.247001 

.243875 

42 

43 

.263623 

.261608 

.259415 

.257038 

.254470 

.251688 

.248686 

.245447 

43 

44 

.265691 

.263588 

.261305 

.258832 

.256164 

.253279 

.250170 

.246822 

44  / 

1 

1 

26 

27 

28 

29 

30 

31 

32 

33 

Contiuued  on  Page  *58. 


TABLE     XLIY. 


♦53 


LIFE  AND'  TEMPORARY  ANNUITIES.     LOGARITHM    OF    THE    PRESENT  VALUE  OF  n 
ANNUAL  PAYMENTS  OF  1   AT  THE  BEGINNING  OF  EACH  YEAR. 

4  PER  CENT. 


Pay- 

niQiits. 

34 

35 

36 

37 

38 

39 

40 

41 

Pay- 
ments. 

n. 

1.248903 

1.244234 

1.239367 

1.234282 

1.228972 

1.223433 

1.217656 

1.211632 

71. 
1 

1 

0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

2 

.290884 

.290845 

.290806 

.290765 

.290713 

.290660 

.290600 

.290538 

2 

3 

.456885 

.456808 

.456729 

.456641 

.456537 

.456426 

.456306 

.456176 

3 

4 

.571790 

.571674 

.571551 

.571413 

.571255 

.571087 

.570901 

.570699 

4 

5 

0.658721 

0.658564 

0.658395 

0.658205 

0.657991 

0.657761 

0.657507 

0.657231 

5 

6 

.727980 

.727778 

.727559 

.727317 

.727043 

.726748 

.726424 

.726069 

6 

7 

.785055 

.784808 

.784538 

.784239 

.783904 

.783540 

.783142 

.782706 

7 

8 

.833229 

.832932 

.832609 

.832251 

.831851 

.831418 

.830941 

.830419 

8 

9 

.874614 

.874265 

.873886 

.873467 

.872999 

.872491 

.871934 

.871322 

9  1 

10 

0.910652 

0.910251 

0.909813 

0.909329 

0.908792 

0. 908205 

0.907561 

0.906857 

10 

11 

.942375 

.941917 

.941418 

.940867 

.940254 

.939587 

.938854 

.938051 

11 

12 

.970540 

.970024 

.969460 

.968838 

.968148 

.967396 

.966570 

.965665 

12 

13 

.995724 

.995146 

.994515 

.993820 

.993049 

.992208 

.991285 

.990272 

13 

14 

1.018374 

1.017733 

1.017032 

1.016259 

1.015403 

1.014470 

1.013444 

1.012321 

14 

15 

1.038846 

1.038137 

1.037363 

1.036510 

1.035565 

1.034535 

1.033404 

1.032165 

15 

16 

.057424 

.056645 

.055794 

.054856 

.053820 

.052689 

.051448 

.050088 

16 

17 

.074341 

.073490 

.072558 

.071533 

.070401 

.069164 

.067808 

.066323 

17 

18 

.089791 

.088863 

.087848 

.086731 

.085499 

.084154 

.082678 

.081062 

18 

19 

.103935 

.102927 

.101825 

.100613 

.099277 

.097817 

.096218 

.094466 

19 

20 

1.116908 

1.115817 

1.114624 

1.113313 

1.111869 

1.110291 

1.108563 

1.106671 

20 

21 

.128827 

.127649  .126362 

.124948 

.123391 

.121691 

.119830 

.117793 

21 

22 

.139791 

.138524 

.137138 

.135617 

.133944 

.132117 

.130117 

.127931 

22 

23 

.149886 

.148525 

.147038 

.145406 

.143612 

.141654 

.139512 

.1371711  23  1 

24 

.159186 

.157729 

.156136 

.154389 

.152471 

.150377 

.148088 

.145589 

24 

25 

1.167759 

1.166201 

1.164499 

1.162633 

1.160585 

1.158352 

1.155913 

1.153250 

25 

26 

.175660 

'.173998 

.172183 

.170195 

.168014 

.165638 

.163044 

.160214 

26 

27 

.182941 

.181172 

.179240 

.177126 

.174809 

.172286 

.169532 

.166533 

27 

28 

.189648 

.187767 

.185716 

.183472 

.181016 

.178341 

.175427 

.172254 

28 

29 

.195820 

.193825 

.191651 

.189274 

.186675 

.183847 

.180768 

.177420 

29 

30 

1.201495 

1.199383 

1.197082 

1.194569 

1.191824 

1.188841 

1.185595 

1.182070 

30 

31 

.206705 

.204473 

.202043 

.199392 

.196348 

.193357 

.189943 

.186240 

31 

32 

.211481 

.209126 

.206564 

.203772 

.200729 

.197428 

.193845 

.189964 

32 

33 

.215849 

.213369 

.210674 

.207739 

.204544 

.201083 

.197332 

.193274 

33 

34 

.219835 

.217228 

.214397 

.211319 

.207973 

.204351 

.200433 

.196199 

34 

35 

1.223463 

1.220727 

1.217760 

1.214538 

1.211039 

1.207259 

1.203174 

1.198769 

35 

36 

.226753 

.223888 

.220784 

.217417 

.213768 

.209831 

.205583 

.201010 

36 

37 

.229727 

.226732 

.223491 

.219981 

.216183 

.212092 

.207685 

.202950 

37 

38 

.232404 

.229279 

.225902 

.222252 

.218307 

.214065 

.209505 

.204614 

38 

39 

.234802 

.231548 

.228038 

.224248 

.220161 

.215774 

.211067 

.206029 

39 

40 

1.236940 

1.233559 

1.229916 

1.225992 

1.221767 

1.217241 

1.212394 

1.207218 

40 

41 

.238834 

.235328 

.231558 

.227503 

.223146 

.218488 

.213510 

.208205 

41 

42 

.240502 

.236874 

.232980 

.228800 

.224319 

.219537 

.214437 

.209014 

42 

43 

.241959 

.238214 

.234202 

.229904 

.225305 

.220407 

.215197 

.209668 

43 

44 

.243222 

.239366 

.235241 

.230832 

.226124 

.221122 

.215811 

.210187 

44 

34 

35 

36 

37 

38 

39 

40 

41 

Continued  on  Page  *57. 


N 


*54 


TABLE     XLIY. 


LIFE  AND  TEMPORARY  ANNUITIES.     LOGARITHM    OF  THE    PRESENT   VALUE   OP    n 
ANNUAL  PAYMENTS   OF  1   AT  THE  BEGINNING   OF   EACH   YEAR. 

4  PER   CENT. 


Pay. 

a;=42 

43 

44 

45 

46 

47 

48 

49 

Pay- 

ments. 

ments. 
n. 

11. 

1 

1.205342 

1.198793 

1.191959|1.184839 

1.177421 

1.169692 

1.161644 

1.153265 

0.000000 

0.000000 

0.000000  0.000000 

0.000000 

0.000000 

0. 000000 

0.000000 

1 

2 

.290463 

.290386 

.290301  .290205 

.290101 

.289986 

.289861 

.289722 

2 

3 

.456026 

.455868 

.455691  .455496 

.455283 

.455047 

.454790 

.454507 

3 

4 

.570471 

.570227 

.569956  .569656 

.569329 

.568968 

.568573 

.568137 

4 

5 

0.656921 

0.656587 

0.656216  0.655808 

0.6553610.654869 

0.654329 

0.653735 

5 

6 

.725673 

.725245 

.724770  .724248 

.723676 

.723046 

1  .722356 

.721596 

6 

7 

.782220 

.781693 

.781110  .780468 

.779765 

.778992 

.778144 

.777212 

7 

8 

.829838 

.829208 

.828512 

.827746 

.826906 

.825983 

.824972'  .823860 

8 

9 

.870643 

.869904 

.869089 

.868194 

.867212 

.866133 

.864951  .863650 

9 

10 

0.906075 

0.905224 

0.904285 

0.903253 

0.902123 

0. 900882 

0.8995210.898025 

10 

11 

.937162 

.936194 

.935126 

.933953 

.932668 

.931257 

.929710 

.928011 

11 

12 

.964664 

.963572 

.962370 

.961050 

.959604 

.958016 

.956275 

.954366 

12 

13 

.989154 

.987935 

.986593 

.985120 

.983506 

.981735 

.979794 

.977665 

13 

14 

1.011081 

1.009729 

1.008241 

1.006608 

1.004820 

1.002858 

1.000711 

.998356 

14 

15 

1.030798 

1.029307 

1.027667 

1.025869 

1.023900 

1.021742 

1.019379 

1.016790 

15 

16 

.048589 

.046954 

.045157 

.043187 

.041030 

.038668 

.036084 

.033255 

16 

17 

.064687 

.062902 

.060942 

.058794 

.056444 

.053871 

.051058,  .047981 

17 

18 

.079284 

.077344 

.075214 

.072882 

.070333 

.067543 

.064496  .061164 

18 

19 

.092541 

.090440 

.088136 

.085614 

.082859 

.079847 

.076558  .072965 

19 

20 

1.104593 

1.102326 

1.099842 

1.097126 

1.094159 

1.090918 

1.0873821.083525 

20 

21 

.115561 

.113119 

.110450 

.107533 

.104349 

.100874 

.097087 

.092959 

21 

22 

.125532 

.122919 

.120059 

.116936 

.113531 

.109818 

.105775 

.101374 

22 

23 

.134605 

.131811 

.128756 

.125423 

.121792 

.117837 

.113536 

.108859 

23 

24 

.142852 

.139872 

.136618 

.133071 

.129211 

.125011 

.120449 

.115496 

24 

25 

1.150337 

1.147169 

1.143712 

1.139948 

1.135856 

1.131410 

1.126586 

1.121356 

25 

26 

.157122 

.153761  .150098 

.146115 

.141790 

.137096 

.132012 

.126509 

26 

27 

.163258 

.159702 

.155832 

.151628 

.147069 

.142129 

.136786 

.131012 

27 

28 

.168794 

.165041 

.160962 

.156536 

.151745 

.146561 

.140963 

.134925 

28 

29 

.173774 

.169822 

.165533 

.160888 

.1558651  .150441  .144593 

1      1 

.138298 

29 

30 

1.178236 

1.1740861.169589 

1.164725 

1.1594751.153815:1.147726 

1.141185 

30 

31 

.182218 

.177871 

.173168 

.168089 

.162617 

.156729  .150408 

.143630 

31 

32 

.185755 

.181213 

.176307 

.171018 

.165331 

.159224 

.152681 

.145682 

32 

33 

.188880 

.184146 

.179041 

.173550 

.167656 

.161340 

.154589 

.147383 

33 

34 

.191624 

.186703 

.181406 

.175719 

.169629 

.163117 

.156170 

.148775 

34 

35 

1.194016 

1.188913 

1.183433 

1.177560 

1.171285 

1.164590 

1.1574661.149897 

35 

36 

.196086 

.190809 

.185153 

.179107 

.172659 

.165797 

.158510;  .150789 

36 

37 

.197862 

.192420 

.186599 

.180390 

.173785 

.166770 

.159339 

.151484 

37 

38 

.199370 

.193773 

.187799 

.181442 

.174693!  .167543 

.159986 

.152015 

38 

39 

.200637 

.194896 

.188782 

.182290 

.175414  .168146 

.160431 

.152413 

39 

40 

1.201690 

1.195816 

1.189576 

1.182964 

1.175977 

1.168607 

1.160852 

1.152703 

40 

41 

.202553 

.196559 

.190206 

.183490 

.176408 

.168952 

.161122 

.152910 

41 

42 

.203249 

.197150 

.190698 

.183892 

.176730 

.169204 

.161314 

.153050 

42 

43 

.203803 

.197610 

.191074 

.184193 

.176965 

.169384 

.161445 

.153141 

43 

44 

.204234 

.197963 

.191356 

.184413 

.177133 

.169505 

.161530 

.153197 

44 

42 

43 

44 

45 

46 

47 

48 

49 

Continued  on  Page  *56. 


TABLE     XLIY. 


♦55 


LIFE  AND  TEMPORARY  ANNUITIES.      LOGARITHM    OP    THE    PRESENT  VALUE  OF  n 
ANNUAL  PAYMENTS  OP  1   AT  THE  BEGINNING  OP  EACH   YEAR. 

4  PER  CENT. 


Pay- 

50 

51     52 

53 

54 

55   1   56 

57 

Pay- 

ments 

71. 

! 

ments, 

1.14454S 

5 1.135469  1.12603l|l.ll6217 

1.106014 

1.09541C 

U.08440C 

1.072966 

11. 
1 

1 

O.OOOOOolo.  000000  !o.OOOOOO|o.  000000 

O.OOOOOC 

0.000000  O.OOOOOC 

O.OOOOOC 

2 

.389571 

.289400  .289216 

.289015 

.288795 

.2885481  .288281 

.28798!^ 

2 

3 

.454196 

.453849  .453474 

.453064 

.452609 

.4521081  .451558 

.450952 

3 

4 

.567659 

.567130 

.566556 

.565925 

.56522!^ 

.564458  .563617 

.562691 

4 

6 

0.653082'0. 652363 

0.651580 

0.650718 

0.649767 

0.6487210.647576 

0.646315 

5 

6 

.720763 

.719845 

.718842 

.717740 

.716526 

.715191 

1  .713729 

.712123 

6 

7 

.776190 

.775063 

.773833 

.772481 

.770993 

.769358 

.767569 

.765604 

7 

8 

.822640 

.821297 

.819829 

.818217 

.816445 

.814499 

.812371 

.810033 

8 

9 

.862225 

.860656 

.858942 

.857061 

.854994 

.852727 

.850245 

.847525 

9 

10 

0.896385l0. 894583 

0.892613 

0.890452 

0.888081 

0.885479  0.882637 

0.879518 

10 

11 

-.926149 

.924104 

.921869 

.919419 

.916732 

.913789 

.910569 

.907045 

11 

12 

.952275 

.949978 

.947469 

.944720 

.941709 

.938409 

.934807 

.930865 

12 

13 

.975335 

.972779 

.969987 

.966931 

.963583 

.959922 

.955925 

.951558 

13 

14 

.995779 

.992955 

.■989871 

.986498 

.982807 

.978774 

.974375 

.969578 

14 

15 

1.013960 

1.010859 

1.007475 

1.003778 

0.999736 

0.995322 

0.990519 

0.985279 

15 

16 

.030162 

.026777 

.023087 

.019057 

1.014656 

1.009861 

1.004640 

.998959 

16 

17 

.044619 

.040945 

.036941 

.032573 

.027811 

.022622 

.016986 

1.010859 

17 

18 

.057527 

.053556 

.049232 

.044522 

.039390 

.033811 

.027756 

.021188 

18 

19 

.069049 

.064775 

.060127 

.055071 

.049569 

.043596 

.037127 

.030117 

19 

20 

1.079322il.074743'l.069768 

1.064362 

1.058491 

1.052128 

1.045244 

1.037800 

20 

21 

.088468 

.083579  .078276 

.072521 

.066284 

.059531 

.052239 

.044373 

21 

22 

.096590 

.091392 

.085760 

.079657 

.073056 

.065920 

.058234 

.049957 

22 

23 

.103782 

.098274 

.092315 

.085870 

.078908 

.071404 

.063332 

.054663 

23 

24 

.110126 

.104310 

.098030 

.091247 

.083938 

.076071 

.067634 

.058591 

24 

25 

1.115697 

1.109578 

1.102979 

1.095870 

1.088222 

1.080014 

1.071227 

1.061835 

25 

26 

.120563 

.114144 

.107239 

.099814 

.091845 

.083309 

.074197 

.064480 

26 

27 

.124787 

.118078 

.110875 

.103148 

.094873 

.086035 

.076619 

.066608 

27 

28 

.128426 

.121439 

.113953 

. 105940 

.097381 

.088259 

.078569 

.068295 

28 

29 

.131537 

.124284 

.116531 

.108251 

.099428 

.090050 

.080116 

.069610 

29 

30 

1.134173 

1.126669 

1.118665 

1.110140 

1.101077 

1.091471 

1.081322 

1.070611 

30 

31 

.136383 

.128644 

.120411 

.111662 

.102385 

.092580 

.082240 

.071362 

31 

32 

.138214 

.180260 

.121817 

.112869 

.103407 

.093423 

.082929 

.071909 

32 

33 

.139713 

.131563 

.122933 

.113809 

.104183 

.094057 

.083430 

.072299 

33 

34 

.140922 

.132596 

.123803 

.114528 

.104767 

.094518  .083788 

.072563 

34 

35 

1.141880 

1.133402 

1.124468 

1.115067 

1.105193 

1.094847  1.084031 

1.072733 

35 

36 

.142628 

.134018 

.124966 

.115459 

.105495 

.095070 

.084187 

.072838 

36 

37 

.143200 

.134479 

.125329 

.115739 

.105701 

.095214 

.084284 

.072899 

37 

,38 

.143628 

.134816 

.125587 

.115928 

.105834 

.095303 

.084339 

.072935 

38 

39 

.143940 

.135055 

.125763 

.116051 

.105916 

.095354 

.084373 

.072953 

39 

40 

1.144163 

1.1352181.125876 

1.116127 

1.105963 

1.095385 

1.084388 

1.072961 

40 

41 

.144314 

.135323 

.125946 

.116171 

.105991 

.095399 

.084396 

.072964 

41 

42 

.144412 

.135388 

.125987 

.116195 

.106004 

.095406 

.084399 

.072965 

42 

43 

.144472 

.135426 

.126010 

.116208 

.106011 

.095409 

.084399 

.072966 

43 

44 

.144507 

.135447 

.126022 

.116214 

.106013 

.095409 

.084400 

44 

45 

1.144526 

1.135458 

1.126028 

1.116216 

1.106013 

1.095410 

45 

46 

.144537 

.135463 

.126029 

.116217 

.106014 

46 

47 

.144541 

.135466 

.126030 

.116217 

47 

48 

.144541 

.135467 

.126031 

• 

48 

49 

.144542 

.135469 

49 

50 

51 

52 

53 

54 

55 

56 

57 

*56 


TABLE     XLIV. 


LIFE  AND  TEMPORARY  ANNUITIES.     LOGARITHM    OF  THE    PRESENT 
ANNUAL   PAYMENTS  OF  1   AT  THE  BEGINNING  OF  EACH  YEAR. 


VALUE    OF 
4  PER  CENT. 


Pay- 
ments. 

n. 


1 
2 
3 

4 

5 
6 

7 
8 
9 

10 
11 
12 
13 
14 

15 
16 
17 
18 
19 

20 
21 
22 
23 
24 

25 
26 
27 
28 
29 

30 
31 
32 
33 
34 


37 
38 
39 

40 
41 
42 


51 
50 

49 

48 
47 
46 
45 


x=bS 


1.06110 


59 


60 


0.000000 
.287660 
.450294 
.561680 

0.644940 
.710369 
.763457 
.807481 
.844552 

0.876115 
.903200 
.926569 
.946804 
.964355 

0.979585 
992791 

1.004222 
.014080 
.022546 

1.029777 
.035912 
.041075 
.045381 
.048935 

1.051830 
.054158 
.056003 
.057441 
.058535 

1.059355 
.059953 
.060379 
.060667 
.060853 


35  11.060968 

36  .061035 


.061074 
.061094 
.061102 

1.061106 
.061107 
.061107 


1.0488031.036042 


61 


1.022821 


0.000000  0.000000 


.286912 
.448766 
.559343 


.287305 
.449567 
.560568 

0.643427 

708441 
761100 
804679 
841294 

0.872389 
.898995 
.921878 
.941615 
.958664 

0.973391 

.986096 

.997024 

1.006388 

014370 

1.021132 
.026815 
.031550 
.035454 
.038632 

1.041187 
043210 
044786 
045985 
046884 

1.047539 
.048005 
.048320 
.048524 
.048650 

1.048723  1.036001 1.022802 


62 


63 


64 


1. 009130  0. 994950  0. 980284 


65 


0.965118 


0.000000  10.000000  0.000000  0.000000  0.000000 
.2864811  .286011  .285490  .2849211  .284292 
.447888!  .446929  .4458691  .444707|  .443431 
.558003,1  .556534    .5549151  .553142:  .551197 


0.641765  0.639943 
.706324;  .704004 
.758512  .755680 
.801608i  .798249 
.8377271  .833828; 

0.8683130.863865 
.894402!  .889392; 
.916756'  .9111761 
.9359591  .929808! 
.952472   .9457481 

0.966663  0.9593671 

.978832   .9709621 

.989233    .980817! 

.998078  .989123J 
1.005558!  .996082! 

1.0118351.001865' 
.017058  .006623 
.0213611  .010490 
.024861!  .013593!  1.001641 
.027672  .016048  .003753 


0.637947  0.63575l!0.633349|0. 630712 
.701465  .698676!  .695623!  .692286 
.752582  .749182  .7454711  .741409 
.794577  .790557  .786166  .781369 
.829572  .824914  .819834  .814292 


Pay- 
ments. 
n. 


0.859010  0. 
.883930 
.905105 
.923125 
.938453 

0.951469  0, 
.9624771 
.9717431 
.979490' 
.985917| 

0.991199  0 
.995485 
.998923 


853706  0.847930  0.841641 
877975^  .871501  .864458 
898497  .891319  .883533 
915860:  .907991  .899465 
,930543^  .921985  .912738 


1.0298971.017958 
.031629  .019410' 
.032946  .020498 
.033934  .021291 
.034654  .021855 

1.035166'l.  022237 
.035512  .022484 
.035736  .022636 
.035875  .0227251 
.035955  .022775! 


.048766 
.048788 
.048797 
.048801 


.036025  .022813 
.036035  .022820 
.036041  .022820 
.036041;  .022821 


1.048802' 1.036042! 
.048803 


49 


1.153265 
.153265 

1.153264 
.153262 
.153258 
.153248 
.153230 


49 


48 


47 


46 


1.177421 
1.1696921  .177420 
1.161644   .169691!  .177420 
161644   .1696911  .177418 


.161644 

1.161642 
.161638 
.161629 
.161612 
.161582 


48 


.169689  .1774141 

1.169685 
.169677 
.169661 
.169633 
.169584 


1.005360  0. 
.006562  . 
.007439  . 
.008062  . 
.008484  . 


1.008758 
.008925 
.009024 
.009079 
.009108 


,942918  0. 
,9533041  . 
,9619671  . 
.969141;  , 

.975027!  . 

,9797980. 
.983621:  . 
,9866411  . 
,988985:  . 
,9907691  . 

992103  0. 
993075'  . 
993766!  . 
994234;  . 
9945381  . 

994723'o. 

994833 

994894 

994926 

994941 


,933690  0.923742 
,943427  .932811 
,951472  .940221 
,958060  .946210 
,963393,  .950996 

9676610.954769 
,971029  .957693 
,973642  .959917 
.975629  .961578 
.9771151  .962787 

,978197  0.963646 
.978966  .964228 
,979487  .964606 
,979825'  .964837 
,9800321  .964974 

9801540.965049 
,9802221  .965088 
980257  .965107 
980274  .965116 
9802821  .965117 


45 


1.184839 

.184838 
.184838 
.184836 
.184833 
.184826 

1.177407  1.184812 


.177392 
.177365 
.177320 

.177246 


47 


46 


.184787 
.184745 
.184676 
.184570 


45 


44 


43 


42 


1.191959 
.191960 


1.205342 
1.198793  .205342 


.198792 
.198792 


.1919591.198790 
.1919581  .198787 
.191955  .198781 
.191948  .198769 
.191935  .198747 

1.1919121.198710 
.191872  .198650 
.1918081  .198557 
.191708'  .198419 
.191562  .198227 


44 


43 


42 


1 
2 
3 

4 

5 
6 

7 
8 
9 

10 
11 
12 
13 
14 

15 
16 
17 
18 
19 

20 
21 
22 
23 
24 

25 
26 
27 
28 
29 

30 
31 
32 
33 
34 


1.009121  0. 994948 0.980282lo. 965118  35 
.009128!  .9949481  .9802841 
.009128'  .994950 
.009130 


58 
57 


.205342i  56 
.2053411  55 

1.205338!  54 

.2053321  53 

.205321  52 

.205300,  51 

.205266  50 

1.205209 
.205122 
.204993 
.204812 
.204565 


49 
48 
47 
46 
45 


Continued  from  Page  *54. 


TABLE    XLIY. 


*57 


LIFE   AND  TEMPORARY  ANNUITIES. 


LOGARITHM   OF  THE    PRESENT    VALUE    OF    n 
ITT   YP.AR 

4  PER  CENT. 


Pay- 
ments. 


7 
8 
9 

10 
11 
12 
13 
14 

15 
16 
17 
18 
19 


27 

28 
29 


30 
31 
32 


59 
58 
57 
56 
55 

54 
53 
52 
51 
50 

49 
48 
47 
46 
45 


66 


0.949453 


67 


68 


0.9332710.916583 


0.000000  0 
.283608 
.442034 
,549005 

0.627836  0 
.688638 
.736976 
.776139 
.808262 

0.834803  0 
.856820 
.875100 
.890254 
.902769J 

0.91305010 
.921430' 
.928190J 
.933583 

^  .937829| 

20  J0.941117!0 

21  i  .9436161 

22  .945481! 

23  I  .946838! 

24  i  .947802J- 

25  0.948455  0 

26  \  .948878 
.949138 
.949291 
.949375 


0.949419  0 
.949440 
.949450 


33  .949451 

34  .949453 


0000000. 
282848J  . 
440493}  . 
546733j  . 

6246790. 

684643 

732127 

770433 

801690 

827369  0. 

848531 

865969 

880304 

892036 

901568  0. 
909241  . 
915351  . 
920154  . 

923868  . 

926690  0. 
928793  . 
930324  . 
931411  . 
932147  . 

932623  0. 
932916  . 
933089  . 
933183  . 
933232  . 

9332560. 
933267  . 
933269  . 
933271  - 


69 


0.899356 


70 


71 


0.88162310.863356 


000000 
280119 
434958 
538313 


000000 
282028 
438825 
544183 

621234 

680284 
726850 
764225 
794553 

819311 
839564 
856116 
869599 
880516 

889279 
896241 
901704 
905923 
909125 

911510  0. 89555^1 10. 878878 
913245  .896956!  .879966 
914476  .8979081  .880668 
915310  .898522;  .881100 
915849  .898899  .881354 


.000000 
.281111 
.436973 
.541374 

.617447 
.675511 
.721076 
.757451 

.786785, 

.810560' 
.829851 
.845477 
.858073 
.868150 

.876134'|o. 

.8823861  . 
.8872061  . 
.890861'  . 
.893580!!  . 


0.000000 
.279023 
.432742 
.534961 


0.613328  0.608817 


.670316 
.714804 
.750105 

.778375 

.801106 
.819388 
.834046 
.845724 
.854946 

862149 
867691 

871888 
875008 

877272 


916181!0.899121 
916376'  .899243 
916483  .899307 


916539 
916566 


.899338 
.899351 


916578  0.899355 
916581  .899356 
916583 


38 


41 


40 


1.217656 

1.2116321.217656 
211632  .217656 
217655 


.211632 
.211630 
.211628 

1.211622 
.211612 
.211592 
.211560 


.217652 
.217647 

1.217637 
.217619 

.217588 
.217538 


.2115071  .217461 

1.2114251.217348 
.2113041  .217189 
.211134  .216971 
.210902!  .216679 
.2105921  .216299 


41 


40 


39 

— — —  1.228972 

.223433  .228971 
.223433  .228970 


1.223433 
.223432 
.223430 
.223425 
.223415 

1.223398 
.223369 
.223323 
.223250 
.223144 

1.222994 
.222789 
.222515 
.222157 
.221699 


1.228969 
.228967 
.228963 
.228954 
.228938 

1.228911 

.228867 
.228799 
.228698 
.228557 

1.228364 
.228111 

.227770 
.227339 
.226796 


39 


38 


0.881494 
i  .881567 
I  .881602 
!  .881617 
j  .881622 

0.881623 


.664644 
.707970 
.742118 
.769254 

0.790885 
.808109 
.821761 
.832499 
.840860 

0.847278 
.852130 
.855732 
.858343 
.860194 

0.861448 
.862256 
.862754 
.863046 
.863208 


863291 
863332 
863349 
863355 
863356 


37 


1.234282 
.234283 
.234283 
.234282 

1.234280 
.234276 
.234267 
.234252 
.234227 

1.234185 
.234121 
.234027 
.233894 
.233712 

1.233470 
.233153 
.232746 
.232236 
.231603 


36 

239367 
,239367 
,239366 
,239366 
,239364 


37 


72 


73 


0.844568  0.825252 


0.000000  0.000000 


.277826 
.430325 
.531297 


.276518 
.427673 
.527292 


0.603900  0.598536 


.658470 
.700546 
.733460 
.759395 

0.779868 
795989 
808606 
818391 

825882 

0.831533 
.835721 

.838754 
.840902 
.842356 

0.843294 
.843870 
.844209 
.844396 
.844493 

0.844540 
844560 
844567 
844568 


.651748 
.692480 

.724082 
.748748 

0.768008 
.782987 
.794547 
.803367 
.810003 

0.814911 
.818460 
.820971 

.822670 
.823765 

0.824438 
.824833 
.825051 
.825164 
.825219 

0.825242 
.825250 
.825252 


35 


1.244234 

1.244234 
.244234 
.244233 
.244231 
.244228 


1.2393601.244220 


34 


1.248902 
.248901 

1.248901 
.248900 
.248898    62 


Pay- 
ments. 
n. 


.239352 
.239338 
.239314 
.239274 


.244207 
.244184 
.244147 
.244090 


1.2392141.244006 
.239125'  .243889 
.239000  .243727 
.238829  .243512 
.238600?  .243230 

1.2383011.242869 
.237919  .242415 
.237437  .241854 
.236842  .241169 
.236115  .240345 


36 


35 


.248894 
.248888 

1.248875 
.248853 
.248819 
.248765 
.248686 

1.248574 

.248422 
.248219 
.247953 
.247613 


34 


1 
2 
3 

4 

5 
6 
7 
8 
9 

10 
11 
12 
13 
14 

15 
16 
17 
18 
19 

20 
21 
22 
23 

24 

25 
26 
27 


65 

64 
63 


61 
60 

59 
58 
57 
56 
55 

54 
53 
52 
51 
50 


1.247184  49 

.246654  48 

.246009!  47 

.2453211  46 

.244308;  45 


Continued  from  Page  *53. 


*58 


TABLE    XLIY. 


LIFE  AND  TEMPORARY  ANNUITIES.    LOGARITHM  OP    THE    PRESENT  VALUE    OF  fi 

ANNUAL   PAYMENTS  OF  1   AT  THE  BEGINNING  OF  EACH  YEAR.      . 

4  PER  CENT. 


Pay- 
ments. 
n. 


1 
2 
3 
4 

5 
6 

7 
8 
9 

10 
11 
12 
13 
14 

15 
16 
17 
18 
19 

20 
21 
22 
23 
24 

25 
26 


67 
66 
65 

64 
63 
62 
61 
60 

59 
58 
57 
56 
55 

54 
53 
52 
51 
50 

49 
48 
47 
46 
45 


:74  i  76 


76 


0. 805400  0. 785049  0. 764174 


0.000000 
.275065 
.424759 
.522908 

0.592676 
.644425 
.683722 
.713931 
.737262 

0.755259 
.769063 
.779550 
.787413 
.793214 

0.797403 
.800361 
.802362 
.803651 
.804443 

0.804907 
.805163 
.805295 
.805360 
.805387 

0.805397 
.805400 


33 


0.000000 
.273492 
.421598 
.518143 

0.586317 
.636495 
.674263 
.702999 
.724930 

0.741621 
.754228 
.763641 
.770563 
.775551 

0.779068  0.759860 
781446,  .761692 


0.000000 
.271774 
.418136 
.512941 

0.579393 
627890 
664030 
691214 
711690 

0.727040 
.738439 
.746788 
.752788 
.757010 


77 


0.742769 


.782975 
,783914 
.784464 

0.784768 
.784925 
.785001 
.785033 
.785046 

0.785049 


0.000000 
.269873 
.414336 
.507254 

0.571857 
.618553 
.652969 
.678528 
.697499 

0.711486 
.721678 
.728977 
.734101 
.737552 

0.739769 
.741127 
.741923 
.742363 
.742590 

764026'0. 742699 
7641171  .742746 
764156  .742764 

7641711  .742769 
764174 


.762816 
.763475 
.763838 


31 


32 


1.257654 
1.2533721  .257654 


.253373 
.253373 


.257654 
.257653 


1.2533721.257652 
.253371!  .257649 


.253367 
.253361 
.253349 


.257642 
.257631 
.257612 


1.2533291.257581 
.253296'  .257533 
.253245  .257462 
.253170i  .257363 
.2530651  .257227 

1.25292l'l.257046 

.252729  .256809 


.252478 
.252157 
.251753 


.256505 
.256124 
.255651 


1.2512531.255075 

.250643  .254383 

249910  .253560 


.249038 
.248014 


33 


.252592 
.251467 


32 


1.261752 
.261752 
.261752 
.261751 
.261749 

1.261746 
.261740 
.261730 
.261712 
.261682 


30 


1.265675 

1.265676 
.265676 
.265675 
.265674 
.265671 

1.265665 
.265655 
.265638 
.265610 
.265568 


1.2616371.265504 


.261570 
.261476 
.261348 


.265416 
.265294 
.265132 


.261177  .264920 

1.2609531.264649 
.264308 
.263886 
.263371 
.262752] 

1.262017 
.261154 
.260149 
.258991 

.257667 


.260666 
.260305 
.259858 
.259314 

1.258660 
.257882 
.256968 
.255906 
.254680 


31 


78 


0.720875 


0.000000 
.267807 
.410203 
.501088 

0.563698 
.608478 
.641076 
.664943 
.682372 

0.694987 
.703979 
.710270 
.714497 


79 


80 


81 


0.698471  0.675562  0.652146 


0.000000  0.000000 
.2655471  .263074 
.4057001  .400793 
.494380|  .487095 

0.554856  0.545289 


.597600 
.628292 
.650410 
.666274 


.585882 
.614587 
.634915 
.649192 


0.677512  0.65907' 


.685338 
.690583 
.693941 
.71720R  .695994 


0.718869 
.719842 
.720379 
.720656 
.720789 


72084610. 
720868  . 

720875  = 


29 


.665675 
.669890 
.672462 
.673966 

0.674796 
.675225 
.675430 
.675517 
.675551 

698463'o.  675562 
698471 


0.697196 
.697859 
.698202 
.698366 
.698436 


27 


1.269428 
.269428 

1.2694281 
.269427 
.269426 
.269423 
.269418 

1.269409  1 
.269392! 
.269366 
.269325 


_?? 1.276466 

273025'  .276467 
,273025    .276467 


30 


.269266 

1,269182 
.269067 
.268913 
.268713 

.268456 

1.2681331, 
.267734 

.267247 
.266662 
.265967 

1.265150 
.264200 
.263105 
.261854 
.260433 


.273025|  .276467 

,273024!l.276465 
,273023!  .276463 
,273020,  .276458 
273015'  .276450 
,273006i  .276435 

,27299lll. 276412 
.272966  .276375 
.272928'  .276322 
.272871'  .276246 
.272792   .276143 

1.272683'l.276006 

.2725371  .275826 
.272348;  .275596 
.2721051  .275307 


Pay- 
ments, 
n. 


26 


1.279753 

.279749 
.279741 

.279727 
.279705 

1.279670 
.279620 
.279548 
.279451 
.279320 


27142111 

270961! 

270407 

269749 

268976J 

268077!l 

267041! 

265858 

264514 

263000 


29 


28 


,2745131 
,273988 
,273365 
,272634 

,271783 

2708031 

,269682; 

2684111 

266979 

265375i 


276819 
276126 
275321 
274392 

273332 
272128 
270773 
269255 
267565 


27 


26 


0.000000 
.260385 
.395450 
.479197 

0.534963 
.573294 
.599946 
.618441 
.631143 

0.639575!  10 

.644944  11 

.648213  12 

.650123  1  13 

.651175  14 

0.651718'  15 

.651979  16 

.652090  17 

.652133  18 

.652146  19 


1.279758  74 
.279758  73 
.279758 
.279757 
.279756 


72 
71 
70 


69 
68 
67 
66 
65 

64 
63 
62 
61 
60 


1.279150  59 

.278932  58 

.278658  57 

.278319  56 


.271799    .274949   .277906 1   55 


,277409'   54 


53 
52 
51 
50 

49 
48 
47 
46 
45 


Continued  from  Page  *52. 


TABLE   XLIT. 


*59 


LIFE  AND  TEMPORARY 
ANNUAL   PAYMENTS 


ANNUITIES.       LOGARITHM  OF  THE    PRESENT  VALUE    OF  fl 

OF  1   AT  THE  BEOINNING  OF  EACH  YEAR.    - 

4  PER  CENT. 


Pay- 
ments. 


1 

2 
3 
4 

5 
6 

7 
8 
9 

10 
11 
12 
13 

14 

15 
16 
17 
18 


75 

74 
73 
72 
71 
70 

69 
68 
67 
66 
65 

64 
63 
62 
61 
60 

59 
58 
57 
56 
55 

54 
53 
52 
51 
50 

49 
48 
47 
46 
45 


82 

0.628187 


83 


0.603703 


0.000000 
.257424 
.389631 
.470629 

0.523818 
.559791 
.584318 
.600972 
.611946 

0.618899 
.623121 

.625583 
.626938 
.627637 

0.627973 
.628115 
.028170 

.628187 


25 


0.000000 
.254238 
.383339 
.461402 

0.511880 
.545384 
.567754 
.582338 
.591516 

0.597065 
.600294 
.602070 
.602984 
.603424 

0.603609 
.603682 
.603703 


24 


1.285924 

1.282910    .285924 

1.282909  1.285924  1.288808 
.282909    .2859241  .288807 


84 


0.578554 


0.000000 
.250719 
.376475 
.451421 

0.499024 
.529994 
.549865 
.562249 
.569691 

0.574008 
.576377 
.577596 
.578182 
.578428 

0.578525 

.578554 


23 


1.288808 
.288808 
.288808 


.282908,  .285923 
.28290?!  .285921 
.282905!  .285917 


1.282901 
.282893 
.282880 
.282859 
.282826 

1.282778 
.282711 
.282618 
.282495 
.282333 

1.282127 

.281867 
.281546 
.281154 
.280683 

1.280124 
.279468 

.278704 
.277825 
.276820 

1.275681 
.274397 
.272960 
.271360 
.269587 


25 


1.285909 
.285897 
.285877 
.285846 
.285800 

1.285736 

.285648 
.285531 
.285378 
.285182 

1.284936 
.284631 
.284260 
.283814 
.283284 

1.282661 
.281938 
.281105 
.280153 
.279073 

1.277857 
.276496 
.274981 
.273302 
.271450 


24 


.288805 
.288801 
.288794 

1.288783 
.288764 
.288734 
.288691 
.288630 

1.288547 
.288436 
.288291 
.288105 

.287871 

1.287582 
.287230 
.286807 
.286304 
.285714 

1.285028 
.284238 
.283336 
.282312 
.281160 

1.279870 
.278435 
.276844 
.275091 
.273165 


23 


85 


86 


0.55271210.525914 


0.000000  0.000000 


.246926 
.369109! 

.440707 1 

0.485329i 
.513258 
.530408 
.540626 
.546524 

0.549752 
551409 
552205 
552541 
552671 

0.552712 


22 


.291567 
.291567 
.291567 
.291566 

1.291565 
.291563 
.291560 
.291553 
.291542 

1.291524 
.291496 
.291455 
.291397 
.291319 

1.291213 
.291075 
.290899 

.290677 
.290403 

1.290069 
.289668 
.289191 
.288631 
.287981 

1.287231 
.286375 
.285405 
.284312 
.283090 

1.281729 
.280222 
.278561 
.276736 

.274740 


.242837 
.361116 
.429204 

0.470086 
.494585 
.509034 
.517295 
.521796 

0.524104 
.525209 
.525677 
.525857 
.525914 


21 


22 


87 


0.497713 


0.000000 
238267 
352422 
415840 

0.452376 
473468 
485385 
491835 
495133 


88 


89 


0.46771810.434386 


496709 
497375 
497632 
497713 


20 


296729 

296729 
296729 
296729 
296728 
296726 


0. 000000  0. 
.2334961  , 
.341682!  , 
.399517'  , 

0.4316950. 
.449522!  . 
.459073 
.463930 
.466244 


0.467223 
.467599 
.467718 


19 


1.299144 
.299144 

1.299144 
.299144 
.299143 
.299141 
.299138 


1.2967231.299133 
.296717  .299123 


.296707 
.296691 
.296666 


.299108 
.299084 
.299049 


1.294205 

.294205 

.294205 
^  .294205 

.294204 

1.294202 
.294199 
.294193 
.294182 
.294165 

1.294138 

.294099 

.294045 
,  .293970 

.293870 

1.293739 
.293572 
.293361 
.293101 

.292784 

1.292403 
.291950 
.291419 
.290802 
.290091 

1.289279  1.29118011.292942 
.288359  .290197  .291898 


1.2966291.298999 
.2965771  .298932 
.296506|  .298841 
.296410  .298724 
.2962871  .298573 

1.29612811.298383 
.295928  .298148 
.295681  .297863 
.295380  .297519 
.295018  .297111 

1.2945891.296632 
.294084;  .296076 
.293498  .295435 
.2928241  .294704 
.292053!  .293875 


.287322 
.286163 
.284873 

1.283444 

.281869 
.280141 
.278250 
.276188 


21 


.289097 

.287873 
.286518 

1.285025 
.283386 
.281593 
.279640 
.277516 


20 


.290737 
.289451 
.288035 

1.286481 
.284781 
.282929 
.280916 
.278735 


19 


000000 
225360 
326255 
378512 

406483 
.421206 
.428627 
.432148 
.433635 

0.434205 
.434386 


18 


1.301453 
.301453 
.301453 

1.301453 
.301452 
.301450 
.301448 
.301442 

1.301433 
.301419 
.301396 
.301362 
.301316 

1.301251 
.301166 
.301054 
.300910 
.300730 

1.300507 
.300236 
.299909 
.299522 
.299067 

1.298539 
.297931 
.297236 
.296449 
.295563 

1.294572 
.293470 
.292250 
.290906 
.289431 

1.287819 
.286063 
.284154 
.282087 
.279852 


18 


Pay- 
ments, 
n. 


1 

2 
3 

4 

5 
6 

7 
8 
9 

10 
11 


82 
81 
80 

79 
78 
77 
76 
75 

73 
74 
72 
71 
70 

69 
68 
67 
66 
65 

64 
63 
62 
61 
60 

59 
58 
57 
56 
55 

54 
53 
52 
51 
50 

49 
48 
47 
46 
45 


Continued  from  Page  *51. 


♦60 


TABLE    XLIV. 


LIFE  AND  TEMPORARY  ANNUITIES.      LOGARITHM   OF  THE   PRESENT  VALUE  OP    n 
ANNUAL   PAYMENTS   OF   1   AT   THE   BEGINNING   OF   EACH   YEAR. 

4  PER  CENT. 


Pay-  I  a;=90 

ments. 


78 
77 
76 
75 


73 
72 
71 
70 

69 
68 
67 
66 
65 

64 
63 
62 
61 


57 
56 
55 

54 
53 
52 
51 
50 

49 
48 
47 
46 
45 


0.402608 


1 
2 
3 

4 

5 
6 

7 
8 
9 

10 


0.000000 
.216431 
.310577 
.357604 

0.381571 
.393460 
.399061 
.40141? 
.402319 

0.402608 


17 


83 
82 
81 
80 

79  1.303660 


1.303662 
.303662 
.303662 
.303661 


91 


0.373607 


0.000000 
.208653 
.296383 
.338221 


358362 
367723 
371634 
373129 

373607 


16 


92 


0.344609 


93 


0.314696 


0.000000 
.200520 
.281311 
.317835 

0.334359 
.341183 
.343779 
.344609 


15 


0.000000 
.191140 
.264501 

.295797 

0.308421 
.313181 
.314696 


14 


.303659 
.303656 
.303651 
.303643 


1.305773 
.305774 
.305774 
.305773 
.305772 

1.305771 
.305769 
.305764 
.305755 
.305742 


1.309720 
1.307791|  .309720 

1.30779l!l.309720 

30779l!  .309720 

.307791  .309719 

.3077901  .309718 

.3077891  .309716 

1.3077861.309712 
.3077821  .309705 
.307775  .309692 
.307761  .309674 


.307742 


.309646 


74  1.303629  1.305722  1.307713  1.309608 


.303607 
.303575 
.303531 
.303470 


.305692!  .307673!  .309556 

.'3056491  .307618;  .309486 

.305591  .307544;  .309395 

.305514  .307448!  .309277 


1.303388  1.305413  1.3073251.309130 


.303^82 
.303146 
.302975 
.302763 

1.302505 
.302195 
.301827 
.301395 


60  i  .300893 

59  1 1.300315 

58  i  .299655 
.298907 
.298066 
.297125 


1.296078 
.294920 
.293644 
.292245 
.290715 

1.289049 
.287239 
.285278 
.283160 
.280875 


17 


.305283!  .307170  .308948 

.305120  .306979]  .308727 

.304919  .3067461  .308460 

.3046741  .306466  .308144 

1.304379  1.306133'l.307773 
3040291  .305743  .307342 


.303619 
.303142 
.302593 


.305290 
.304768 
.304172 


1.3019661.303497 
.301255j  .302737 
.300456  .301888 
.299563  .300944 
.298568  .299898 

1.297469!  1.298748 

.296257|  .297486 

.294928  .296107 

.293476  .294606 

291895  .292976 


1.290178 
.288318 
.286309 
.284142 
.281811 


16 


1.291211 
.289304 
.287250 
.285039 
.282666 


15 


.306846 
.306279 
.305638 

1.304916 
.304109 
.303211 
.302219 
.301125 

1.299926 
.298617 
.297191 
.295643 
.293968 

1.292159 
.290209 
.288112 
.285861 
.283446 


14 


94 


0.284280 


0.000000 
.180950 
.246836 
.272024 

0.281336 
.284280 


13 


1.311567 
.311567 
.311567 

1.311567 
.311566 
.311565 
.311563 
.311558 

1.311551 
.311540 
.311522 
.311496 
.311460 

1.311410 
.311343 
.311257 
.311145 
.311005 


95 


0.252440 


0.000000 
.170487 
.226526 
.246291 

0.252440 


12 


1.313333 
.313333 
.313333 
.313333 

1.313333 
.313331 
.313329 
.313325 
.313318 

1.313308 
.313291 
.313266 
.313231 
.313184 


96 


0.214754 


0.000000 
.153574 
.200677 
.214754 


11 


1.315019 
.315020 
.315020 
.315019 
.315019 

1.315018 
.315016 
.315011 
.315006 
.314995 

1.314979 
.314956 
.314923 
.314878 
.314817 


97 


0.178369 


000000 
,141329 
,178369 


Pay- 
ments, 


1.316633'  89 

.3166331  88 

.316G33I  87 

.316632  86 

.316631  85 

1.316629 
.316626 
.316620 
.316610 
.316595 

1.316572 
.316541 
.316498 
.316441 
.316367 


1.313120  1.314739,1.316271 
.313038  .314638  .316150 


.312932 
.312799 
.312634 


.3145111  .316000 
.314354  .315819 
.314163  .315601 


1.3108321.3124341.3139341.315342 


.310621:  .312193 
.310368'  .311906 


.310067 
.309714 

1.309305 
.308833 
.308295 
.307685 
.306998 

1.306231 
.305378 
.304435 
.303395 
.302256 

1.301012 
.299658 
.298188 
.296597 
.294879 

1.293029 
.291038 
.288903 
.286613 
.264163 

13 


.311571 


3136621  .315038 


.313343 
.312972 


311181  .312545 


1.310732 
.310220 
.309640 
.308987 
.308258 

1.307447 
.306550 
.305562 
.304480 
.303298 


1.312058 
.311506 
.310885 
.310191 
.309420 

1.308567 
.307628 
.306599 
.305475 
.304252 


1.3020101.302926 


.300614 
.299103 
.297472 
.295714 

1.293825 
.291798 
.289626 
.287302 
.284817 


12 


.301489 
.299939 
.298270 
.296476 

1.294552 
.292490 
.290285 
.287928 
.285413 


11 


.314685 
.314279 
.313814 

1.313289^  64 

.312699  63 

.312039  62 

.311305  61 

.310494  60 

1.309601 
.308622 
.307554 
.306391 
.305130 

1.303765 
.302293 
.300707 
.299003 
.297176 

1.295218  49 
.293124!  48 
.290888  47 
.288502 
.285958 


10 


Continued  from  Page  *50. 


TABLE     XLY. 


♦61 


LIFE  AND  TEMPORARY  ANNUITIES.      LOGARITHM   OF  THE  PRESENT  VALUE  OF  n 
ANNUAL  PAYMENTS  OF  1   AT  THE  BEGINNING  OF  EACH   YEAR. 

The  first  Value  under  the  Age  a;  is  A(l  +  Oas)  for  the  whole  Life.  4i    PER  CENT. 


Pay- 

a;=10 

11 

12 

13 

14 

15 

16  1   17 

Pay- 

ments. 
n. 

1 

ments. 
n. 

1 

1.281791 

1.280417 

1.278977 

1.277464 

1.275875!l.274211^1.272467 

i       1 

1.270632 

0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

o.oooooo'o.ooodoo 

0.000000 

2 

.290199 

.290194 

.290191 

.290187 

.290180 

.290174 

.290170 

.290163 

2 

3 

.455548 

.455540 

.455533 

.455523 

.455510 

.455500 

.455490 

.455475 

3 

4 

.569836 

.569823 

.569811 

.569796 

.569778 

.569762 

.569745 

.569723 

4 

5 

0.656184 

0.656166 

0.656149 

0.656129 

0.656106 

0.656083 

0.656060 

0.656031 

5 

6 

.724891 

.724869 

.7248471  .724822 

.724792 

.724764 

.724734 

.724696 

6 

7 

.781454 

.781427 

.781400 

.781369 

.781333 

.781299 

.781260 

.781213 

7 

8 

.829151 

.829119 

.829087 

.829049 

.829008 

.828964 

.828918 

.828863 

8 

9 

.870097 

.870061 

.870022 

.869979 

.869929 

.869879 

.869825 

.869761 

9 

10 

0.905737 

0.905694 

0.905650 

0.905600 

0.905544 

0.905486 

0.905423 

0.905350 

10 

11 

.937099 

.937051 

.937001 

.936944 

.936880 

.936814 

.936742 

.936657 

11 

12 

.964945 

.964891 

.964834 

.964770 

.964699 

.964624 

.964542 

.964448 

12 

13 

.989852 

.989792 

.989728 

.989657 

.989577 

.989493 

.989401 

.989296 

13 

14 

1.012269 

1.012202 

1.012131 

1.012052 

1.011963 

1.011870 

1.011767 

1.011651 

14 

15 

1.032550 

1.032477 

1.032398 

1.032310 

1.032214 

1.032109 

1.031996 

1.031867 

15 

16 

.050984 

.050902 

.050815 

.050721 

.050612 

.050498 

.050374 

.050235 

16 

17 

.067801 

.067712 

.067620 

.067513 

.067396 

.067271 

.067137 

.066984 

17 

18 

.083199 

.083105 

.083000 

.082885 

.082758 

.082624!  .082476 

.082306 

18 

19 

.097341 

.097235 

.097123 

.096998 

.096862 

.096715 

.096551 

.096368 

19 

20 

1.110358 

1.110246 

1.110124 

1.109991 

1.109842 

1.109680 

1.109504 

1.109307 

20 

21 

.122374 

.122252 

.122123 

.121978 

.121815 

.12164] 

.121451 

.121239 

21 

22 

.133486 

.133357 

.133216 

.133057 

.132884 

.132696 

.132493 

.132263 

22 

23 

.143783 

.143643 

.143489 

.143322 

.143134 

.142935  .142713 

.142466 

23 

24 

.153339 

.153186 

.153024 

.152842 

.152644 

.152427  .152190 

.151925 

24 

26 

1.162219 

1.162058 

1.161882 

1.161690 

1.161476 

1.161243  1.160989 

1.160705 

25 

26 

.170486 

.170312 

.170127 

.169919 

.169689 

.169441 

.169169 

.168867 

26 

27 

.178187 

.178005 

.177804 

.177582 

.177338 

.177072 

.176783 

.176459 

27 

28 

.185374 

.185177 

.184962 

.184727 

.184465 

.184183 

.183874 

.183528 

28 

29 

.192081 

.191871 

.191644 

.191392 

.191115 

.190814 

.190483 

.190119 

29 

30 

1.198348 

1.198126 

1.197884 

1.197617 

1.197322 

1.197000 

1.196653 

1.196259 

30 

31 

.204210 

.203974 

.203716 

.203433 

.203118 

.202781 

.202404 

.201993 

31 

32 

.209695 

.209443 

.209171 

.208868 

.208539 

.208174 

.207780 

.207340 

32 

33 

.214828 

.214564 

.214272 

.213955 

.213600 

.213219 

.212798 

.212332 

33 

34 

.219639 

.219355 

.219050 

.218709 

.218339 

.217932 

.217486 

.216993 

34 

1  35 

1.224142 

1.223846 

1.223519 

1.223163 

1.2227681.222337 

1.221866 

1.221347 

35 

36 

.228367 

.228049 

.227708 

.227329 

.226910  .226455 

.225960 

.225410 

36 

37 

.232323 

.231991 

.231629 

.231226 

.230785 

.230308 

.229782 

.229201 

37 

38 

.236034 

.235684 

.235298 

.234875 

.234412 

.233905 

.233351 

.232739 

38 

39 

.239513  .239141 

.238735  .238291 

.237800 

.237267 

.236684  .236038 

39 

40 

1.242772 

1.242380 

1.2419551.241485 

1.240969 

1.240408  1.239792  1.239114 

40 

41 

.245827 

,245417 

.244966 

.244473 

.243930 

.2433381  .242691'  .241977 

41 

42 

.248692 

.248257 

.247785 

.247265 

.246693 

.246072  .245391  .244640 

42 

43 

.251372 

.250917 

.250420 

.249872 

.249273 

.248619  .247903  .247117 

43 

44 

.253883 

.253405 

.252881 

.252308 

.251677 

.250990  .250240  .249414 

44 

10 

11 

12 

13 

14 

15     16     17 

Continued  on  Page  *71. 


FOEMULA,   A(l-f  ^^-1)   =  A  ^=^~^^^^  =  Agg=l. 

Dx  VPx—l 


♦62 


TABLE    XLV. 


LIFE   AND  TEMPORARY  ANNUITIES.     LOGARITHM    OF  THE    PRESENT    VALUE    OF  W 
ANNUAL  PAYMENTS  OF  1  AT  THE  BEGINNING  OF  EACH  YEAR. 

4|^  PER  CENT. 


1  Pay- 

niPTits 

a;=18 

19 

20 

21 

22 

23 

24 

25 

Pay- 
ments. 
n. 

i  n. 
1* 

1.268708|l.366691 

1.264573 

1.262353 

1.260026 

1.257585,1.255025 

1.252341 

0.000000  0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

1 

2 

.290155 

.290148 

.290139 

.290129 

.290119 

.290107 

.290094 

.290081 

2 

3 

.4554601  .455445 

.455426 

.455406 

.455385 

.455361 

.455335 

.455306 

3 

4 

.569701 

.569677 

.569647 

.569617 

.569584 

.569547 

,569506 

.569462 

4 

5 

0.655999 

0.655965 

0.655926S0. 655884 

0.655840 

0.655789 

0.655733 

0.655673 

5 

6 

.724655 

.724612 

.724562 

.724509 

.724452 

.724387 

.724316  .724239 

6 

7 

.781164 

.781111 

.781050 

.780984 

.780914 

.780835 

.780748:  .780653 

7 

8 

.828805 

.828741 

.828668 

.828590 

.828506 

.828411 

.828307 

.828194 

8 

9 

.869692 

.869617 

.869532 

.869441 

.869342 

.869231 

.869110 

.868976 

9 

10 

0.905269 

0.905182 

0. 905086 

0.904980 

0.904866 

0.904739 

0.904598 

0.904444 

10 

11 

.936567 

.936469 

.936358 

.936238 

.936109 

.935963 

.935802 

.935627 

11 

n 

.964346 

.964234 

.964110 

.963976 

.963828 

.963663 

.963483 

.963285 

12 

13 

.989182  .989057 

.988920 

.988768 

.988602 

.988418 

.988217 

.987997 

13 

14 

1.0115231.011387 

;.  011233 

1.011063 

1.010880 

1.010676 

1.010453 

1.010207 

14 

15 

1.031729  .031577 

1.031404 

1.031219 

1.031017 

1.030792 

1.030544 

1.030273 

15 

16 

.050082  .049911 

.049724 

.049521 

.049298 

.049051 

.048779 

.048481 

16 

17 

.066813  .066629 

.066425 

.066202 

.065958 

.065687 

.065391 

.065065 

17 

18 

.082122  .081922 

.081699 

.081456 

.081189 

.080896 

.080572 

.080217 

18 

19 

.096170  .095952 

.095710 

.095445 

.095157 

.094836 

.094486 

.094102 

19 

20 

1.1090921.108856 

1.108593 

1.108308 

1.107993 

1.107649 

1.107270 

1.106852 

20 

21 

.121006 

.120750 

.120468 

.120157 

.119821 

.119449 

.119037 

.118586 

21 

22 

.132011 

.131737 

.131430 

.131099 

.130736 

.130332 

.129891 

.129406 

22 

23 

.142196 

.141899 

.141573 

.141217 

.140823 

.140392 

.139917 

.139397 

23 

24 

.151634  .151318 

.150968 

.150583 

.150164 

.149700 

.149192 

.148633 

24 

25 

1.1603961.160056 

1.159680 

1.159270 

1.158819 

1.158325 

1.157780 

1.157181 

25 

26 

.168535 

.168171 

.167771 

.167331 

.166852 

.166321 

.165738 

.165099 

26 

27 

.176104 

.175718 

.175288 

.174822 

.174308 

.173741 

.173120 

.172441 

27 

28 

.183153 

.182737 

.182283 

.181783 

.181235 

.180633 

.179973 

.179247 

28 

29 

.189714 

.189277 

.188791 

.188258 

.187676 

.187037 

.186333 

.185563 

29 

30 

1.195835 

1.195367 

1.194849 

1.194284 

1.193668 

1.192987 

1.192240 

1.19.1422 

30 

31 

.201539 

.201041 

.200493 

.199896 

.199239 

.198517 

.197725 

.196859 

31 

32 

.206858 

.206332 

.205753 

.205118 

.204421 

.203656 

.202820 

.201900 

32 

33 

.211823 

.211266 

.210652 

.209978 

.209241 

.208434^  .207546 

.206577 

33 

34 

.216456 

.215865 

.215214 

.214503 

.213726 

.212870 

.211935 

.210909 

34 

35 

1.220777 

1.220152 

1.219465 

1.218714 

1.217892 

1.216991 

1.216002 

1.214921 

35 

36 

.224807 

.224148 

.223423 

.222631 

.221765 

.220810 

.219771 

.218631 

36 

37 

.228566 

.227870 

.227107 

.226272 

.225356 

.224355 

.223258 

.222059 

37 

38 

.232069 

.231337 

.230532 

.229651 

.228690 

.227635 

.226482 

.225222 

38 

39 

.235334 

.234563  .233714 

.232789 

.231777 

.230669 

.229458 

.228136 

39 

40 

1.2383721.237559 

1.2366691.235696 

1.234634 

1.233471 

1.232201 

1.230815 

40 

41 

.2411961  .240344 

.239408]  .238388 

.237273 

.236054 

.234723 

.233272 

41 

42 

.243822 

.242926 

.241946 

.240875 

.239707 

.238430 

.2370371  .235520 

42 

43 

.246257 

.245319 

.244290 

.243169. 

.241946 

.240610 

.239156  .237571 

43 

44 

.248515 

.247530 

.246454 

.245280, 

.244002 

.242608 

.241088 

.239436 

44 

18 

19 

20 

21 

22 

23 

24 

25 

Continued  on  Page  *70. 


TABLE     XLY. 


♦63 


LIFE  AND  TEMPORARY  ANNUITIES.     LOGARITHM    OF  THE    PRESENT   VALUE   OF    n 
ANNUAL  PAYMENTS  OF  1   AT  THE  BEGINNING  OF  EACH  YEAR. 

4^  PER   CENT. 


Pay. 

26 

27 

28 

29 

30 

31 

32 

.  33 

Pay- 

ments, 
n. 

ments. 

1.249527 

1.246580 

1.243489 

1.240250 

1.236862 

1.233310 

1.229589 

1.225692 

n. 
1 

1 

0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

2 

.290064 

.290047 

.290029 

.290005 

.289984 

.289960 

.289933 

.289903 

2 

3 

.455372 

.455239 

.455200 

.455154 

.455111 

.455060 

.455003 

.454943 

3 

4 

.569412 

.569360 

.569299 

.569232 

.569163 

.569084 

.568999 

.568903 

4 

5 

0.655606 

0. 655533 

0.655452 

0.655360 

0.655265 

0.655159 

0.655039 

0.654910 

5 

6 

.724152 

.724060 

.723955 

.723838 

.723718 

.723578 

.723428 

.723261 

6 

7 

.780547 

.780431 

.780303 

.780162, 

.780009 

.779842 

.779656 

.779452 

7 

8 

.828066 

.827929 

.827777 

.827605 

.827427 

.827224 

.827003 

.826758 

8 

9 

.868827 

.868667 

.868486 

.868290 

.868077 

.867843 

.867582 

.867296 

9 

10 

0.904273 

0.904086 

0.903882 

0.903653 

0.903410 

0.903137 

0.902838 

0.902507 

10 

11 

.935431 

.935221 

.934987 

.934729 

.934449 

.934140 

.933798 

.933423 

11 

12 

.963067 

.962828 

.962565 

.962273 

.961958 

.961609 

.961225 

.960801 

12 

13 

.987751 

.987485 

.987190 

.986864 

.986512 

.986122 

.985691 

.985221 

13 

14 

1.009935 

1.009639 

1.009312 

1.008950 

1.008560 

1.008125 

1.007650 

1.007127 

14 

15 

1.029973 

1.029647 

1.029285 

1.0288881.028454 

1.027977 

1.027452 

1.026874 

15 

16 

.048152 

♦.047793 

.047398 

.046958;  .046485 

.045961 

.045384 

.044750 

16 

17 

.064705 

.064314 

.063878 

.063401  .062883 

.062309 

.061679 

.060985 

17 

18 

.079827 

.079397 

.078926 

.078406  .077841 

.077217 

.076539 

.075775 

18 

19 

.093675 

.093211 

.092699 

.092135!  .091522 

.090843 

.090099 

.089381 

19 

20 

1.106391 

1.105889 

1.105335 

1.104725  1.104060 

1. 103327 

1.103533 

1.101637 

20 

21 

.118090 

.117548 

.116950 

.116291!  .115574 

.114785 

.113915 

.113964 

21 

22 

.128872 

.128288 

.127644 

.126935  .126165 

.125313 

.134383 

.133356 

22 

23 

.138823 

.138195 

.137503 

.136744  .135915 

.135004 

.134001 

.133903 

23 

24 

.148018 

.147344 

.146605 

.145789  .144904 

.143925 

.142855 

.141679 

24 

25 

1.156522 

1.155804 

1.155011 

1.154142  1.153192 

1.152150 

1.151004 

1.149749 

25 

26 

.164398 

.163628 

.162784 

.1618541  .160844 

.159730 

.158510 

.157173 

26 

27 

.171690 

.170873 

.169970 

.1689831!  .167905 

.166720 

.165422 

.163999 

27 

28 

.178451 

.177578 

.176621 

.1755691  .174424 

.173165 

.171785 

.170374 

28 

29 

.184715 

.183790 

.182772 

.181657  .180440 

.179104 

.177641 

.176040 

29 

30 

1.190524 

1.189540 

1.188463 

1.187279  1.185990 

1. 184574 

1.183026 

1.181333 

30 

31 

.195905 

.194866 

.193723 

.192471!  .191105 

.189609 

.187973 

.186184 

31 

32 

.200894 

.199792 

.198584 

.197259; 

.195818 

.194238 

.192512 

.190635 

32 

33 

.205511 

.204348 

.203071 

.201674 

.200153 

.198489 

.196669 

.194684 

33 

34 

.209785 

.208556 

.207211 

.2057381 

1 

.204137 

.202384 

.200471 

.198385 

34 

35 

1.213735 

1.212440 

1.211023 

1.209475: 

1.207790 

1.205948 

1.203940 

1.301749 

35 

36 

.217382 

.216020 

.214532 

.212904; 

.211134 

.209202  .207094 

.304803 

36 

37 

.220746 

.219316 

.217752 

.216043! 

.214189 

.212162 

.209959 

.307560 

37 

38 

.223844 

.222343 

.220702 

.218913 

.216968 

.214851 

.212540 

.310046 

38 

39 

.226691 

.225117 

.223399 

.221525 

.219495 

.217275 

.214880 

.212273 

39 

40 

1.229301 

1.227653 

1.225856 

1.223900 

1.221773 

1.219474 

1.216972 

1.214262 

40 

41 

.231688 

.229966 

.228090 

.226043 

.223840 

.221440 

.218840 

.216027 

41 

42 

.233865 

.232068 

.230107 

.227987 

.225689 

.233196 

.220500 

.217586 

42 

43 

.235845 

.233967 

.231936 

.229727 

.227341 

.224757 

.221965 

.318953 

43 

44 

.237634 

.235690 

.233575 

.231282 

.228809 

.226135 

.223249 

.330140 

44 

26 

27 

28 

29 

30 

31 

32 

33 

Continued  on  Page  *69. 


♦64 


TABLE    XLY. 


LIFE  AND  TEMPORARY  ANNUITIES.     LOGARITHM  OF  THE    PRESENT    VALUE    OF    n 
ANNUAL  PAYMENTS    OF  1   AT  THE  BEGINNING  OF  EACH  YEAR. 

4^  PER  CENT. 


Pay- 
mcnts. 

a;=34 

35 

36 

37 

38 

1.203309 

39 

40 

41 

Pay- 
ments. 

11. 

n. 

1.2216121.217341 

1.212877 

1.208201 

1.198189 

1.1928391.187248 

1 

0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

0.000000  0.000000 

1 

2 

.289869 

.289829 

.289792 

.289749 

.289699 

.289644 

.289585  .289524 

2 

3 

.454871 

.454795 

.454715 

.454627 

.454525 

.454414 

.454295!  .454164 

3 

4 

.568797 

.568679 

.568557 

.568419 

.568263 

.568095 

.567910!  .567709 

4 

5 

0.654765 

0.654607 

0.654438 

0.654249 

0.654038 

0.653808 

0.653556  0.653281 

5 

6 

.723078 

.722875 

.722658 

.722416 

.722146 

.721852 

.7215301  .721178 

6 

7 

.779226 

.778977 

.778710 

.778412: 

.778081 

.777721 

.777325 

.776892 

7 

8 

.826489 

.826192 

.825872 

.825516, 

.825123 

.824691 

.824218 

.823701 

8 

9 

.866980 

.866634 

.866258 

.865844 

.865382 

.864877 

.864325 

.863717 

9 

10 

0.902145 

0.901745 

0.901314 

0.900835 

0.900303 

0.899723 

0.899084 

0.898388 

10  1 

11 

.933010 

.932558 

.932065 

.931518 

.930915 

.930253 

.929530 

.928738 

11  : 

12 

.960338 

.959827 

.959270 

.958656 

.957975 

.957233 

.956419 

.955525 

12 

13 

.984702 

.984130 

.983509 

.982821 

.982064 

.981235 

.980325 

.979329 

13 

14 

1.006550 

1.005917 

1.005226 

1.004465 

1.0036251.002706 

1.001698 

1.000592 

14 

15 

1.0262391.025539 

1.024779 

1.023939 

1.02301411.022001 

1.020890 

1.019673 

15 

16 

.044051 

.043286 

.042450 

.0415301  .040516 

.039405 

.038187 

.036854 

16 

17 

.060224 

.059387 

.058475^  .057470 

.056362 

.055150 

.053823 

.052366 

17 

18 

.074947 

.074037 

.073045;  .071951 

.070747 

.069432;  .067987 

.066407 

18 

19 

.088382 

.087397 

.086320^  .085135^ 

.083834 

.0824061  .080844 

.079135 

19 

20 

1.100668 

1.099602 

1.0984381.097161 

1.095753 

1.094215 

1.092530 

1.090686 

20 

21 

.111917 

.110769 

.109518  .108140 

.1066261  .104971 

.103159 

»101175 

21 

22 

.122232 

.121000 

.119654:  .118175 

.116551  .114775 

.112830 

.110708 

22 

23 

.131699  .130377 

.128935 

.127351 

.125612  .123711 

-121635 

.119364 

23 

24 

.140390 

.138977 

.137436 

.135743 

.133886 

.131860 

.129643 

.127224 

24 

25 

1.148374 

1.146867 

1.145221 

1.143417 

1.141441 

1.139282 

1.136925 

1.134351 

25 

26 

.155707 

.154101 

.152351 

.150434 

.148332 

.146040 

.143535 

.140805 

26 

27 

.162440 

.160735 

.158877 

.156840 

.154613 

.152181 

.149530 

.146642 

27 

28 

.168621 

.166813 

.164842 

.162687 

.160327 

.157756 

.154955 

.151907 

28 

29 

.174289 

.172375 

.170291 

.168011 

'  .165519 

.162806 

.159854 

.156641 

29 

30 

1.179481 

1.177459 

1.175258 

1.172852 

1.170225!l.  167370 

1.164262 

1.160891 

30 

31 

.184230 

.182098 

.179777 

.177243 

.174483'  .171480 

.168222;  .164682 

31 

32 

.188567 

.186321 

.183879 

.181220 

.178318 

.175174 

.171756,  .168056 

32 

33 

.192519 

.190158 

.187597 

.184803 

.181768 

.178472 

.174904  .171042 

33 

34 

.196110 

.193636 

.190948 

.188028 

.184851 

.181412 

.177691  .173673 

34 

35 

1.1993681.196774 

1.193966 

1.190912 

1.187599 

1.1840171.180148 

1.175973 

35 

36 

.202308:  .199601 

.196666 

.193483 

.190035 

.186313 

.182297 

.177971 

36 

37 

.204958  .202131 

.199075 

.195764  .192183 

.188323 

.184163 

.179690 

37 

38 

.207330 

.204389 

.201212 

.197775 

.194065 

.190068 

.185770 

.181162 

38 

39 

.209449 

.206393 

.203096 

.199538 

.195698  .191571 

.187146 

.182407 

39 

40 

1.211329 

1.208160 

1.204749 

1.201068 

1.1971061.192859 

1.188311 

1.183447 

40 

41 

.212988 

.209710 

.206183 

.202387 

.198311  .193949 

.189283 

.184307 

41 

42 

.214443 

.211056 

.207420 

.203517 

.199333 

.194860 

.190088 

.185011 

42 

43 

.215707 

.212218 

.208481 

.204475 

.200186 

.195613 

.190746 

.185576 

43 

44 

.216799 

.213213 

.209379  .205275 

.200892 

.196229 

.191275 

.186022 

44 

34 

35 

36 

37 

38 

39 

40 

41 

Continued  on  Page  *68. 


TABLE    XLY. 


*65 


LIFE  AND  TEMPORARY  ANNUITIES.    LOGARITHM  OP   THE    PRESENT  VALUE   OF  n 
ANNUAL  PAYMENTS  OF  1  AT  THE  BEGINNING  OF  EACH  YEAR. 

4^  PER  CENT 


Pay- 

42 

43 

44 

45 

46 

47 

48 

49 

Pay- 

ments. 

n. 

ments. 
n. 

1 

1.181397 

1.175290J1.168905 

1.162240 

1.155279 

1.148013 

1.140432 

1.132524 

1 

0.000000 

0.000000  0.000000 

0.000000 

0.000000,0.000000 

0.000000 

0.000000 

2 

.289449 

.289373 

.289286 

.289192 

'  .2890881  .288973 

.288847 

.288710 

2 

3 

.454015 

.453858 

.453681 

.453487 

.453275  .453040 

.4527841  .452501 

3 

4 

.567483 

.567240 

.566968 

.566672 

.566344  .565986  .565592  .565158 

4 

5 

0.652973 

0.652640^0. 652271 

0.651865 

0.6514210.650931 

0.650393  0.649804 

6 

6 

.720784 

.720358 

.719885 

.719369 

.7187991  .718173 

.717488;  .716733 

6 

7 

.776409 

.775885 

.775307 

.774671 

.773972J  .773206 

.772363  .771439 

7 

8 

.823124 

.822501 

.821809 

.821051 

.820219  .819303 

.818300  .817198 

8 

9 

.863047 

.862316 

.861507 

.860623 

.859649!  .858581 

.857409  .856121 

9 

10 

0.897616 

0.896773 

0.895845 

0.894825 

0.8937070.892480 

0.8911310.889653 

10 

11 

.927859 

.926903 

.925846 

.924690 

.923421 

.922025 

.920497i  .918819 

11 

12 

.954538 

.953460 

.952274 

.950975 

.949545 

.947980 

.9462621  .944379 

12 

13 

.978226 

.977025 

.975703 

.974251 

.972661 

.970916 

.969003 

.966906 

13 

14 

.999373 

.998042 

.996575 

.994972 

.993212 

.991281 

.989166 

.986851 

14 

15 

1.018330 

1.016862 

1.015252 

1.013488 

1.011551 

1.009429 

1.007108 

1.004566 

15 

16 

.035381 

.033778 

.032014 

.030082 

.027964 

.025648 

.023112 

.020338 

16 

17 

.050764 

.049016 

.047094 

.044990 

.042689 

.040168 

.037413 

.034397 

17 

18 

.064668 

.062770 

.060685 

.058408 

.055912 

.053185 

.050201 

.046944 

18 

19 

.077254 

.075201 

.072953 

.070491 

.067800 

.064857 

.061645 

.058136 

19 

20 

1.088658 

1.086451 

1.084027 

1.081380 

1.078486 

1.075327 

1.071877 

1.068119 

20 

21 

.099001 

.096628 

.094029 

..0911901  .088092 

.084708!  .0810231  .077005 

21 

22 

.108377 

.105838 

.103057 

.100025 

.096714;  .093108 

.0891781  .084904 

22 

23 

.116876 

.114165 

.111201 

.107969 

.104448'  .100610 

.096439  .091903 

23 

24 

.124573 

.121688 

.118536 

.115104 

.111365  .107301 

.102882  .098085 

24 

25 

1.131535 

1.128473 

1.125132 

1.121495 

1.117542  1.113243  1.108579'l.l03526 

25 

26 

.137823 

.134581 

.131047 

.127208;  .123033|  .118504'  .1135981  .108290 

26 

27 

.143489 

.140065 

.136340 

.132291  .127900;  .123143 

.117998 

.112438 

27 

28 

.148581 

.144978 

.141054 

.  136802  ii  .132195 

.127213 

.121831 

.116027 

28 

29 

.153147 

.149356 

.145240 

.140784  1  .135967 

.130761 

.125150 

.119106 

29 

30 

1.157219 

1.153246 

1.148938 

1.144285  '1.139256 

1.133836 

1.127999 

1.121733 

30 

31 

.160839 

.156685 

.152192 

.147339! 

.142108 

.136476 

.130431 

.123949 

31 

32 

.164042 

.159713 

.155031 

.149988 

.144558 

.138731 

.132484 

.125799 

32 

33 

.166863 

.162356 

.157496 

.152266 

.146652 

.140635 

.134197 

.127326 

33 

34 

.169327 

.164652 

.159615 

.154212 

.148421 

.142224 

.135612 

.128572 

34 

35 

1.171468 

1.166626 

1.161427 

1.155857 

1.149897 

1.143537 

1.1367671.129572 

35 

36 

.173309 

.168315 

.162959 

.157230 

.151117 

.144609 

.1376941  .130360 

36 

37 

.174885 

.169743 

.164237 

.158365 

.152114 

.145471 

.138425;  .130975 

37 

38 

.176217 

.170935 

.165295 

.159294 

.152915 

.146149 

.1389951  .131442 

38 

39 

.177330 

.171922 

.166160 

.160039 

.153545 

.146678 

.139428  .131789 

39 

40 

1.178251 

1.172728 

1.166854 

1.160625 

1.154037 

1.147080 

1.139750 

1.132039 

40 

41 

.179004 

.173376 

.167401 

.161083 

.154411 

.147380 

.139982 

.132219 

41 

42 

.179609 

.173886 

.167827 

.161432 

.154690 

.147595 

.140149 

.132342 

42 

43 

.180086 

.174284 

.168153 

.161691 

.154890 

.147750 

.140263 

.132419 

43 

44 

i 

.180457 

.174588 

.168394 

.161877 

.155034 

.147856 

.140335 

.132467 
49 

44 

42 

43 

44 

46 

46 

47 

48 

Cont 

nued  oa  Vs 

ige  *67. 

*66 


TABLE    XLV. 


LIFE   AND  TEMPORARY  ANNUITIES.      LOGARITHM  OF  THE    PRESENT  VALUE   OF    n 

ANNUAL  PAYMENTS  OF  1   AT  THE  BEGINNING  OF  EACH  YEAR. 

4|^  PER  CENT. 


Pay- 

x=50 

51 

52    53 

54 

55 

56 

57 

Pay- 

ments. 
n. 

1 

ments. 
n. 

1.1242741.115680 

1.1067231.097392 

1.0876761.077558 

1.0670371.056095 

0. 000000  0.  OOOOOOJO.  000000  0. 000000 1 

0.000000  0.000000 

0.000000  0.000000 

1 

2 

.288556 

.288390 

.288206 

.288005 

.287785 

.287538 

.287272 

.286974 

2 

3 

.452188 

.451848 

.451473 

.451062 

.450610 

.450110 

.449562 

.448958 

3 

4 

.564681 

.564158 

.563584 

.562954 

.562262 

.561495 

.560657 

.559736 

4 

5 

0.649153 

0.648441 

0.647660  0. 646801  i 

0.645857 

0.644815 

0.643677 

0.642425 

5 

6 

.715902 

.714995 

.713995 

.7128991 

.711694 

.710368 

.708916 

.707320 

6 

7 

.770422 

.769307 

.768083 

.766740 

.765266 

.763642 

.761866 

.759916 

7 

8 

.815985 

.814658 

.813200 

.811601 

.809846 

.807916 

.805805 

.803489 

8 

9 

.854707 

.853158 

.851458 

.849594 

.847549 

.845302 

.842846 

.840152 

9 

10 

0.888028 

0.886250 

0.884299  0.882161 

0.879816  0.877243 

0.874430 

0.871348 

10 

11 

.916977 

.914961 

.912751  .910330 

.907677  .904767 

.901588 

.898107 

11 

12 

.942311 

.940051 

.937573  .934860 

.931889  .928634 

.925079 

.921195 

12 

13 

.964608 

.962094 

.959341 

.956327 

.953031 

.949422 

.945488 

.941187 

13 

14 

.984313  .981539 

.978501 

.975182 

.971551 

.967585 

.963259 

.958538 

14 

15 

1.001782  0.998739  0.995413 

0.991777 

0.987811 

0.983476 

0.978755 

0.973610 

15 

16 

.017299  1.013984 

1.010359 

1.006408 

1.002094 

.997388 

.992268  .986694 

16 

17 

.031102 

.027505 

.023584 

.019304 

.014642 

1.009560 

1.004038!  .998040 

17 

18 

.043382 

.039506 

.035274 

.030668 

.0256521  .020193 

.0142731.007849 

18 

19 

.054311 

.050142 

.045603 

.040663 

.035293  .029461 

.023143  .016300 

19 

20 

1.0640191.059560 

1.054708 

1.049435 

1.0437151.037510 

1.030799J1.023545 

20 

21 

.072632 

.067879 

.062713 

.057113 

.051043  .044470 

.037375 

.029718 

21 

22 

.080253 

.075205 

.069732 

.063803 

.057388  .050456 

.042984 

.034942 

22 

23 

.086975 

.081638 

.075856 

.069604 

.062853  .055568 

.047738 

.039328 

23 

24 

.092885 

.087257 

.081173 

.074606 

.067525  .059906 

.051733 

.042973 

24 

25 

1.098053 

1.092142 

1.085762 

1.078886 

1.071493 

1.063554 

1.055055 

1.045971 

25 

26 

.102550 

.096362 

.089692 

.082525 

.074833 

.066590 

.057791 

.048407 

26 

27 

.106438 

.099978 

.093036 

.085590 

.077614 

.069092 

.060014 

.050357 

27 

28 

.109772 

.103058 

.095855 

.088143 

.079907 

.071126 

.061794 

.051896 

28 

29 

.112614 

.105655 

.098204 

.090249 

.081772 

.072756 

.063200 

.053089 

29 

30 

1.115011 

1.107820 

1.100142 

1.091963 

1.083268ll.074042 

1.064290 

1.053994 

30 

31 

.117011 

.109607 

.101720 

.093338 

.084448!  .075041 

.065117 

.054670 

31 

32 

.118661 

.111063 

.102987 

.094423 

.085865 

.075798 

.065735 

.055158 

32 

33 

.120007 

.112232 

.103986 

.095266 

.086060 

.076364 

.066181 

.055506 

33 

34 

.121087 

.113154 

.104763 

.095906 

.086579 

.0767731  .066499 

.055742 

34 

35 

1.121939 

1.113871 

1.105353 

1.096383 

1.086955 

1.0770641.066714 

1.055891 

35 

36 

.122602 

.114416 

.105792 

.096729 

.087222 

.0772611  .066851 

.055985 

36 

37 

.123106 

.114821 

.106111 

.096975 

.087403 

.077387  .066937 

.056038 

37 

38 

.123481 

.115115 

.106338 

.097141 

.087519 

.077466  .066986 

.056069 

38 

39 

.123752 

.115325 

.106491 

.097248 

.087591 

.077511 

.067014 

.056082 

39 

40 

1.123946 

1.115467 

1.106589 

1.097314 

1.087633 

1.077536 

1.067026 

1.056091 

40 

41 

.124078 

.115557 

.106650 

.097353 

.087656 

.077547 

.0670341  .056094 

41 

42 

.124161 

.1156131  .106686 

.097374 

.087666 

.077555 

.067037^  .056094 

42 

43 

.124213 

.115646 

.106706 

.097383 

.087673 

.077557 

.067037'  .056095 

43 

44 

.124244 

.115665 

.106714 

.097389 

.087675 

.077557 

.067037 

44 

45 

1.124261 

1.115672 

1.106720 

1.097390 

1.087675 

1.077558 

45 

46 

.124268 

.115678 

.106721 

.097391 

46 

47 

.124273 

.115679 

.106722 

47 

48 

.124274 

.115679 

48 

49 

.124274 

49 

50    51 

52 

53 

54 

55 

56 

57 

TABLE    XLY. 


*61 


LIFE  AND  TEMPORARY  ANNUITIES.       LOGARITHM  OF  THE    PRESENT  VALUE    OF  n 
ANNUAL   PAYMENTS  OF  1   AT   THE  BEGINNING  OF  EACH  YEAR. 


4i  PER   CENT. 


Pay- 
ments. 

n. 

58 

59    60 

61 

62 

63 

64 

65 

Pay- 
ments. 

n. 

1 

1.044728 

1.03291o'l.020646 

1.007916 

0.994716 

0.981025 

0.966846 

0.952166 

0.000000 

O.OOOOOO'0. 000000 

0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

2 

.286653 

.286298 

.285906 

.285476 

.285008 

.284488 

.283919 

.283293 

2 

3 

.448302 

.447578 

.446779 

.445905 

.444948 

.443891 

.442734 

.441463 

3 

4 

.558730 

.557622 

.556403 

.555067 

.553605 

.551993 

.550229 

.548291 

4 

5 

0.641055 

0.639550 

0.637896 

0.636084 

0.634099 

0.631916 

0.629525 

0.626906 

5 

6 

.705576 

.703660 

.701557 

.699252 

.696730 

.693958 

.690928 

.687611 

6 

7 

.757784 

.755444 

.752876 

.750067 

.746991 

.743619 

.739934 

.735903 

7 

8 

.800957 

.798179 

.795136 

.791806 

.788167 

.784181 

.779828 

.775073 

8 

9 

.837207 

.833982 

.830450 

.826591 

.822376 

.817764 

.812734 

.807248 

9 

10 

0.867981 

0.864297 

0.860267 

0.855867 

0.851067 

0.845822 

0.840110 

0.833891 

10 

11 

.894310 

.890158 

.885620 

.880672[ 

.875279 

.869397 

.863002 

.856049 

11 

12 

.916957 

.912327 

.907277 

.901773 

.895785 

.889266 

.882188 

.874509 

12 

13 

.936501 

.931391 

.925819 

.9197611 

.913178 

.906024 

.898272 

.889876 

13 

14 

.953401 

.947802 

.941713 

.935098 

.927923 

.920143 

.911726 

.902632 

14 

15 

0.968015 

0.961932  0.955322 

0.948156^ 

0.940400 

0.932002 

0.922939 

0.913173 

15 

16 

.980646 

.9740761  .966953 

.959245 

.950914 

.941918 

.932235 

.921823 

16 

17 

.991536 

.984488  .976859 

.968617 

.959731 

.950161 

.939883 

.928862 

17 

18 

1.000898 

.993377  .985252 

.976495 

.967078 

.956958 

.946119 

.934533 

18 

19 

.008908 

1.000926  .992321 

.983072 

.973146 

.962510 

.951152 

.939045 

19 

20 

1.015723 

1.007294  0.998233 

0.988513 

0.978111 

0.966998 

0.955160 

0.942585 

20 

21 

.021481 

.012629  1.003131 

.992971 

.982129 

.970575 

.958310 

.945317 

21 

22 

.026311 

.017054;  .007148 

.996582 

.985335 

.973388 

.960742 

.947387 

22 

23 

.030321 

.020686  .010405 

.999466 

.987858 

.975563 

.962586 

.948926 

23 

24 

.033616 

.023634  .013009 

1.001737 

.989810 

.977212 

.963958 

.950040 

24 

25 

1.036292 

1.0259911.015060 

1.003495 

0.991290 

0.978440 

0.964950 

0.950829 

25 

26 

.038433 

.027850!  .016649 

.004829 

.992393 

.979328 

.965654 

.951364 

26 

27 

.040122 

.029290!  .017854 

.005822 

.a93191 

.979957 

.966131 

.951703 

27 

28 

.041431 

.0303821  .018752 

.006542 

.993756 

.980385 

.966433 

.951914 

28 

29 

.042424 

.031197  .019403 

.007051 

.994140 

.980655 

.966622 

.952037 

29 

30 

1.043165 

1.0317871.019863 

1.007398 

0.994383 

0.980825 

0.966731 

0.952105 

30 

31 

.043701 

.032205 

.020178 

.007616 

.994536 

.980922 

.966792 

.952138 

31 

32 

.044082 

.032489 

.020375 

.007754 

.994623 

.980977 

.966821 

.952155 

32 

33 

.044340 

.032669 

.020500 

.007833 

.994672 

.981003 

.9668361  .952163 

33 

34 

.044504 

.032782 

.020571 

.007877 

.994696 

.981016 

.9668431  .952165 

34 

35 
36 
37 
38 
39 

40 
41 
42 

1.044607 
.044666 
.044699 
.044714 
.044723 

1.044727 
.044727 
.044728 

1.032847 
.032883 
.032900 
.032909 
.032914 

1.032914 

1.020611 
.020630 
.020640 
.020645 
.020645 

1.020646 

1.007899 
.007909 
.007915 
.007915 
.007916 

0.994707 
.994714 
.994714 
.994716 

0.981023 
.981024 
.981025 

0.966845 
.966846 

0.952166 

35 

58 
57 
56 
55 

54 
53 

42 

43 

44 

1.181397 
.181395 
.181395 
.181395 

1.181393 
.181389 

45 

1.175290 
.175289 
.175289 

1.175288 
.175286 

46 

1.168905 
.168905 

1.168905 
.168904 

.032915 

1.162240 

1.162239 
.162239 

47 

1.155279 

.155278 

48 

49 

1.148013 

1. 140432 

.148012 

.155278 

.162238 

.168902 

.175282 

.181380 

52 

51 

1.132524 

.140431 

.148012 

.155277 

.162235 

.168897 

.175272 

.181362 

51 

50 

.132523 

.140431 

.148011 

.155273 

.162230 

.168886 

.175253 

.181334 

50 

49 

1.132523 

1.140430 

1.148007 

1.155268 

1.162218 

1.168866 

1.175223 

1.181287 

49 

48 

.132522 

.140426 

.148002 

.155255 

.162197 

.168834 

.175173 

.181211 

48 

47 

.132518 

.140420 

.147988 

.155233 

.162162 

.168780 

.175091 

.181102 

47 

46 

.132511 

.140405 

.147964 

.155195 

.162104 

.168692 

.174975 

.180951 

46 

45 

.132495 

.140379 

.147923 

.155133 
46  ( 

.162011 

.168568 

.174813 

.180741 

45 

49 

48 

47 

45 

44 

43 

42 

Continued  from  Page  *65, 


♦68  TABLE     XLT. 

LIFE  AND  TEMPORARY  ANNUITIES.      LOGARITHM   OF  THE  PRESENT  VALUE  OF   n 
ANNUAL  PAYMENTS  OF  1   AT  THE  BEGINNING  OF  EACH  YEAR.  41    „^^  ^^^.^ 


Pay- 
ments. 

71. 


1 

2 
3 

i 

5 
6 

7 
8 
9 

10 
11 
12 
13 
14 

15 
16 
17 
18 
19 

20 
21 
22 
23 
24 

25 
26 
27 
28 
29 

30 
31 
32 
33 
34 


59 
58 
57 
56 
55 

54 
53 
52 
51 
50 

49 
48 
47 
46 
45 


3^=66   67 


0.936983,0.921279 


0.000000 
.282611 
.440070 
.546174 

0.624044 
.683985 
.731504 

.769890 
'.801278 

0.827131 

848506 
866193 
880805 
892832 

0.902672 
910659 
917083 
922185 
926183 

0.929266 
.931600 
.933334 
.934590 
.935478 

0.936080 
.936462 
.936700 
.936838 
.936914 

0.936951 
.936971 
.936979 
.936982 
.936983 


41 


1.187248 
.187246 
.187246 
.187246 
.187244 

1.187241 
.187232 
.187215 
.187189 
.187145 

1.187074 
186972 
186831 
186635 
186369 


41 


0.000000 
.281852 
.438541 
.543847 

0.620902 
.680015 
.726692 
.764233 

.794771 

0.819779 
.840319 
.857190 
.871009 
.882275 

0.891393 
.898708 
.904508 
.909047 
.912543 

0.915188 
.917150 
.918572 
.919577 
.920257 

0.920690 
.920959 
.921115 
.921201 
.921243 

0.921265 
921274 
921278 
921279 


68 


0.905066 


69 


70 


0.888311  0.871044 


71 


72 


73 


0.853238  0.834905  0.816036 


0. 000000  0.  OOOOOOi  |0. 000000  0. 000000 
.2810351  .2801201  .279130  .278037 
.436872  .435027L  .433019  .430811 
.541309  .538512!  .535465  .532128 


0. 61747610. 613710  0. 609614 


,675686 
,721455 

.758081 

,787707 


,6709441:  .665786 
,715727:  .709502 
.  7513671 '  .744086 
.7800171  .771693 


.811813 
.831469 

.847477 
.860468 
.870947 

.879328  0 

.885960 

.891141 

.895127 

.898140 


,8031631  0 
,821880 
,836986 
,849118 

,858787 

866419 
872370 
876940: 
880391! 

882946 


0.605131 
.660148 
.702722 
.736172 
.76266 


0.900372^0.884796 


40 


1.192839 

1.192837 
.192837 
.192837 
.192835 
.192833 

1.192824 
.192808 
.192784 
.192743 
.192677 

1.192581 
.192449 
.192266 
.192017 
.191692 


40 


.901990 
.903132 
.903904 
.904397 

0.904702 
.904879 
.904977 
.905025 
.905050 

0.905060 
.905065 
.905066 


39 


1.198189 
.198187 

1.198187 
.198187 
.198186 
.198184 
.198175 

1.198160 
.198138 
.198099 
.198037 
.197948 

1.197824 
.197653 
.197419 
.197115 
.196724 


39 


.886101 
.886983 
.887547 
.887895 

0.888097 
.888209 
.888264 
.888293 
.888304 

0.888309 
.888311 


38 


1.203309 
.203304 
.203304 

1.203304 
.203303 
.203301 
.203292 
.203278 

1.203258 
.203222 
.203164 
.203080 
.202964 

1.202804 
.202584 
.202299 
.201933 
.201469 


38 


793818  0.783714 
811550|  .800415 
825715'  .813603 
836958!  .823938 
845804;  .831952 

8526850.838081 
8579581  .842695 
861935!  .846104 
8648771  .848567 
867004  .850301 

0.868504'o.  851473 
869518:  .852224 


.870167 
.870566 
.870799 

0.870927  0, 
.87099li 
.871023! 
.871036! 
.871042 

0.871044 


.852685 
.852955 


O.OOOOOOlO.  000000 
.276843  .275538 
.428403  .425760 
.528482  .524492 

0.600238  0.594904 
.654017  .647340 
.695357  .687355 
.727594  .718300 
.752909  .742371 

0.772824  0.761101 
.788450  .775614 
.800034  .786774 
.810047  .795255 
.817225!  .801609 

0.822618  0.806288 
.826596!  .809660 
.8294671  .812031 
.8314871  .813631 
.832852!  .814656 

0.833726  0.815284 


.834262 
.834575 


.815650 
.815852 


853102  .834834  .816005 


37 


1.208201 
.208199 
.208199 
.208199 

1.208198 
.208196 
.208188 
.208175 
.208156 

1.208122 
.208068 
.207989 
.207880 
.207730 

1.207524 

.207256 
.206913 
.206478 
.205937 


37 


853177 
853213 
853229 
853235 
853238 


.834747  .815954 


0.83487710.816025 
.834895!  .816034 
.834902'  .816036 
.834905 


34 


36 


1.212877 
.212875 
.212875 
.212875 
.212874 

1.212872 
.212864 
.212852 
.212834 
.212802 

1.212751 
.212677 
.212575 
.212434 
."212241 

1.211989 
.211667 
.211259 
.210751 
.210130 


36 


35 


1.221612 
1.217341!  .221612 


1.2173401.221612 
.217340!  .221611 
.217339;  .221610 
.217338!  .221608  61 
.217336'  .221601  60 


Pay- 
ments, 
n. 


1.217329!l. 221591 
.217318!  .221575 


.217301 
.217271 
.217223 


.221547 
.221502 
.221437 


1.2171541.221346 
.217058!  .221221 


.216925 
.216744 
.216508 

1.2162051.220184 


.215821 
.215345 
.214761 
.214056 


36 


.219736 
.219187 
.218526 
.217733 


34 


1 
2 
3 
4 

5 
6 
7 
8 
9 

10 
11 
12 
13 

14 

15 
16 
17 
18 
19 

20 
21 
22 
23 
24 

25 
26 
27 


66 
65 

64 
63 
62 


.221051 
.220829 
.220545  50 


59 
58 
57 
56 
55 

54 
53 
52 
51 


49 
48 
47 
46 
45 


Continued  from  Page  *64. 


TABLE     XLY. 


^69 


LIFE  AND  TEMPORAET  ANNUITIES.      LOGARITHM    OF    THE  PRESENT  VALUE  OF   n 
ANNUAL  PAYMENTS  OF  1  AT  THE  BEGINNING  OF  EACH  YEAR. 


4^  PER  CENT. 


Pay- 
ments. 

n. 

1 

74 

75 

76 

77 

78 

79 

80 

81 

-...  -  -  ] 

' 

Pay- 
ments. 

0.796626 

0.776711 

0.756264 

0.735279 

0.713797 

0.691797  ( 

3.669283  ( 

3. 646255' 

0.000000 

o.oooooolo.ooooool 

0.000000 

0.000000 

0. 000000 

3.000000 

3.  OOOOOo' 

1 

2 

.274089 

.272521 

.270807 

.268910 

.266851 

.264595 

.262129 

.2594471 

2 

3 

.422855 

.419707 

.416256 

.412470 

.408356 

.403865 

.398975 

.393652 

3 

4 

: 520129 

.515387  .510208 

.504550 

.498410 

.491733 

.484479 

.476622 

4 

5 

0.589077 

0.582756  0.575872 

0.568376 

0.560266 

0.551472 

0.541963 

0.531696 

5 

6 

.640067 

.632192 

.623643 

.614371 

.604364 

.593563 

.581926 

.569428 

6 

7 

.678666 

.669282 

.659130 

.648157 

.636363 

.623682 

.610091 

.595572 

7 

8 

.708241 

.697409  .6857321 

.673164 

.659708 

.645312 

.629962 

.613646 

8 

9 

.731003 

.718801 

.705699 

.691659 

.676693 

.660765 

.643866 

.626012 

9 

10 

0.748499 

0.735023 

0.720614 

0.705242 

0.688938 

0.671670 

0. 653455 

0.634186 

10 

11 

.761871 

.747230 

.731645 

.715100 

.697634 

.679234 

.659827 

.639362 

11 

12 

.771990 

.756308 

.739691 

.722134 

.703690 

.684280 

.663875 

.642509!  12 

13 

.779547 

.7629541  .745453 

.727048 

.707743 

.687494 

.666342 

.644336  13 

14 

.785096 

.767728  .749487 

.730344 

.710329 

.689456 

.667776 

.645339:  14 

1 

15 

0.789090 

0.771075  0.752198 

0.732450 

0.711910 

0.690597 

0.668563 

0.645853 

15 

16 

.791895 

.773328 

.753933 

.733738 

.712829 

.691223 

.668967 

.646101 

16 

17 

.793785 

.774771 

.754994 

.734488 

.713334 

.691545 

.669162 

.646203  17  h 

18 

.794996 

.775654 

.755612 

.734900 

.713594 

.691701 

.669242 

.646243 

18 

19 

20 
21 
22 
23 
24 

25 
26 

.795738 

0.796170 
.796408 
.796529 
.796589 
.796613 

0.796623 

.776169 

0.776452 
.776596 
.776668 
.776696 
.776708 

0.776711 

.755952 

0.756126 
.756211 
.756245 

.735112 

0.735215 
.735256 
.735273 

.713719 

0.713770 
.713791 
.713797 

.691764 

0.691790 
.691797 

.669274 
0.669283 

.646265 

19 

74 
73 
72 
71 
70 

69 
68 

26 

27 

1.249527 
.249527 
.249527 
.249527 
.249526 

1.249524 
.249519 

28 

.756259 

.735279 

29 

1.246580 
.246580 
.246580 
.246580 

1.246579 
.246577 

.756264 

30 

1.243489 
.243489 
.243489 

1.243489 
.243488 

31 

1.240250 
.240249 

1.240249 
.240249 

.796626 

1.236862 

1.236861 
.236861 

oo 

33 

Oti 

1.233310 

1.229589 

.233309 

67 

1.225692!  .229589 

.233309 

.236861 

.240248 

.243486 

.246572 

.249514 

67 

66 

.225692;  .229589 

.233309 

.236860 

.240246 

.243481 

.246566 

.249502 

66 

65 

.225692 

.229588 

.233308 

.236858 

.240241 

.243474 

.246554 

.249485 

65 

64 

1.225691 

1.229587 

1.233306 

1.236853 

1.240233 

1.243462 

1.246536 

1.249459 

64 

63 

.225690 

.229585 

.233300 

.236845 

.240221 

.243443 

.246508 

.249418 

63 

62 

.225688 

.229579 

.233292 

.236832 

.240201 

.243413 

.246465 

.249363 

62 

61 

.225682 

.229570 

.233278 

.236810 

.240169 

.243368 

.246406 

.249285 

61 

60 

.225672 

.229556 

.233255 

.236776 

.240121 

.243305 

.246323 

.249178 

60 

59 

1.225657 

1.229531 

1.233218 

1.236725 

1.240054 

1.243217 

1.246211 

1.249039 

59 

58 

.225631 

.229492 

.233164 

.236654 

.239961 

.243098 

.246063 

.248863 

58 

57 

.225589 

.229434 

.233089 

.236556 

.239835 

.242942 

.245877 

.248641 

57 

56 

.225528 

.229354 

.232985 

.236422 

.239669 

.242745 

.245641 

.248361 

56 

55 

.225442 

.229244 

.232843 

.236246 

.239460 

.242494 

.245345 

.248022 

55 

54 

1.225325 

1.229093 

1.232656 

1.236024 

1.239194 

1.242181 

1.244985 

1.247613 

54 

53 

.225165 

.228895 

.232420 

.235741 

.238862 

.241799 

.244552 

.247121 

53 

52 

.224955 

.228644 

.232119 

.235389 

.238456 

.241339 

.244030 

.246546 

52 

51 

.224688 

.228325 

.231746 

.234958 

.237969 

.240786 

.243420 

.245868 

51 

50 

.224349 

.227928 

.231289 

.234441 

.237382 

.240139 

.242702 

.245088 

50 

49 

1.223928 

1.227443  1.23074C 

1.233819 

1.336695 

1.239378 

1.241875 

1.244192 

49 

48 

.223412 

.226859  .23007S 

.233089 

.235888 

.238500 

.240924 

.243168 

48 

47 

.222790  .226157  .22930S 

.232233 

.234956 

.237491 

.239839 

.242011 

47 

46 

.222045  .225332  .22839^ 

t  .231243 

.233886 

.236340 

.238612 

.240712 

46 

45 

.22116^ 
33 

n  .224366  .22734^ 

;  .230107 

.^32664 

:  .235038 

.237234 

.239258 

45 

1   32     31 

30 

1  29 

28 

27 

26 

Continued  from  Page  *63. 


^70 


TABLE    XLV. 


LIFE   AND  TEMPORARY  ANNUITIES.     LOGARITHM    OF  THE    PRESENT    VALUE    OP  « 


ANNUAL  PAYMENTS  OF  1  AT  THE  BEGINNING  OF  EACH  YEAR. 


4|^  PER  CENT. 


.Pay- 
ments. 
n. 


5 
6 

7 
8 
9 

10 
11 
12 
13 
14 

15 
16 
17 
18 


2^=83 


83 


0.622676  0.598565 


84 


85 


0.573780  0.548297 


0.000000  0.000000  0.000000  0.000000 


2  .256494 

3  i  .387854 

4  .468093 


67 
66 
65 

64 
63 
62 
61 
60 

59 
58 
57 
56 
55 

54 
53 
52 
51 
50 

49 
48 
47 
46 
45 


.2533161  .249806 
.3815841  .374746 
.458911  .448980 


.246024 
.367409 
.438319 


0.520618  0.508753i0.495976  0.482365 


.556023 
.580075 
.596346 
.607023 


.541721 
.563652 
.577893 
.586809 


0.613752  0.592192 
.617831!  .595305 
.6201961  .597009 
.621492;  .597883 
.6221571  .598301 


0.622476 
.622609 
.622661 
.622676 


25 


75 

74 
73 
72 
71 
70 

69  1.252334 
68   .252329 


1.252341 

1.252342 
.252342 
.252342 
.252341 
.252339 


.526442 
.545916 
.557991 
.565240 


.509831 
.526616 
.536606 
.542334 


0.569416  0.545455 


.571699 
.572869 
.573427 
.573662 


0.598476  0.573752 
.598544  .573780 
.598565! 


24 


28 


.252318 
.252302 

.252277 

1.252239 
252187 
252113 
252012 


1.255025 
.255025 

1.255025 
.255025 
.255024 
.255022 
.255017 

1.255013 
.255002 
.254987 
.254964 
.254928 

1.254879 
.254809 
.254714 
.254590 


.251881  .254433 


1.251715 
.251505 
.251241 
.250921 
.250535 

1.250071 
.249528 
.248888 
.248152 
.247307 

1.246341 
.245249 
.244024 
.242653 
.241122 


1.257585 
.257585 

.257585 

1.257585 

.257584 
.257582 
.257578 
.257574 


.547053 
.547814 
.548135 
.548258 

0.548297 


22 


1.260026 
.260027 
.260027 
.260027 

1.260026 
.260024 
.260020 
.260016 
.260006 

1.257563  1.259993 
.257549  .259972 
.257527'  .259940 
.257493  .259896 
.257447  .259833 

1.257381  1.259749 


86 


0.521852 

I- 


87 


0.493999 


88 


0.464345 


89 


0.431342 


0. 000000  0. 000000:0. 000000 


.241946: 
.359446 
.426874 


.237388 
.350786 
.413580 


.232632 
.340091 
.397349 


Pay- 
ments, 
n. 


0.000000 
.22451 
.324725 
.376450 


0.467218  0.449629  0.429089  0.404031 
.491308'  .470362!  .446604  .418493 


.505459 
.513513 

.517883 


.482025 
.488313 
.491513 


.455950 
.460680 
.462925 


0.520115  0.493035  0.463870 


.521178 
.521627, 
.521798! 
.521852! 


.4936771  .464230 
.493921  .464345 
.493999 


21 


20 


1.264573 


1.262353 
.262354 
.262354 
.262354 
.262353 


19 


1.266691 
.266692 


1.2645741.266692 
.264574|  .266692 
.264574!  .266691 
.264573!  .266689 
.264571:  .266686 


.257291 
.257174 
.257026 


.259638 
.259498 
.259322 


1.254235 
.253986 
.253683 
.253319 

.252881 

1.252368 
.251764 
.251068 
.250271 
.249360 

1.248329 
.247174 
.245880 
.244437 

242847 


1.262351  1.264567  1.266682 
262347!  .264563:  .266674 
262343  .264555  .266663 


.262334 
.262322 


.264543;  .266646 
.264525!  .266618 


.425749 
.429178 
.430618 

0.431167 
431342 


18 


1.262302  1.2644961.266580 
.2622711  .264456'  .266528 
.262229|  .264400  .266457 
.262170|  .264325'  .266363 
.262091!  .264226  .266244 


1.2619861.264100 
.2618531  .263943 
.261687!  .263744 


25 


24 


.256839 

.259100 

1.256604 

1.258828 

.256317 

.258504! 

.255973 

.258113: 

.255560 

.257655 

.255075 

.257116| 

1.254505 

1.256496 

.253848 

.255785; 

.253095 

.254972 

.252235 

.254054 

.251262 

.253023 

1.250171 

1.251871 

.248950 

.250586j 

.247589 

.249170; 

.246089 

.247.605! 

.244430 

.245886j 

23 

22 

.261477 

.261220 


.263501 
.263212 


1.260914 1.262863  1.264687 


.260545 
.260112 
.259602 


1.266095 
.265907 
.265677 
.265404 
.265074 


259016  .260784 


1.258345 

.257577 
.256709 
.255736 
.254648 


.262454  .264231 


.261972 
.261418 


.263707 
.263108 
.262422 


1.2600581.261646 
.2592381  .260776 
.258317  .259805 


.257290 
.256143 


.258722 
.257529 


1.2534341.254881 1.256211 
.252097  .2534861  .254765 
.2506201  .251955  .253180 
.248998^  .250276:  .251452 
.247220  .248445!  .249572 


21 


1.268708 
.268709 
.268709' 

1.268709 
.268708 
.268706 
.268703 
.268699 

1.268692 
.2^8681 
.268665 
.268639 
.268603 

1.268554 
.268487 
.268398 
.268285 
.268144 

1.267966 
.267749 
.267490 
.267178 
.266812 

1.266381 
.265885 
.265319 
.264670 
.263936 

1.263114 
.262195 
.261172 
.260045 
.258799 

1.257433 
.255935 
.254304 
.252529 
.250601 


20 


19 


18 


Continued  from  Page  *62. 


TABLE    XLY. 


m 


LIFE  AND  TEMPORARY  ANNUITIES.     LOGARITHM  OF  THE    PRESENT    VALUE    OF  n 
ANNUAL  PAYMENTS  OF  1   AT  THE  BEOmNING  OF  EACH  YEAR,      ^j   ^^^  ^^^.j. 


Pay- 
ments. 
n. 

90 

91 

92 

93 

94 

95 

96 

97 

0.177500 

Pay.  ' 
ments.j 

n.    1 

1 

0.399866 

0.371143 

0.342412 

0.312760 

0.282598 

0.251018 

0.213605 

1 

0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

1 

2 

.215615 

.207859 

.199751 

.190399 

.180240 

.169812 

.152954 

.140751 

2 

3 

4 

5 
6 

7 
8 
9 

10 

.309111 
.355648 

0.379276 
.390948 
.396423 
.398714 
.399587 

0.399866 

.294974 
.336370 

0.356220 
.365406 
.369226 
.370680 
.371143 

.279967 
.316098 

0.332378 
.339071 
.341606 
.342412 

.263229 
.294182 

0.306615 
.311281 
.312760 

.245642 
.270547 

0.279714 
.282598 

.225430 
.244967 

0.251018 

.199694 
.213605 

.177500 

3 

90 

89 
88 
87 
86 
85 

10 

11 

12 

1.281791 

1.281791 
.281791 
.281791 
.281790 
.281789 

13 

1.280417 
.280417 
.280417 
.280417 
.280416 

14 

1.278977 
.278977 
.278977 
.278977 

15 

1.277464 

.277464 
.277464 

16 

1.275875 
.275876 

1.274211 

17 

1.272467 

1.274213 

1.275876 

1.277464 

1.278976 

1.280415 

1.281787 

84 

83 

1.270632 

.272468 

.274213 

.275876 

.277463 

.278975 

.280413 

■  .281785 

83 

82 

.270633 

.272468 

.274213 

.275875 

.277462 

.278973 

.280411 

.281780 

82 

81 

.270633 

.272468 

.274212 

.275873 

.277460 

.278971 

.280405 

.281774 

81 

80 

.270633 

.272467 

.274210 

.275871 

.277458 

.278965 

.280399 

.281761 

80 

79 

1.270632 

1.272465 

1.274208 

1.275869 

1.277452 

1.278958 

1.280385 

1.281745 

79 

78 

.270630 

.272463 

.274205 

.275863 

.277444 

.278944 

.280369 

.281723 

78 

77 

.270628 

.272460 

.274199 

.275854 

.277430 

.278927 

.280345 

.281691 

77 

76 

.270624 

.272453 

.274190 

.275840 

.277412 

.278901 

.280312 

.281648 

76 

75 

.270617 

.272444 

.274175 

.275820 

-.277384 

.278866 

.280267 

.281591 

75 

74 

1.270607 

1.272428 

1.274154 

1.275791 

1.277348 

1.278819'l. 280206 

1.281518 

74 

73 

.270591 

.272406 

.274123 

.275752 

.277297 

.2787541  .280128 

.281426 

73 

72 

.270567 

.272373 

.274081 

.275699 

.277229 

.278672!  .280032 

.281310 

72 

71 

.270533 

.272329 

.274025 

.275627 

.277142 

.278571 

.279908 

.281170 

71 

70 

.270486 

.272270 

.273950 

.275535 

.277036 

.278440 

.279762 

.281003 

70 

69 

1.270423 

1.272190 

1.273852 

1.275423 

1.276898 

1.278286:1.279585 

1.280801 

69 

68 

.270339 

.272087 

.273734 

.275278 

.276735 

.278099!  .279373 

.280563 

68 

67 

.270231 

.271962 

.273581 

.275106 

.276537 

.277875 

.279122 

.280287 

67 

66 

.270098 

.271801 

.273399 

.274897 

.276301 

.277610 

.278829 

.279966 

66 

65 

.269929 

.271608 

.273179 

.274647 

.276022 

.277301 

.278491 

.279599 

65 

84 

1.269724 

1.271376 

1.272915 

1.274352 

1.275695 

1.276945 

1.278105 

1.279181 

64 

63. 

.269479 

.271097 

.272604 

.274007 

.275319 

.276536 

.277662 

.278707 

63 

62 

.269184 

.270769 

.272239 

.273610 

.274888 

.276069 

.277162 

.278178 

62 

61 

.268838 

.270383 

.271819 

.273156 

.274394 

.275542 

.276604 

.277587 

61 

60 

.268430 

.269939 

.271340 

.272634 

.273838 

.274952 

.275980 

.276928 

60 

59 

1.267961 

1.269433 

1.270789 

1.272046 

1.273215 

1.274293 

1.275284 

1.276203 

59 

58 

.267426 

.268851 

.270167 

.271388 

.272519 

.273558 

.274519 

.275403 

58 

57 

.266811 

.268194 

.269472 

.270652 

.271742 

.272750 

.273674 

.274526 

57 

56 

.266117 

.267459 

.268694 

.269832 

.270889 

.271857 

.272748 

.273566 

56 

55 

.265340 

.266637 

.267828 

.268931 

.269945 

.270880 

.271734 

.272521 

55 

54 

1.264471 

1.265722 

1.266876 

1.267934 

1.268913 

1.269809 

1.270629 

1.271387 

54 

53 

.263503 

.264715 

.265822 

.266843 

.267781 

.268641 

.269432 

.270157 

53 

52 

.262438 

.263601 

.264668 

.265646 

.266547 

.267376 

.268133 

.268827 

52 

51 

.261260 

.262380 

.263403 

.26434.2 

.265210 

.266003 

.266726 

;267391 

51 

50 

.259969 

.261043 

.262024 

.262928 

.263758 

.264516 

.265208 

.265845 

50 

49 

1.258554 

1.259585 

1.260528 

1.261392 

1.262186 

1.262911 

1.263574 

1.264181 

49 

48 

.257012 

.258002 

.258903 

.259730 

.260489 

.261183 

.261815 

.262395 

48 

47 

.255336 

.256282 

.257145 

.257934 

.258660 

.259322 

.259924 

.260481 

47 

46 

.253516 

.254422 

.255244 

.255999 

.256691 

.257322 

.257901 

.258429 

46 

45 

.251,546 

.252409 

.253196 

.253915 

.254575 

.255181 

.255729 

.256233 

45 

17 

16 

16 

14 

13 

12 

11 

10 

Continued  from  Page  *61. 


*72 


TABLE     XLTI 


LIFE  AND  TEMPORARY  ANI^UITIES.     LOGARITHJtf    OF  THE    PRESENT  VALUE  OF   n 
ANNUAL  PAYMENTS  OF  1    AT  THE  BEGINNING   OF  EACH  YEAR. 


The  first  Value  under  the  Age  X  is  A(l  +  Ox)   for  the  whole  Life. 

5  PER  CENT. 

Pay- 

niATltlS 

a;=10 

11 

12 

13 

14 

15 

16 

17 

Pay- 
ments. 

UIVUUo* 

n. 
1 

1.249190 

1.248018 

1.2467871.2454871 

1.244118 

1.242680 

1.241167 

1.239571 

7?. 

1 

0.000000 

0.000000 

0. 000000  0. 000000  0. 000000 

0.000000 

0.000000 

0.000000 

2 

.289190 

.289185 

.2891821  .289178l|  .289171 

.289165 

.289161  .289154 

2 

3 

.453548 

.453539 

.4535341  .453523  .453510 

.453500 

.453490  .453475 

3 

4 

.566862 

.566850 

.566838  .566823  .566805 

.566789 

.566773  .566751 

4 

5 

0.652256 

0.652239 

0.652223,0.652202 

0.652179 

0.652157 

0.652133  0.652104 

5 

6 

.720028 

.720006 

.719985  .719959! 

.719930 

.719901 

.719871 

.719834 

6 

7 

.775673 

.775646 

.775620^  .775588 

.775553 

.775518 

.775480 

.775435 

7 

8 

.822470 

.822438 

.822407' .822370 

.822328 

.822285 

.822240 

.822186 

8 

9 

.862534 

.862497 

.862461  .862417! 

.862368 

.862319 

.862265 

.862201 

9 

10 

0.897309 

0.897268 

0.897225;0.897175  0.897120 

0.897062 

0.896999 

0.896928 

10 

11 

.927826 

.927779 

.9277301  .927674i  .927611 

.927544 

.927474 

.927390 

11 

12 

.954845 

.954791 

.954737 

.954673  .954601 

.954528 

.954446 

.954353 

12 

13 

.978941 

.978883 

.978821 

.978749  .978671 

.978587 

.978496 

.978394 

13 

14 

1.000565 

1.000500 

1.000431 

1.000353  1.000264 

1.000172 

1.000073 

.999957 

14 

15 

1.020071 

1.019999 

1. 019924 

1.019835  1.019740 

1.019639 

1.019527 

1.019401 

15 

16 

.037746 

.037668 

.037582 

.037488  .037384 

.037271 

.037149 

.037010 

16 

17 

.053824 

.053737 

.0536461  .053543  .053427 

.053305 

.053171 

.053022 

17 

18 

.068498 

.068405 

.0683061  .068192  .068067 

.067933 

.067790 

.067625 

18 

19 

.081933 

.081831 

.081722 

.081600  .081463 

.081322 

.081163 

.080983 

19 

20 

1.094262 

1.094152 

1.094035 

1.093901  1.093758 

1.093601 

1.093428 

1.093237 

20 

21 

.105604 

.105486 

.105358 

.105218  .105061 

.104890 

.104707 

.104497 

21 

22 

.116060 

.115932 

.115798 

.115644  .115474 

.115293 

.115092 

.114870 

22 

23 

.125716 

.125581 

.125434 

.125268  .125088 

.124891 

.124678 

.124439 

23- 

24 

.134649 

.134503 

.134344  .134169  .133974 

.133765 

.133537 

.133281 

24 

25 

1.142924 

1.142766 

1.142598 

1.142409  1.142202 

1.141980 

1.141734 

1.141460 

25 

26 

.150597 

.150431 

.150250 

.150049  .149830 

.149590 

.149329 

.149037 

26 

27 

.157725 

.157546 

.157355 

.157141  .156905 

.156651 

.156367 

.156061 

27 

28 

.164349 

.164160 

.163956 

.163728  .163478 

.163203 

.162911 

.162579 

28 

29 

.170513 

.170312 

.170095 

.169853  .169584 

.169300 

.168983 

.168631 

29 

30 

1.176252 

1.176039 

1.1758081.175549  1.175270 

1.174964 

1.174628 

1.174257 

30 

31 

.181599 

.181373 

.181127 

.180859.  .180559 

.180234 

.179880 

.179483 

31 

32 

.186585 

.186344 

.186089 

.185800;  .185483 

.185141 

.184762 

.184343 

32 

33 

.191235 

.190985 

.190710 

.190405  .190072 

.189706 

.189307 

.188867 

33 

34 

.195578 

.195310 

.195019 

.194699  .194344 

.193958 

.193539 

.193069 

34 

35 

1.1996281.199345 

1.199041 

1.198700  1.198325 

1.197921 

1.197473 

1.196983 

35 

36 

.203409 

.203114 

.202790 

.202430;  .202038 

.201606 

.201140  .200619 

36 

37 

.206942 

.206629  .206287 

.205911 

.205493 

.205044 

.204548  .204001 

37 

38 

.210240 

.209909  .209552 

.209152 

.208717 

.208240 

.207720 

.207147 

38 

39 

.213319 

.212974  .212594 

.212177 

.211716 

.211217 

.210671 

.210067 

39 

40 

1.216197 

1.2158301.215434 

1.214992 

1.214511 

1.213987 

1.213412 

1.212777 

40 

41 

.218880'  .218498 

.218078 

.217618 

.217112 

.216561 

.215957 

.215294 

41 

42 

.221388  .220983 

.220546 

.220061; 

.219530 

.218951 

.218322 

.217623 

42 

43 

.223724  .223303 

.222842 

.222334 

.221777 

.221174 

.220510 

.219779 

43 

44 

.225906  .225462 

.224979 

.224447 

.223867 

.223231 

.222537 

.221773 

44 

10     11 

12 

13 

.14 

15 

16 

17 

Continued  on  Page  82. 


Formula,  A,(l4-a!J-i).=  k  ?£:z??£±«=A^£=i. 
*  Da;  vpx-t 


TABLE    XLVl. 


^73 


LIFE  AND  TEMPORARY  ANNUITIES.    LOGARITHM  OF    THE    PRESENT  VALUE    OF   n 
ANNUAL  PAYMENTS  OF  1  AT  THE  BEGINNING  OF  EACH  YEAR. 

5  PER  CENT. 


Pay- 

18 

19 

20 

21 

22 

23 

24 

25 

Pay-  i 

ments. 
n. 

1 

1.223420 

ments. 

1.23789l!l.236125'l.234365 

1       1 

1.232309 

1.230253 

1.228089 

1.225813 

n. 
1 

0. OOOOOO'0. 000000  0. 000000 

0. 000000 ''o.  000000 

0.000000 

0. 000000 

0. 000000 

2 

.289146  .289139  .289130 

.289120 

.289110 

.289099 

.289085!  .289072 

2 

3 

.453460 

.453445'  .453426 

.453406 

.453386 

.453362 

.453336 

.453307 

3 

4 

.566728 

.566704 

.566675 

.566645 

.566613 

.566577 

.566536 

.566492 

4 

5 

0.652073 

0.652039 

0.652000 

0.651959:  0.651916!o. 651865 

0,651810 

0.651750 

5 

6 

.719794 

.719751 

.719702 

.719650 

.719592 

.719528 

.719458 

.719380 

6 

7 

.775386 

.775333 

.775274 

.775207 

.775137 

.775059 

.774972 

.774877 

7 

8 

.822127 

.822065 

.821991 

.821914 

.821831 

.821736 

.821633 

.821520 

8 

9 

.862134  .862058 

.881975 

.861885 

.861786 

.861677 

.861555 

.861424 

9 

10 

0.896847'o.  896762 

0.896667 

0.896562 

0.896449  0.896322 

0.896184 

0.896030 

10 

11 

.927301^  .927205 

.927095 

.926976 

.926847i  .926704 

.926545 

.926371 

11 

12 

.954254^  .954144 

.954021 

.953887 

.953742  .953579 

.953401 

.953207 

12 

13 

.978281^  .978159!  .978021 

.977873 

.977709:  .977528!  .977330 

.977111 

13 

14 

.999833  .999697 

.999545!  .999379 

j 

.999198:  .998998 

1 

.998777 

.998536 

14 

15 

1.0192631.019114 

1.0189461.018763 

1.0185641.018342 

1.018100 

1.017833 

15 

16 

.036861!  .036695 

.036511!  .036311 i  .036091!  .035850 

.035583 

.035291 

16 

17 

.052856'  .052675  .052475  .052255] 

.052017j  .051752 

.051461 

.051143 

17 

18 

.087444'  .067249  .067029  .066793 

.0665321  .066244 

.065929 

.065581 

18 

19 

.080790,  .080575  .080340  .080082' 

.079800!  .079489 

.079145 

.078770 

19 

20 

1.093024  1.092796  1.0925401.092262 

1.091957 

1.091619 

1.091250 

1.090842 

20 

21 

.104271 

.104023 

.103749!  .1034481 

.103119 

.102756 

.102356 

.101916 

21 

22 

.114626 

.114360 

.114064  .1137411 

.113388 

.112996 

.112565 

.112097 

22 

23 

.124178 

.123891 

.123574 

.123229 

.122847 

.122427 

.121969 

.121463 

23 

24 

.133000 

.132693  .132355 

.131982 

.131575 

.131128 

.130635 

.130094 

24 

25 

1.141161 

1.140833  1.140469 

1.140072 

1.139639 

1.139160 

1.138632 

1.138056 

25 

26 

.148717 

.148366 

.147978 

.147557 

.147093 

.148581 

.146021 

.145404 

26 

27 

.155720 

.155346 

.154936 

.1544841 

.153990 

.153447 

.152848 

.152194 

27 

28 

.162216  .161821 

.161382 

.160902; 

.160378 

.159798 

.159164 

.158466 

28 

29 

.168248 

.167825 

.167359 

.166852 

.166293 

.165680 

.165004  .164266 

29 

30 

1.173847 

1.173399 

1.172908 

1.172366 

1.171776 

1.171123 

1.170410 

1.169626 

30 

31 

.179049  .178578;  .178053 

.177483 

.176855 

.176166 

.175412 

.174584 

31 

32 

.183888  .183384'  .182833 

.182226 

.181564 

.180837 

.180039 

.179163 

32 

33 

.188380 

.187852  .187266 

.186628 

.185929 

.185161 

.184317 

.183395 

33 

34 

.192561 

.191999  .191383 

.190710 

.189972 

.189161 

.188273 

.187300 

34 

35 

1.196442 

1.195852 

1.195204 

1.194493 

1.193715 

1.192862 

1.191926 

1.190902 

35 

36 

.200051 

.199431 

.198747 

.197998 

.197180 

.196282 

.195298 

.194222 

36 

37 

.203405 

.202751 

.202030 

.201244 

.200384 

.199439 

.198406 

.197278 

37 

38 

.206518 

.205829 

.205074 

.204247 

.203342 

.202352 

.201270 

.200085 

38 

39 

.2094051  .208685 

1 

.207889 

.207021 

.206073 

.205037 

.203901 

.202663 

39 

40 

1.212086 

1.211326 

1.210492 

1.209583 

1.208592 

1.207504 

1.206318 

1.205022 

40 

41 

.214566 

.213769 

.212897 

.211947 

.210907 

.209772 

.208530 

.207174 

41 

42 

.216860 

.216027 

.215116 

.214120 

.213035 

.211847 

.210549 

.209139 

42 

43 

.218981 

.218112 

.217157 

.216118 

.214984 

.213743 

.212393 

.210921 

43 

44 

.220940 

.220030 

.219034 

.217949 

.216765 

.215474 

.214066 

.212531 

44 

18 

19 

20 

21 

22 

23 

24 

26 

Continued  on  Page  *81. 


74 


TABLE    XLYl. 


LIFE  AND  TEMPORARY  ANNUITIES.      LOGARITHM  OF  THE   PRESENT  VALUE  OF    fl 

ANNUAL  PAYMENTS  OF  1   AT  THE  BEGINNING  OF  EACH  YEAR. 

5  PER  CENT. 


Pay- 

ments. 

n. 

a:=26  j  27 

28 

29 

30 

31    32  !  33 

Pay- 
ments. 

1.2209041.218261 

1.215481 

1.212561 

1.209497 1.206277|l.202896 

1.199343 

n. 

1 

0.000000  0.000000 

0.000000 

0.000000 

0.000000  0.000000 

0.000000 

0.000000 

1 

2 

.289055 

.289039 

.289020 

.288997 

.288976!  .288951 

.288925 

.288894 

2 

3 

.453274 

.453240 

.453200 

.453156;  .453111!  .453061 

.453006 

.452944 

3 

4 

.566442 

.566388 

.566328 

.566262 

.566194:  .566115 

.566031 

.565934 

4 

5 

0.651681 

0.651609 

0.651528 

0.651439 

0.651343i0. 651237 

0.651120 

0.650988 

5 

6 

.719293 

.719201 

.719098 

.718982 

.718861 

.718725  .718574 

.718408 

6 

7 

.774771 

.774658 

.774530 

.774390 

.774241 

.774072!  .773889 

.773684 

7 

8 

.821394 

.821258 

.821107i  .820940 

.820759 

.820559!  .820340 

.820097 

8 

9 

.861276  .861117 

.860941 

.860744 

.860534 

.860300  .860044 

.859760 

9 

10 

0.8958610.895679 

0.895474 

0.895250 

0.895007 

0.894738  0.894444 

0.894116 

10 

11 

.926180  .925971 

.925739 

.925484 

.925209 

.924903,  .924567 

.924195 

11 

12 

.952990i  .952755 

.952494:  .952209 

.951897 

.951553:  .951175 

.950756 

12 

13 

.976871 

.976607 

.976318  .975997 

.975650 

.9752661  .974843 

.974377 

13 

14 

.998267 

.997977 

.997654  .997301 

.996916 

.996488  .996021 

.995504 

14 

15 

1.017539 

1.017217 

1.0168631.016473 

1.016046 

1.0155771.015062 

1.014493 

15 

16 

.034968  .034616!  .0342281  .033798' 

.033332 

.032818  .032252 

.031628 

16  1 

17 

.050790;  .050407 

.049980  .049513. 

.049005 

.048442  .047825 

.047147  17 

18 

.065199 

.064779 

.064317 

.063810 

.063256 

.062644  .061976 

.061235  18 

19 

.078353 

.077899 

.077400 

.076849 

.076249 

.0755891  .074861 

.074063  19  1 

20 

1.090392 

1.089904 

1.089363 

1.088769 

1.088122 

1.0874054.086624 

1.085758  20 

21 

.101435 

.100907 

.100324 

.099686' 

.098985 

.098218:  .097372 

.096444!  21 

22 

.111577 

.111009 

.110385 

.109695 

.108947 

.1081191  .107214 

.106217 

22 

23 

.120906 

.120299 

.119626 

.118891 

.118086 

.11720l|  .116231 

.115166 

23 

24 

.129499 

.128846 

.128131 

.127342 

.126483 

.125537!  .124501 

.123361 

24 

25 

1.137418 

1.136724 

1.135958 

1.135118 

1.13420lk.l33193'l.l32087 

1.130873  25 

26 

.144727 

.143985 

.143170 

.142275 

.141299  .140225'  .139049 

.137758  26 

27 

.151471 

.150684 

.149816 

.148866 

.147827  .146687!  .145438 

.144066 

27 

28 

.157701 

.156862 

.155944 

.154934 

.153833 

.152623 

.151297 

.149846 

28 

29 

.163452 

.162567 

.161591 

.160522 

.159355 

.158072 

.156672 

.155136 

29 

30 

1.168768 

1.167827 

1.166796 

1.165665 

1.164429 

1.163076 

1.161596 

1.159973 

30 

31 

.173673  .172681 

.171591 

.170394 

.169091 

.167664 

.166101 

.164394 

31 

32 

.178204 

.177155 

.176003 

.174743 

.173370 

.171864 

.170221 

.168423 

32 

33 

.182382 

.181275 

.180063 

.178737 

.177290 

.175708 

.173979  .172090 

33 

34 

.186233 

.185069 

.183794 

.182398 

.180879 

.179216 

.177402 

.175422 

34 

35 

1.189780 

1.188557 

1.187216 

1.185752 

l.i84157 

1.182413 

1.180513 

1.178438 

35 

36 

.193044 

.191758 

.190354 

.188818 

.187145 

.185320 

.183330 

.181164 

36 

37 

.196041 

.194695 

.193222 

.191612 

.189864 

.187954 

.185879  .183620 

37 

38 

.198792 

.197381 

.195837 

.194157 

.192328 

.190338 

.188175 

.185820 

38 

39 

.201308 

.199830 

.198221 

.196464 

.194550 

.192487 

.190233 

.187785 

39 

40 

1.203603 

1.2020641.200382 

1.198545 

1.196572 

1.194413 

1.192071 

1.189534 

40 

41 

.205698 

.204089  .202332 

.200439 

.198375 

.196133 

.193708 

.191077 

41 

42 

.207597 

.205918  .204107 

.202129 

.199986 

.197667 

.195152 

.192435 

42 

43 

.209312 

.207583  .205692 

.203639 

.201424 

.199019 

.196424 

.193621 

43 

44 

.210875 

.209070,  .207108 

.204987 

.202691 

.200211 

.197534 

.194646; 

44 

26 

27  1  28 

29  1 

30 

31 

32 

33 

Continued  on  Page  *80. 


TABLE    XLYL 


♦75 


LIFE   AND   TEMPORARY  ANNUITIES.       LOGARITHM  OF  THE    PRESENT  VALUE    OF  n 

ANNUAL   PAYMENTS  OF   1   AT  THE  BEGINNING  OF  EACH  YEAR. 

5   PER   CENT. 


Pay- 
ments. 
n. 

34 

35 

36 

37 

38 

39 

40 

41 

Pay-  j 

ments. 

n. 

1.195615 

1.191703 

1.187604 

1.183299 

1.178783 

1.174051 

1.169091 

1.163896 

1 

0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

1 

2 

.288861 

.288821 

.288783 

.288741 

.288690 

.288637 

.288577 

.288516 

2  ! 

3 

.452874 

.452797 

.452719 

.452629 

.452528 

.452418 

.452299 

.452168 

3  ! 

4 

.565828 

.565712 

.565590 

.565452 

.565297 

.565131 

.564945 

.564745 

4  ! 

5 

0.650846 

0.650688 

0.650521 

0.650332 

0.650122 

0.649894 

0. 649642 

0.649369 

5 

6 

.718225 

.718025 

.717809 

.717569 

.717300 

.717008 

.716688 

.716337 

6 

7 

.773461 

.773214 

.772950 

.772653 

.772324 

.771967 

.771573 

.771143!   7 

8 

.819830 

.819536 

.819219 

.818865 

.818474 

.818047 

.817578 

.817064   8 

9 

.859447 

.859104 

.858733 

.858320 

.857862 

.857365 

.856815 

.856216   9 

[ 

10 

0.893757 

0.893362 

0.892935 

0.892459 

0.891934 

0.891359 

0.890729 

0.890039!  10 

11 

.923787 

.923339 

.922852 

.922312 

.921715 

.921064 

.920348 

.919565  11 

12 

.950298 

.949793 

.949245 

.948637 

.947967 

.947235 

.946431 

.945549:  12 

13 

.973865 

.973302 

.972690 

.972013 

.971266 

.970450 

.969552 

.9685711  13 

14 

.994937 

.994313 

.993636 

.992885 

.992059 

.991155 

.990162  .989074|  14 

15 

1.013868 

1.013183 

1.012434 

1.011610 

1.010699 

1.009706 

1.0086121.007416  15 

16 

.030946 

.030192 

.029375 

.028469 

.027475 

.026385 

.025190  .023879  16 

17 

.046399 

.045581 

.044686 

.043701 

.042616 

.041430 

.040125  .038701  17 

18 

.060427 

.059535 

.058565 

.057495 

.056318 

.055028 

.0536171  .0520721  18 

19 

.073184 

.072221 

.071171 

.070014 

.068738 

.067349 

.065823!  .0C4153  19 

20 

1.084812 

1.083773- 

1.082642 

1.081390 

1.080021 

1.078522 

1.0768791.075080  20 

21 

.095425 

.094310 

.093088 

.091749 

.090276 

.088667 

.086900:  .0849721  21 

22 

.105126 

.103926 

.102620 

.101183 

.099606 

.097879 

.095991,  .093921  22 

23 

.113995 

.112714 

.111317 

.109780 

.108092 

.106252 

.104229  .102035 

23 

24 

.122113 

.120746 

.119254 

.117614 

.115818 

.113850 

.111711  .109366 

24 

1 

25 

1.129544 

1.128087 

1.126498 

1.124755 

1.122839 

1.120761 

1.118479!l.ll5994 

25 

26 

.136344 

.134796 

.133110 

.131254 

.129233 

.127020 

.124606 

.121973 

26 

27 

.142567 

.140926 

.139134 

.137178 

.135030 

.132692 

.130139 

.127358 

27 

28 

.148258 

.146519 

.144630 

.142554 

.140289 

.137821 

.135127 

.132199!  28  | 

29 

.153456 

.151623 

.149623 

.147437, 

.145049 

.142448 

.139616 

.136537 

29 

30 

1.158204 

1.156267 

1.154162 

1.151860 

1.149346 

1.146614 

1.143641 

1.140412 

30 

31 

.162527 

.160491 

.158276 

.155855 

1  .153218 

.150354 

.147238 

.143859 

31 

32 

.166461 

.164322 

.161995 

.159458 

1  .156696 

.153697 

.150441 

.146913!  32  1 

33 

.170032 

.167786 

.165350 

.162696 

.159807 

.156676 

.153279 

.149605 

33 

34 

.173263 

.170915 

.168368 

.165594 

.162580 

.159317 

.155783 

.151967 

34 

35 

1.176182 

1.173729 

1.171070 

1.168178 

1.165041 

1.161648 

1.157980 

1.154022 

35 

36 

.178810 

.176251 

.173480 

.170473 

i  .167212 

.163694'  .159893 

.155800 

36 

37 

.181165 

.178500 

.175622 

.172497 

1  .169119 

.1654761  .1615481  .157326 

37 

38 

.183266 

.180501 

.177511 

.174276 

1  .170782 

.1670181  .162969!  .158626 

38 

39 

.185136 

.182266 

.179172 

.175828 

i  .172219 

.168342 

.164179 

.159718 

39 

40 

1.186786 

1.183818 

1.180621 

1.177169 

1.173454 

1.169470 

1.165197 

1.160629 

40 

41  . 

.188237 

.185172 

.181874 

.178322 

.174507 

.170419 

.166046 

.161380 

41 

42 

.189504 

.186343 

.182952 

.179306 

.175392 

.171211 

.166746 

.161989 

42 

43 

.190599 

.187351 

.183871 

.180132 

.176131 

.171864 

.167313 

.162474 

•43 

44 

.191542 

.188210 

.184643 

.180822 

.176741 

.172393 

.167765 

.162861 

44 

34 

35 

36 

37 

38 

39 

40 

41 

Continued  on  Page  *79. 


*76 


TABLE    XLTI. 


LIFE  AND  TEMPORARY  ANNUITIES.     LOGARITHM    OF  THE    PRESENT    VALUE    OF  n 

ANNUAL  PAYMENTS  OF  1  AT  THE  BEGINNING  OF  EACH  YEAR. 

5  PER  CENT 


Pay- 

x=^2 

43 

44 

45 

46 

47 

48 

49 

Pay. 

ments. 
n. 

1 

ments. 

n. 

1.158448 

1.152750 

1.146778 

1.140532 

1.133997 

1.127159 

1.120012 

1.112544 

0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

0. 000000 

1 

2 

.288442 

.288366 

.288279 

.288184 

.2880811 

.287967 

.287841 

.287704 

2 

3 

.452020 

.451864 

.451686 

.451494 

.451283 

.451048 

.450792 

.450511 

3 

4 

.564520  .564278 

.564007 

.563710 

.563388 

.563029 

.562637 

.562206 

4 

5 

0.649063  0.648732 

0.648362 

0.647962 

0.647519 

0.647032  0.646498 

0.645909 

5 

6 

.715947 

.715523 

.715054 

.714539: 

.713975 

.713353  .712670 

.711921 

6 

7 

.770664 

.770146 

.769569 

.7689391 

.768247 

.767485  .766649 

.765730 

7 

8 

.816495 

.815875 

.815189 

.814438 

.813614 

.812705 

.811709 

.810616 

8 

9 

.855551 

.854828 

.854026 

.853150 

.852187 

.851127 

.849966 

.848693 

9 

10 

0.889276!o.  888444 

0.887524 

0.886516 

0.885410 

0.884194 

0.882862 

0.881400 

10 

11 

.9186981  .917753 

.916709 

.915566 

.914311 

.912933 

.911424 

.909766 

11 

12 

.944576  .943514 

.942341 

.941057 

.939649 

.938105 

.9364091  .934551 

12 

13 

.9674861  .966301 

.934996 

.963567 

.962002 

.960281 

.958396 

.956332 

13 

14 

.987874  .986564 

.985121 

.983544' 

1 

.981812 

.979912  .977833 

.975556 

14 

15 

1.006096(1.004656 

1.003073 

1.001338;  0.999437 

0. 997354|0. 995073  0. 992575 

15 

16 

.022438;  .020865 

.019133 

.01723811.015164 

1.0128901.010401 

1.007676 

16 

17 

•  .037133  .035420 

.033537 

.031478, 

.029223 

.026753  .024051 

.^21100 

17 

18 

.050372  .048515 

.046478 

.044248 

.041809 

.039138  .036222 

.033036 

18 

19 

.062316  .060315 

.058107 

.055713' 

1 

.053084 

.050211  .047074 

.043650 

19 

20 

1.0731071.070944 

1.068590 

1.0660071 

1.063188 

1.06010711.056746 

1.053080 

20 

21 

.082848  .080546 

.078013 

.075253! 

.072237 

.0689451  .0653571  .061448 

21 

22 

.091665  .089195 

.086495 

.083548' 

.080334 

.076828;  .073011  .068857 

22 

23 

.099320  .096992 

.094116 

.090982' 

.087567 

.083846!  .079799^  .075400 

23 

24 

.106802|  .104008 

.100956 

.097633 

.094016 

.090079  .085800 

.081156 

24 

25 

1.1132731.110314 

1.107083 

1.103570 

1.099750 

1.09559511.091087 

1.086204 

25 

26 

.119096'  .115969 

.112559 

.108856 

.104830 

.100460 

.095728 

.090606 

26 

27 

.124324;  .121028 

.117440 

.113542 

.109315 

.104734 

.099779 

.094424 

27 

28 

.129005  .125541 

.121770 

.117684 

.113258 

.108468 

.103294 

.097711 

28 

29 

.133185  .129549 

.125600 

.121328 

.116706 

.111711 

.106323 

.100525 

29 

30 

1.136899:1.133093 

1.128973 

1.124515 

1.119702 

1.114507 

1.108917 

1.102914 

30 

31 

.140188  .136221 

.131924 

.127287 

.122286 

.116901 

.111121 

.104919 

31 

32 

.143087!  :  138957 

.134492 

.129679 

.124500 

.118938 

.112971 

.106586 

32 

33 

.145628;  .141339 

.136709 

.131730 

.126384 

.120647 

.114510 

.107957 

33 

34 

.147839 

.143397 

.138610 

.133475 

.127966 

.122070 

.115776 

.109070 

34 

35 

1.149751 

1.145161 

1.140229 

1.134940 

1.129283 

1.123240 

1.116804 

1.109957 

35 

36 

.151390 

.146665 

.141588 

.136161 

.130366 

.124191 

.117623 

.110657 

36 

37 

.152788 

.147926 

.142721 

.137165 

.131247 

.124949 

.118270 

.111196 

37 

38 

.153981 

.148979 

.143653 

.137982 

.131949 

.125547 

.118768 

.111605 

38 

39 

.154940 

.149845 

.144411 

.138632 

.132503 

126007 

.119145 

.111910 

39 

40 

1.155746 

1.150550 

1.145014 

1.139147 

1.132929 

1.126356 

1.119427 

1.112128 

40 

41 

.156401 

.151110 

.145493 

.139542;'  .133252 

.126617 

.119628 

.112283 

41 

42 

.1569221  .151555 

.145859 

.139841}  .133494 

.126803 

.119772 

.112388 

42 

43 

.157337 

.151895 

.146137 

.140065]  .133666 

.126937 

.119869 

.112455 

43 

44 

1  .157653 

1 

.152154 

.146345 

.140225  1  .133790 

.127026 

.119931 

.112496 

44 

i  42 

43 

44 

45 

1  46 

47 

48 

49 

Continued  on  Page  *78. 


TABLE     XLYI. 


*n 


LIFE  AND  TEMPORARY  ANNUITIES.      LOGARITHM   OF  THE  PRESENT  VALUE  OF   n 

ANNUAL  PAYMENTS  OF  1   AT  THE  BEGINNING  OF  EACH  YEAR.      ,  „„^  __^ 

d  PER  CENT. 


Pay. 

50 

51 

52 

53 

64 

66 

56 

57 

Pay-  1 

ments. 
n. 

1 

ments. 

n. 

1.104739 

1.096590 

1.088084 

1.079208 

1.069947 

1.060290 

1.050232 
0.000000 

1.039753 

O.OOOOOOi 

0.000000 

0.000000 

0.000000 

0.000000 

0. 000000 

0.000000 

1 

2 

.287551 

.287384 

.287201 

.287001 

.286782 

.286535 

.286270 

.285973 

2 

3 

.450200 

.449859 

.449486 

.449078 

.448627 

.448128 

.447584 

.446980 

3 

4 

.561729 

.561209 

.560639 

.560012 

.559322 

.558559 

.557725 

.556805 

4 

5 

0.645263 

0.644555 

0.643778 

0.642925 

0. 641986 

0.  640948 

0.639816 

0.638570 

5 

6 

.711096 

.710193 

.709202 

.708114 

.706914 

.705595 

.704155 

.702568 

6 

7 

.764721 

.763615 

.762403 

.761068 

.759603 

.757993 

.756230 

.754294 

7 

8 

.809416 

.808101 

.806655 

.805069 

.803329 

.801415 

.799323 

.797025 

8 

9 

.847294 

.845758 

.844074 

.842230 

.840S03 

.837978 

.835545 

.832878 

9 

10 

0.879793 

0.878033 

0.876106 

0.873990 

0.871670 

0.869124 

0.866344 

0.863295 

10 

11 

.907947 

.905956 

.903773 

.901381 

.898758 

.895885 

.892746 

.889308 

11 

12 

.932514 

.930282 

.927838 

.925160 

.922230 

.919019 

.915515 

.911680 

12 

13 

.954068 

.951590 

.948876 

.945910 

.942661 

.939107 

.935229 

.930992 

13 

14 

.973058 

.970325 

.967340 

.964074 

.960503 

.956598 

.952343 

.947700 

14 

15 

0.'989837 

0.986849 

0.983583 

0.980013' 

0.976113 

0.971854 

0.967218 

0.962164 

15 

16 

1.004699 

1.001446 

.997893 

.994014 

.989782 

.985165 

.980146 

.974678 

16 

17 

.017873 

.014351 

1.010508 

1.006317 

1.001749 

.996773 

.991366 

.985490 

17 

18 

.029556 

.025761 

.021625 

.017120 

.012215 

1.006876 

1.001088 

.994807 

18 

19 

.039913 

.035843 

.031411 

.026590 

.021345 

.015651 

.009484 

1.002802 

19 

20 

1.049085 

1.044737 

1.040009 

1.034869; 

1.029293 

1.023244 

1.016704 

1.009629 

20 

21 

.057192 

.052566 

.047540 

.042090 

.036181 

.029785 

.022878 

.015427 

21 

22 

.064340 

.059435 

.054118 

.048357 

.042125 

.035386 

.028129 

.020313 

22 

23 

.070621 

.065443 

.059836 

.053773 

.047220 

.040155 

.032560 

.024399 

23 

24 

.076122 

.070673 

.064783 

.058420 

.051563 

.044185 

.036269 

.027781 

24 

25 

1.080915 

1.075201 

1.069031 

1.062385 

1.  055238!l.047560ll. 039340 

1.030548 

25 

26 

.085069 

.079093 

.072659 

.065743 

.058316  .0503571  .041855 

.032789 

26 

27 

.088643 

.082420 

.075734 

.068558 

.060869  .052648,  .043894 

.034575 

27 

28 

.091700 

.085242 

.078313 

.070893 

.062962'  .054507,  .045519 

.035978 

28 

29 

.094294 

.087610 

.080454 

.072809 

.064660;  .055988  .046795 

1 

.03^059 

29 

30 

1.096471 

1.089575 

1.082211 

1.074363 

1. 06601311. 057153|1.047779 

1.037879 

30 

31 

.098279 

.091190 

.083637 

.075602 

.067078  .058051 

.048525 

.038487 

31 

32 

.099766 

.092501 

.084774 

.076578 

.067900  .058731 

.049080 

.038924 

32 

33 

.100973 

.093546 

.085670 

.077331 

.068522  .059238  .049477 

.039232 

33 

34 

.101935 

.094370 

.086360 

.077901 

.068985,  .059600  .049758 

.039441 

34 

35 

1.102694 

1.095004 

1.0868841.078325 

1.0693161.059857 

1.049948 

1.039576 

35 

36 

.103278 

.095486 

.087273 

.078629 

.069552 

.060030 

.050072 

.039657 

36 

37 

.103722 

.095844 

.087553 

.078845 

.069710 

.060144 

.050145 

.039703 

37 

38 

.104052 

.096101 

.087751  .078990 

.069814 

.060210  .050187 

.039730 

38 

39 

.104288 

.096284 

.087884  .079085 

.069875 

.060248  .050212 

j 

.039744 

39 

40 

1.104457 

1.096406 

1.0870711.079141 

1.069910 

1.0602711.050225 

1.039750 

40 

41 

.104570 

.096486 

.088023,  .079173 

.069931 

.060283'  .050230  .039753 

41 

42 

.104643 

.090534 

.088052 

.079193 

.069942 

.060287 

.050233  .039753 

42 

43 

.104687 

.096561 

.088071 

.079203 

.069945 

.060290 

.050233  .039753 

43 

44 

.104712 

.096578 

.088080 

.079205 

.069948 

.060290 

.050230 

45 

1.104728 

1.096586 

1.088082 

1.079208 

1.069948 

1.060290 

46 

.104735 

.096588 

.088083 

.079208 

47 

.104737 

.096590 

.088084 

48 

.104739 

.096590 

49 

.104739 

60 

51 

52 

53 

64 

55 

66 

67 

'78 


TABLi:     XLYI. 


LIFE  AND  TEMPORARY   ANNUITIES.      LOGARITHM    OF    THE  PRESENT  VALUE  OF 

ANNUAL  PAYMENTS  OP  1  AT  THE  BEGINNING  OF  EACH  YEAR.  ~ 

O  PER  CENT. 


^»y-     a;=58  r    59 
ments. . 

n.    '1.0288511.017506 


36 
37 
38 
39 

40 
41 
42 


51 
50 

49 
48 
47 
46 
45 


1    iO.  000000 


2 
3 

4 

5 
6 

7 
8 
9 

10 
11 
12 
13 
14 

15  0.956668 

16  .968745 

17  .979124 

18  !  .988009 

19  .995584 


.285651 
.446325 
.555804 

0.637208 
.700835 
.752177 
.794515 
.829963 

0.859966 
.885556 
.907499 
.926377 
.942646 


20 
21 
22 
23 

24 

25 
26 
27 
28 
29 

30 
31 
32 
33 
34 

35    1.028745 


1.002005 
.007410 
.011925 
.015658 
.018711 

1.021181 
.023150 
.024695 
.025885 
.026788 

1.027457 

.027939 
.028277 
.028508 
.028656 


.028796 
.028825 
.028841 
.028847 

1.028851 
.028851 
.028851 


0.000000 
.285299 
.445605 
.554702 

0.635712 
.698932 
.749855 
.791763 
.826771 

0.856322 
.881455 
.902934 
.921344 
.937140 

0.950694 
.962305 
.972221 
.980655 
.987792 

0.993790 
.998794 

1.002928 
.006306 
.009036 

1.011212 
.012919 
.014233 
.015230 
.015968 

1.016500 
.016873 
.017128 
.017291 


60 


1.005705 


0.000000 
.284908 
.444810 
.553489 

0.63400: 
.696841 


61 


0.993441 


0.000000 
.284479 
.443937 
.552159 

0.632263 
.694552 


.747308  .744519 


.788747 
.823271 

0.852337 
876974 
897952 
915855 
931150 

0.944203 
.955318 
.964748 
.972711 
.979391 

0.98495'6 
,989548 
.993297 
.996325 
.998736 

1.000627 
.002083 
.003186 
.004003 
.004592 

1.005005 
.005286 
.005467 
.005575 


.017389  .005637 


1.017445 
.017477 
.017494 
.017501 
.017505 

1.017506 
.017506 


49 


1.112544 
.112544 

1.112544 
.112542 
.112540 
.112534 
.112519 


49 


48 


1.120012 
.120013 
.120013 

1.120011 
.120010 
.120004 
.119990 
.119969 


48 


1.005673 
.005691 
.005699 
.005703 
.005704 

1.005705 


47 


1.127159 

.127160 
.127160 
.127158 

1.127157 
.127151 
.127138 
.127119 
.127084 


47 


.785443 
.819450 

0.847985 
.872086 
.892522 
.909888 
.924644 

0.937165 
.947756 
.956677 
.964147 
.970359 

0.975478 
.979653 
.983022 
.985703 
.987804 

0. 989422 
.990646 
.991553 
.992207 
.992665 

0.992977 
.993177 
.993297 
.993366 
.993406 

0. 993426 
.993435 
.993439 
.993441 
.993441 


46 


1.133997 
.133997 
.133997 
.133995 
.133994 

1.133989 
.133977 
.133959 
.133927 
.133873 


46 


62 


0.980708 


63 


0.967485 


0.000000 
.284011 
.442984 
.550702 

0.630289 
.692045 
.741465 
.781837 
.815276 

0.843237 
.866758 
.886618 
.903405 

.917588 

0.929544 
.939587 
.947976 
.954939 
.960667 

0.965334 
.969096 
.972087 
.974429 
.976232 

0.977596 
.978606 
.979334 
.979843 
.980191 

0.980413 
.980547 
.980624 
.980669 
.980691 

0.9807010 
.980706 
.980708 
.980708 


0.000000 
.283494 
.441932 
.549098 

0.628118 
.689292 
.738121 
.777885 
.810711 

0.838051 
.860953 
.880190 
.896360 
.909935 

0.921299 
.930766 
.938605 
.945043 
.950280 

0.954497 
.957846 
.960467 
.962484 
.964008 

0.965136 
.965950 
.906519 
.966908 
.967156 


45 


1.140532 

1.140532 
.140532 
.140530 
.140529 
.140525 

1.140513 
.140497 
.140467 
.140417 
.140340 


45 


967305 
967392 
,967442 
967467 
967477 

967483 
,967485 
,967485 


44 


1.146778 
.146779 

1.146779 
.146777 
.146776 
.146772 
.146761 

1.146746 
.146718 
.146672 
.146600 
.146493 


44 


64 


65 


0.95377l!0.939554 


0.000000 
.282926 
.440776 
.547340 

0.625740 
.686282 
.734461 
.773570 
.805730 


0.000000 
.282300 
.439509 
.545411 

0.623135 
.682984 
.730461 
.768856 
.800300 


0.832404  0.826254 


Pay- 
ments. 
n. 


.854637 
.873209 
.888724 
.901658 

0.912399 
.921268 
.928538 
.934441 
.939187 

0.942953 
.945897 
.948161 
.949872 
.951137 

0.952050 
952688 
953124 
953402 
953569 


,953667 
.953722 
.953750 

.953762 
.953768 

.953770 
.953771 


43 


1.152750 
.152750 
.152750 

1.152748 
.152747 
.152744 
.152733 
.152719 

1.152693 
.152651 
.152584 
.152484 
.152347 


43 


.847771 
.865635 
.880456 
.892715 

0.902800 
.911058 
.917744 
.923111 
.927303 

0.930685 
.933238 
.935165 
.936589 
.937618 

0.938335 

.938827 
.939139 
.939328 
.939438 


939499 
939531 
939544 
939551 
939553 

939554  35 


42 


1.158448 
.158448 
.158448 
.158440 

1.158445 
.158443 
.158432 
,158419 
.158395  50 

1.158356 
.158294 
.158201 
.158073 
.157894 


42 


Continued  from  Page  *76, 


TABLE    XLYL 


*79 


LIFE  AND  TEMPORARY  ANNUITIES.     LOGARITHM  OF  THE    PRESENT 
ANNUAL  PAYMENTS  OF  1   AT  THE  BEGINNING  OF  EACH  YEAR. 


VALUE    OFn 
5  PER  CENT. 


25 
26 
27 
28 
29 

30 
31 
32 
33 
34 


59 
58 
57 
56 
55 

54 
53 
52 
51 
50 

49 
48 
47 
46 
45 


Pay. 

66 

ments. 

n. 

1 

0.924834 

0.000000 

2 

.381620 

3 

.438123 

4 

.543304 

5 

0.620287 

6 

.679383 

7 

.726095 

8 

.763720 

9 

.794390 

10 

0.819572 

11 

.840323 

12 

.857436 

13 

.871525 

14 

.883078 

15 

0.892496 

16 

.900110 

17 

.906210 

18 

.911035 

19 

.914800 

20 

0.917691 

21 

.919872 

22 

.921482 

23 

.922646 

24 

.923456 

67 


0.909590 


0.000000 
.280864 
.436599 
.540986 

0.617164 
.675438 
.721322 
.758113 

.787949 

0.812303 
.832240 
.848558 
.861879 
.872697 

0.881419 
888390 
893894 
898184 
901474 


0.924013 
924365 
924579 
924703 
924772 

0.924808 
924823 
924831 
924833 
924834 


41 


0.903953 
.905783 
.907105 
.908025 
.908657 

0.909057 
.909300 
.909441 
.909519 
.909560 

0.909577 
.909586 
.909588 
.909590 


68 


0.893832 


69 


0.877530 


0.000000  0.000000 
.280048  .279136 
.434934  .433097 
.538460  .535675 

0.613755  0.610013 
.671139  .666429 
.716125  .710441 
.752015  .745362 
.780955  .773345 

0.804427  0.795875 
.823499  .814035 
.838981  .828638 
.851498  .840321 
.861555  .849600 

1.86957010.856894 
.875886;  .862558 


.880800 
.884565 

.887398^ 

.889489  0. 

.890998  , 

.892047,  . 

.892768;  . 

.893224  . 

.8935010. 

.893663|  . 

.893752;  , 

.893798  , 

.893818  , 


.866890 
.870146 

.872547 

874279 
875483 
876311 
876833 
.877151 

877337 
877438 
,877491 
,877514 
,877525 


40 


1.163896 
.163896 
.163896 
.163894 
.163893 

1.163891 
.163881 
.163869 
.163846 
.163810 

1.163752 
.163666 
.163546 
.163379 
.163155 


41 


1.169091 

1.169090 
.169090 
.169089 
.169088 
.169086 

1.169076 
.169065 
.169044 
.169010 
.168956 

1.168876 
.168765 
.168609 
.168400 
.168126 


40 


0.893828:0.877528 
.8938301  .877530 
.893832 


39 


1.174051 

.174050 

1.174050 
.174049 
.174048 
.174046 
.174037 

1.174027 
174007 
173976 
173926 
173851 

1.173747 
.173602 
.173406 
.173151 
.172814 


38 


39 


1.178783 
.178781 
.178781 

1.178780 
.178780 
.178778 
.178769 
.178760 

1.178741 
.178712 
.178666 
.178596 
.178499 

1.178363 
.178180 
.177942 
.177628 
.177235 


70 


0.860711 


0.000000 
.278148 
.431094 
.532643 

0.  605938 
.661302 
.704264 
.738146 
.765103 

0.  786638 
.803836 
.817523 
.828349 
.836833 

0. 843404 
.848421 
.852187 
.854962 
.856960 

0.858350 
.859305 
.859907 
.860274 
.860488 

0.860605 
.860666 
.860693 
.860705 
.860709 

0.860711 


38 


37 


1.183299 
.183298 
.183298 
.183297 

1.183297 
.183295 
.183287 
.183278 
.183261 

1.183234 
.183191 
.183125 
.183035 
.182907 

1.182736 
.182514 
.182221 
.181853 
.181392 


37 


71 


73 


0.843350  0.825455 


0.000000  0.000000 


.277058 
.428896 
.529321 

0.601478 
.655705 
.697538 
.730302 
.756171 

0.776651 
.792842 
.805584 
.815530 
.823211 

0.829062 
.833448 
.836674 
.838996 
.840610 

0.841718 
.842417 
.842843 
.843091 
.843227 


843297 
843329 
843343 
843348 
843350 


36 


1. 187604 
.187603 
.187603 
.187612 
.187602 

1.187602 
.187592 
.187584 
.187568 

.187548 

1. 187502 
.187441 

.187357 
.187237 

.187077 

1.186869 
.186596 
.186252 
.185820 
.185288 


36 


73 


0.807021 


.275867 
.426495 
.525690 

0.596614 
.649613 
.690228 
.721801 
.746513 

0.765885 
.781031 
.792797 
.801851 
.808728 

0.813873 
.817651 
.820367 
.822254 
.823550 

0.824366 
.824863 
.825153 
.825311 
.825393 

0.825431 
.825447 
.825453 
.825455 


0.000000 
.274565 
.423862 
.521720 

0.591309 
.642980 
.682291 
.712593 
.736083 

0.754299 
.768362 
.779133 
.787287 
.793372 

0.797832 
.801033 
.803255 
.804781 
.805741 

0.806326 
.806666 
.806852 
.806948 
.806993 

0.807012 
.807019 
.807021 


35 


1.191703 

1.191701 
.191701 
.191701 
.191701 
.191700 

1.191692 
.191684 
.191668 
.191845 
.191607 

1.191550 
.191471 
.191359 
.191210 
.191015 

1.190759 
.190437 
.190033 
.189536 
.188933 


36 


34 


1.195615 
.195614 

1.195614 
.195614 
.195614 
.195613 
.195606 

1.195598 
.195583 
.195562 
.195526 
.195472 

1.195398 
.195294 
.195154 
.194971 
.194732 

1.194437 
.194052 
.193587 
.193023 
.192346 


34 


Pay. 

ments. 

n. 


1 
2 
3 

4 

5 
6 

7 
8 
9 

10 
11 
12 
13 
14 

15 
16 
17 
18 
19 

20 
21 
22 
23 
24 

25 
26 
27 


66 
65 

64 
63 
62 
61 
60 

59 
58 
57 
56 
55 

54 
53 
52 
51 

5a 

49 
48 
47 
46 
45 


Continued  from  Page  *75. 


^80 


TABLE     XLYI. 


LIFE   AND  TEMPORARY  ANNUITIES.    LOGARITHM   OF    THE    PRESENT  VALUE    OF    n 
ANNUAL  PAYMENTS  OF  1  AT  THE  BEGINNING  OF  EACH  YEAR. 

5  PER  CENT, 


Pay- 
ments. 

n. 

1 

X  =  74: 

75 

76 

77 

0.727935 

78 

79 

80 

81 

Pay-| 
ments.  1 
n. 

1 

0.788039 

0.768544 

0.748513 

0. 706853 

0.685247 

0.663118 

0.640468 

0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

O.OOOOOOiO.  000000 

2 

.273121 

.271556 

.269845 

.267955 

.265900 

.263651 

.261191 

.258516 

2 

3 

.420968 

.417828 

.414391 

'.410619 

.406519 

.402044 

.397173 

.391869 

3 

4 

.517374 

.512654 

.507501 

.501868 

.495755 

.489111 

.481890 

.474070 

4 

5 

0.585515 

0.579229 

0.572385 

0.564931 

0.556868 

0.548124 

0.53867l!o.  528466 

5 

6 

.635757 

.627935 

.619444 

.610236 

.600297 

.589573 

.578019  .565609 

6 

7 

.673671 

.664359 

.654291 

.643406 

.631708 

.619132 

.605652:  .591253 

7 

8 

.702624 

.691893 

.680323 

.667874 

.654542 

.640282 

.625077,  .608915 

8 

9 

.724834 

.712758 

.699796 

.685902 

.671094 

.655336 

.638617 

.620953 

9 

10 

0.741844 

0.728525 

0.714284 

0.699094 

0.682982 

0.665917 

0.647917 

0.628878 

10 

11 

.754796 

.740342 

.724961 

.708631 

.691389 

.673227 

.654072 

.633875 

11 

12 

.764558 

.749097 

.732717 

.715406 

\697167 

.678084 

.657966 

.636899 

12 

13 

.771820 

.755481 

.738246 

.720077 

.701106 

.681163 

.660327 

.638648 

13 

14 

.777130 

.780045 

.742067 

.723269 

.703574 

.683032 

.661695 

.639602 

14 

15 

0.780935 

0.763204 

0.744683 

0.725271 

0.705074 

0.684118 

0.662441 

0.640089 

15 

16 

.783573 

.765370 

.746325 

.726489 

.705946 

.684709 

.662822 

.640322 

16  i 

17 

.785383 

.766731 

.7473251  .727198 

.706421 

.685012 

.663004 

.640418 

17 

18 

.786522 

.767560 

.747907 

.727584 

.706665 

.685156 

.663079 

.640456 

18 

19 

20 
21 
22 
23 
24 

25 
26 

.787315 

0.787618 
.787839 
.787952 
.788005 
.788028 

0.788036 

.788039 

.768042 

0.768306 
.768441 
.768504 
.768531 
.768541 

0.768544 

.748225 

0.748387 
.748464 
.748496 
.748508 
.748513 

.727782 

0.727876 
.727915 
.727930 
.727935 

.706780 

0.706828 
.706847 
.706853 

.685215 

0.685239 
.685247 

.663109 
0.663118 

.640468 

19 

74 
73 
72 
71 
70 

89 

26 

27 

1.220904 
.220905 
.220905 
.220905 
.220905 

1.220904 

28 

29 

1.218261 

.218262 

30 

1.215481 

31 

1.212561 
.212562 

1.212562 

.215483,  .218262 
.215483,  .218262 

1.215483ll. 218262 

1.209497 

33 

32 

1.206277 

1.209498 

1.202896 

.206277 

.209498 

212562 

2154831  -2l85»fii 

.220899 

68 

67 

1.199343 

.202895 

.206277 

.209498' 

.212562 

.215482 

.218256 

.220893 

67 

66 

.199342 

.202895 

.206277 

.209498 

.212561 

.215476 

.218250 

.220885 

66 

65 

.199342 

.202895 

.206277 

.209497 

.212555 

.215470 

.218241 

.220873 

65 

64 

1.199342 

1.202895 

1.206276 

1. 209491 j 

1.212548 

1.215460 

1.218228 

1.220851 

64 

63 

.199342 

.202894 

.206270 

.2094841 

.212538 

.215446 

.218205 

.220817 

63 

62 

.199341 

.202888 

.206263 

.209473: 

.212523 

.215422 

.218169 

.220772 

62 

61 

.199335 

.202881 

.206251 

.209457 

.212497 

.215384 

.218121 

.220711 

61 

60 

.199327 

.202868 

.206234 

.2094291 

.212457 

.215333 

.218056 

.220627 

60  1 

59 

1.199313 

1.202850 

1.206204 

1.209387 

1.212403 

1.215263 

1.217967 

1.220516 

59  ! 

58 

.199294 

.202818 

.206159 

.209329 

.212328 

.215169 

.217849 

.220374 

58  ! 

57 

.199260 

.202770 

.206098 

.209249 

.212228 

.215043 

.217697 

.220191 

57 

56 

.199209 

.202705 

.206012 

.209142; 

.212094 

.214881 

.217503 

.219965 

56 

55 

.199140 

.202614 

.205898 

.208999 

.211922 

.214675 

.217262 

.219685 

55 

54 

1.199043 

1.202491 

1.205746 

1.208816 

1.211702 

1.214419 

1.216964 

1.219347 

54 

53 

.198911 

.202330 

.205551 

.208583 

.211429 

.214101 

.216605 

.218940 

53 

52 

.198740 

.202121 

.205302 

.208291' 

.211091 

.213719 

.216172 

.218461 

52 

51 

.198516 

.201856 

.204991 

.207931 

.210683 

.213258 

.215661 

.217895 

51 

50 

.198234 

.201524 

.204607 

.207496 

.210193 

.212713 

.215059 

.217238 

50 

49 

1.197879 

1.201115 

1.204143 

1.206974 

1.209612 

1.212073 

1.214360 

1.216481 

49 

48 

.197443 

.200620 

.203587 

.206355 

.208930 

.211328 

.213554 

.215615 

48 

47 

.196915 

.200027 

.202927 

.205628 

.208137 

.210470 

.212631 

.214632 

47 

46 

.196282 

.199322 

.202152 

.204783;  .207223 

.209487 

.211585 

.213518 

46 

45 



.195529 

.198495 

.201251 

.203808 

.206175 

.208372 

.210398 

.212271 

45 

33 

32 

31 

30 

29 

28 

27 

26 

Continued  from  Page  *74, 


TABLE    XLVI. 


*81 


LIFE  AND  TEMPORARY  ANNUITIES.     LOGARITHM    OF  THE    PRESENT  VALUE  OF    n 

ANNUAL  PAYMENTS  OF  1  AT  THE  BEGINNING  OF  EACH  YEAR. 

5  PER  CENT. 


Pay- 

ments. 

n. 

i 
2 
3 
4 

82 

83 

84 

85 

86 

87 

88 

89 

Pay-  ] 
ments. 

n. 
1 

2 
3 

4 

0.617258 

0.593510 

0.569083 

0.543949 

0.517851 

0.490338 

0.461018 

0.428340 

0.000000 
.255571 
.386091 
.465583 

0.000000 
.252400 
.379847 
.456446 

0.000000 
.248902 
.373034 
.446561 

0.000000 
.245128 
.365722 
.435952 

0.000000 
.241062 
.357791 
.424566 

0.000000 
.236517 
.349165 
.411342 

0. 000000 
.231773 
.338513 
.395201 

0.000000 
.223681 
.323210 
.374409 

5 
6 

7 
8 
9 

0.517453 
.552297 

.575884 
.591780 
.602169 

0.505659 
.538098 
.559600 
.573508 
.582179 

0.492958 
.522932 
.542018 
.553805 
.560851 

0.479431 
.506445 
.522889 
.532637 
.538204 

0.464382 
.488069 
.501928 
.509785 
.514027 

0.446913 
.467291 
.478711 
.484838 
.487942 

0.426510 
.443722 
.452865 

.457472 
.459663 

0.401609 
.415812 
.422907 
.426267 
.427642 

5 
6 

7 
8 
9 

10 
11 
12 
13 
14 

15 
16 
17 
18 

75 

0.608689 
.612625 
.614896 
.616135 
.616767 

0.617070 
.617194 
.617243 
.617258 

0.587392 
.590394 
.592029 
.592863 
.593262 

0.593427 
.593491 
.593510 

0.564895 
.567093 
.568214 
.568750 
.568971 

0.569057 
.569083 

0.541222 
.542759 
.543493 
.543796 
.543913 

0.543949 

0.516183 
.517212 
.517636 
.517799 
.517851 

0.489422 
.490030 
.490264 
.490338 

0.460562 
.460908 
.461018 

0.428172 
.428340 

10 
11 

82 
81 
80 

79 

78 
77 
76 
75 

18 

19 

20 

1.237891 
.237893 
.237893 

1.237893 
.237893 
.237892 
.237889 
.237886 

21 

1.236125 
.236127 

1.236127 
.236127 
.236127 
.236126 
.236123 

1.234265 

1.234266 
.234266 
.234266 
.234266 
.234265 

22 

1.232309 
.232310 
.232310 
.232310 
.232310 

23 

24 

1.230253 
.230254 
.230254 
.230254 

26 

1.223420 

1.228089 
.228090 
.228090 

1.225813 
.225814 

74 
73 
72 
71 
70 

1.223422 
.223422 
.223422 
.223422 
.223421 

1.225814 
.225814 
.225814 
.225813 
.225809 

1.228090 
.228090 
.228089 
.228086 
.228081 

1.230254 
.230253 
.230250 
.230246 
.230238 

1.232309 
.232306 
.232303 
.232295 

.232288 

1.234262 
.234259 
.234251 
.234245 
.234229 

1.236120 
.236112 
.236107 
.236091 
.236068 

1.237879 
.237874 
.237859 
.237837 
.237810 

74 
73 
72 
71 
70 

69 
68 
67 
66 
65 

1.223416 
.223411 
.223403 
.223392 
.223371 

1.225804 

.225796 
.225786 
.225766 
.225736 

1.228073 
.228064 
.228045 
.228016 
.227979 

1.230230 
.230212 
.230185 
.230150 
.230102 

1.232271 
.232245 
.232212 
.232167 
.232105 

1.234204 
.234173 
.234131 
.234073 
.233995 

1.236039 
.235999 
.235945 
.235871 
.235778 

1.237772 
.237721 
.237652 
.237564 
.237453 

69 
68 
67 
66 
65 

64 
63 
62 
61 
60 

1.223339 
.223297 
.223240 
.223161 
.223056 

1.225697 
.225643 
.225569 
.225470 
.225345 

1.227928 
.227859 
.227766 
.227648 
.227497 

1.230037 
.229950 
.229838 
.229696 
.229517 

1.232023 
.231918 
.231785 
.231616 
.231410 

1.233896 
.233771 
.233612 
.233418 
.233184 

1.235660 
.235510 
.235328 
.235108 
.234842 

1.237312 
.237140 
.236933 
.236683 
.236388 

64 
63 
62 
61 
60 

59 
58 
57 
56 
55 

1.222923 
.222751 
.222538 
.222275 
.221957 

1.225184 
.224982 
.224735 
.224436 

.224077 

1.227307 

.227074 
.226794 
.226455 
.226058 

1.229298 
.229034 
.228715 
.228342 

.227899 

1.231161 
.230862 
.230510 
.230093 
.229609 

1.232902 
.232571 
.232178 
.231723 
.231199 

1.234530 
.234160 
.233732 
.233238 
.232674 

1.236040 
.235636 
.235172 
.234641 
.234037 

59 
58 
57 
56 
55 

54 
53 
52 
51 
50 

1.221575 
.221125 

.220593 
.219975 
.219263 

1.223654 
.223154 
.222573 

.221904 
.221140 

1.225588 
.225041 
.224412 

.223694 

.222877 

1.227385 
.226794 

.226118 
.225350 

.224480 

1.229053 
.228417 
.227694 
.226877 
.225962 

1.230600 
.229920 
.229152 
.228290 
.227327 

1.232034 
.231311 
.230500 
.229593 
.228581 

1.233357 
.232593 
.231740 
.230787 
.229741 

54 
53 
52 
51 
50 

49 

48 
47 
46 
45 

1.218450 
.217526 
.216480 
.215309 
.213998 

1.220271 

.219288 
.218188 
.216956 
.215579 

1.221953 
.220919 
.219761 
.218467 
.217045 

1.223508 
.222420 
.221204 
.219867 
.218391 

1.224938 
.223795 
.222538 
.221151 
.219623 

1.226251 
.225070 
.223765 
.222329 
.220755 

1.227470 
.226242 
.224891 
.223412 
.221794 

1.228586 
.227315 
.225923 
.224401 
.222743 

49 
48 
47 
46 
45 

25 

24 

23 

22 

21 

20 

19 

18 

Continued  from  Page  *73. 


*82 


TABLE    XLYL 


LIFE  AND  TEMPORARY  ANNUITIES.      LOGARITHM  OF  THE   PRESENT  VALUE  OF   » 
ANNUAL  PAYMENTS  OF  1   AT  THE  BEGINNING  OF  EACH  YEAR. 

5  PER  CENT. 


Pay- 

ments. 

n. 

1 

;r=90 

91 

92 

93 

1   94 

95 

96 

97 

Pay- 
ments. 

0.397160 

0.368711|0.340242 

0.310847 

0.280937 

0.249611 

0.212464 

0.176638 

n. 
1 

0.000000 

0.000000  0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

2 

.214806 

.207072 

.198987 

.189664 

.179538 

.169142 

.152340 

.140179 

2 

3 

4 

5 
6 

7 
8 
9 

10 

.307656 
.353712 

0.377006 
.388464 
.393850 
.396046 
.396892 

0.397160 

.293579 
.334538 

0.354101 
.363173 
.366849 
.368262 
.368711 

.578635 
.314378 

0.330417 
.336984 
.339458 
.340242 

.261970 
.292583 

0.304829 
.309403 
.310847 

.244460 
.2^9086 

0.278110 
i  .280937 

.224344 
.243655 

0.249611 

.198721 
.212464 

.176638 

3 

90 

89 
88 
87 
86 
85 

84 

10 

11 

12 

1.249190 

1.249191 
.249191 
.249191 
.249190 

1   13 

1.245487 
.245488 
.245488 

1.24,'S488 

1.248018 
.248019 
.248019 
.248019 

14 

1.246787 
.246788 
.246788 
.246788 

1.246788 

15 

16 

1.244118 
.244119 

1.244119 

1.242680 
1.242682 

17 

1.241169 

.248019 
1.248018 

.249190 
1.2491S8 

83 

1.239571 

.241169 

.242682 

.244119'  .245488 

.246787 

.248016 

.249186 

83 

82 

.239572 

.241169 

.242682 

.244119 

;  .245487 

.246785 

.248014 

.249182 

82 

81 

.239572 

.241169 

.242682 

.244118 

1  .245485 

.246783 

.248010 

.249179!  81  1 

80 

.239572 

.241169 

.242681 

.244116!  .245482 

.246778 

.248007 

.249170 

80 

79 

1.239572 

1.241168 

1.242678 

1.244113 

1.245477 

1.246775'l.247997 

1.249156 

79 

78 

.239571 

.241165 

.242675 

.244107 

.245474 

.246764 

.247982 

.249139 

78 

77 

.239568 

.241162 

,242669 

.244104 

.245463 

.246749 

.247964 

.249115 

77 

76 

.239565 

.241156 

.242666 

.244092 

.245447 

.246729 

.247939 

.249083 

76 

75 

.239558 

.241152 

.242653 

.244075 

.245426 

.246703 

.247905 

.249041 

75 

74 

1.239554 

1.241139 

1.242635 

1.244053 

1.2453981.246667 

1.247860 

1.248986 

74 

73 

.239540 

.241119 

.242612 

.244023, 

.245360!  .246620 

.247802 

.248917 

73 

72 

.239519 

.241095 

.242580 

.243983; 

.245310 

.246558 

.247730 

.248827 

72 

71 

.239494 

.241061 

.242537 

.243930' 

.245244 

.246481 

.247633 

.248721 

71 

70 

.239458 

.241016 

.242481 

.243860' 

.245162 

.246379 

.247521 

.248591 

70 

69 

1.239410 

1.240955 

1.242406 

1.243773' 1.245055'l.246260'l.247383 

1.248433 

69 

68 

.239345 

.240877 

.242314 

.243660  .244928  .246113 

.247216 

.248250 

68 

67 

.239262 

.240779 

.242195 

.243525, 

.244773!  .245937 

.247023 

.248032 

67 

66 

.239158 

.240652 

.242051 

.243360i 

.2445861  .245732 

.246791 

.247781 

66 

65 

.239024 

.240500 

.241877 

.243163' 

.244368 

.245486 

.246525 

.247491 

65 

64 

1.238863 

1.240315 

1.241668 

1.242932 

1.244108 

1.245204 

1.246217 

1.247160 

64 

63 

.238667 

.240094 

.241422 

.242656! 

.243809 

.244878 

.245866 

.246782 

63 

62 

.238432 

.239832 

.241130 

.242338] 

.243463 

.244506 

.245466 

.246359 

62 

61 

.238154 

.239523 

.240792 

.2419721 

.243068 

.244082 

.245017 

.245882 

61 

60 

.237826 

.239164 

.240404 

.241553 

.242619 

.243606 

.244512 

.245352 

60 

59 

1.237445 

1.2387521.239959 

1.241076 

1.242114 

1.243070 

1.243950 

1.244761 

59 

58 

.237008 

.238281!  .239454 

. 240541 i 

.241546 

.242474 

.243322 

.244109 

58 

57 

.236508 

.237745'  .238886 

.239938 

.240914 

.241808 

.242632 

.243391 

57 

56 

.235939 

.237142!  .238247 

.239268 

.240207 

.241076 

.241871 

.242604 

56 

55 

.235299 

.236464  .237535 

.238518i 

.239431 

.240269 

.241035 

.241741 

55 

54 

1.234580 

1.2357081.236739 

1.237694' 

1.238575 

1.239383 

1.240120 

1.240799 

54 

53 

.233776 

.234863;  .235865 

.236786 

.237604 

.238411 

.239120 

.239775 

53 

52 

.232879 

.2339351  .234901 

.235787 

.236603 

.237350 

.238034 

.238662 

52 

51 

.231894 

.232912  .233840 

.234693 

.235477 

.236198 

.236853 

.237455 

51 

50 

.230807 

.231785|  .232679 

.233498 

.234254 

.234944 

.235572 

.236152 

50 

49 

1.229610 

1.2305521.231410 

1.232199 

1.232923 

1.233585 

1.234189 

1.234744 

49 

48 

.228301 

.229205  .230030 

.230785 

.231479 

.232116 

.232694 

.233225 

48 

47 

.226869 

.227738,  .228528 

.229252 

.229920 

.230528 

.231081 

.231588 

47 

46 

.225310 

.226142  .226899 

.227595 

.228232 

.228815 

.229342 

.229827 

46 

45 

.223614 

.224410 

.225138 

.225801 

.226412 

.226967 

.227472 

.227936 

45 

17 

16 

16 

14 

13 

12 

11 

10 

Continued  from  Page  *73. 


TABLE    XLYII. 


♦83 


LIFE  AND  TEMPORARY  ANNUITIES.      LOGARITHM  OP   THE  PRESENT  VALUE  OP  « 
ANNUAL  PAYMENTS  OF  1   AT  THE  BEGINNING  OP  EACH  YEAR. 


The  first  Value  under  the  Age  X  is 

A(l  +  aa,) 

for  the  whole  Life. 

6  PER  CENT. 

Pay. 

ments. 

n. 

1 

a;=10 

11 

13 

13 

14 

15 

16 

17 

Pay- 
ments. 

1.189964 

1.189103|l.  188192 

1.187336 

1.186301 

1.185130 

1.183972 

1.183755 

m. 

0.000000 

0.000000  0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

1 

2 

.387194 

.387188  .387185 

.387181 

.387174 

.387169 

.287165 

.387158 

2 

3 

.449596 

.449587  .449581 

.449571 

.449559 

.449549 

.449538 

.449534 

3 

4 

.560996 

.560984  .560972 

.560957 

.560939 

.560933 

.560907 

.560886 

4 

5 

0.644517 

0.644499  0.644483 

0. 644462 

0.  644439 

0.644419 

0.644395 

0.644366 

5 

6 

.710457 

.710435!  .710413 

.710387 

.710360 

.710332 

.710301 

.710364 

6 

7 

.764310 

.764383  .764356 

.764337 

.764193 

.764157 

.764119 

.764074 

7 

8 

.809356 

.809333  .809394 

.809357 

.809316 

.809174 

.809138 

.809075 

8 

9 

.847709 

.847674  .847637 

.847594 

.847546 

.847497 

.847444 

.847383 

9 

10 

0.880815 

0.880773  0.880731 

0.880683 

0.880637 

0.880573 

0.880511 

0.880439 

10 

11 

.909701 

.909654!  .909606 

.909550 

.909490 

.909436 

.909355 

.909277 

11 

12 

.935138 

.935076 

.935031 

.934960 

.934891 

.934819 

.934743 

.934650 

12 

13 

.957674 

.957615 

.957555 

.957486 

.957409 

.957331 

.957341 

.957143 

13 

14 

.977784 

.977731 

.977654 

.977577 

.977495 

.977404 

.977308 

.977197 

14 

15 

0.995818 

0.995747  0.995673 

0.995591 

0. 995496 

0.995400 

0.995393 

0.995171 

15 

16 

1.013057 

1.0119811.0119011.011807 

1.011708 

1.011603 

1.011483 

1.011349 

16 

17 

.036739 

.036656  .036565 

.036468 

.036359 

.026343 

.036113 

.035973 

17 

18 

.040054 

.039963 

.039869 

.039763 

.039643 

.039514 

.039378 

.039318 

18 

19 

.053165 

.053069 

.051966 

.051849 

.051719 

.051585 

.051431 

.051263 

19 

20 

1.063311 

1.063107 

1.0639951.063867! 

1.063733 

1.062581 

1.063430 

1.063335 

20 

21 

.073305 

.073193 

.073070 

.073939! 

.072788 

.073630 

.073453 

.072356 

21 

22 

.083549 

.083436 

.083300 

.083153 

.081995 

.081832 

.081635 

.081431 

22 

23 

.091036 

.090900 

.090759 

.090606 

.090434 

.090352 

.090047 

.089837 

23 

24 

.098818 

.098678 

.098533 

.098366 

.098185 

.097987 

.097776 

.097535 

24 

25 

1.105983 

1.105838 

1.105679 

1.105504 

1.105308 

1.105104 

1.104873 

1.104631 

25 

26 

.113585 

.113439 

.113361 

.113073 

.111871 

.111649 

.111407 

.111134 

26 

27 

.118671 

.118506 

.118337 

.118133 

.117914 

.117680  .117420 

.117139 

27 

28 

.134389 

.134113 

.133937 

.133716 

.133488 

.123338 

.133960 

.133656 

28 

29 

.139478 

.139395 

.139095 

.138875 

.138630 

.128363 

.128073 

.137751 

29 

30 

1.134377 

1.134081 

1.133873 

1.133637 

1.133376 

1.133097 

1.132791 

1.133449 

30 

31 

.138713 

.138509 

.138386 

.138035 

.137764 

.137470 

.137145 

.136787 

31 

32 

.143831 

.143604 

.143366 

.143105 

.141820 

.141508 

.141168 

.140788 

32 

33 

.146633 

.146391 

.146144 

.145870- 

.145568 

.145343 

.144881 

.144484 

33 

34 

.150141 

.149901 

.149640 

.149353 

.149036 

.148690 

.148313 

.147891 

34 

35 

1.153403 

1.153150 

1.153877 

1.153574' 

1.153240 

1.151880 

1.151479 

1.151038 

35 

36 

.156434 

.156160 

.155873 

.155554 

.155306 

.154833 

.154405 

.153943 

36 

37 

.159336 

.158948 

.158645 

.158313 

.157944 

.157545 

.157106  .156631 

37 

38 

.161831 

.161539 

.161313 

.1608631 

.160478 

.160058 

.159599  .159093 

38 

39 

.164334 

.163930 

.163587 

.163331 

.163817 

.163380 

.161900 

.161371 

39 

40 

1.166453 

1.166133 

1.165785 

1.165400 

1.164980 

1.1645331.164021 

1.163468 

40 

41 

.168514 

.168180 

.167815 

.167415 

.166977 

.166498 

.165975 

.165396 

41 

42 

.170433 

.170073 

.169694 

.169377 

.168818 

.168319 

.167771 

.167170 

42 

43 

.173188 

.171835 

.171430 

.170994 

.170515 

.169994 

.169435 

.168798 

43 

44 

.173833 

.173444 

.173033 

.173576 

.172077 
14 

.171537 

.170943 

.170390 

44 

10 

11 

13 

13 

15 

16 

17 

Cont 

maed  on  Page  93.                       -v.   ,^       n 

F( 

)EMULA, 

m+ar' 

)=A^ 

~^x^n^ 

:A^^-». 

Da;  Vpj^x 


*84 


TABLE    XLTII. 


LIFE  AND  TEMPORARY  ANNUITIES.     LOGARITHM    OF  THE    PRESENT    VALUE    OF  n 
ANNUAL  PAYMENTS  OF  1  AT  THE  BEGINNING  OF  EACH  YEAR. 

6  PER  CENT. 


Pay- 

a:=18 

19 

20 

21 

22 

23 

24 

25 

Pay- 
ments. 

n. 

1 

1.181467 

1.180102 

1.178657 

1.177130 

1.175513 

1.173803 

1.171993 

1.170082 

n. 

0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

1 

2 

.287151 

.287143 

.287133 

.287123 

.287113 

.287101 

.287088 

.287076 

2 

3 

.449510 

.449493 

.449474 

.449455 

.449433 

.449410 

.449385 

.449358 

3 

4 

.560863 

.560838 

.560809 

.560779 

.560748 

.560712 

.560672 

.560629 

4 

5 

0.644335 

0.644301 

0.644262 

0.644223 

0.644179 

0.644129 

0.644075 

0.644017 

5 

6 

.710235 

.710181 

.710134 

.710082 

.710025 

.709962 

.709894 

.709818 

6 

7 

.764026 

.763974 

.763914 

.763851 

.763781 

.763705 

.763620 

.763526 

7 

8 

.809019 

.808955 

.808885 

.808809 

.808727 

.808635 

.808533 

.808423 

8 

9 

.847316 

.847243 

.847160 

.847072 

.846975 

.846868 

.846750 

.846621 

9 

10 

0.880364 

0.880277 

0.880184 

0.880083 

0.879971 

0.879848 

0.879713 

0.879565 

10 

11 

.909188 

.909092 

.908986 

.908870 

.908745 

.908605 

.908452 

.908282 

11 

12 

.934553 

.934445 

.934325 

.934196 

.934055 

.933898 

.933724 

.933534 

12 

13 

.957033 

.956912 

.956779 

.956636 

.956478 

.956301 

.956109 

.955898 

13 

14 

.977076 

.976943 

.976797 

.976638 

.976462 

.976267 

.976055 

.975816 

14 

15 

0.995038 

0.994897 

0.994732 

0.994556 

0.994362 

0.994149 

0.993910 

0.993659 

15 

16 

1.011210 

1.011046 

1.010870 

1.010676 

1.010465 

1.010228 

1.009977 

1.009696 

16 

17 

.025811 

.025637 

.025443 

.025234 

.025001 

.024752 

.024472 

.024171 

17 

18 

.039048 

.038857 

.038649 

.038419 

.038174 

.037898 

.037600 

.037264 

18 

19 

.051076 

.050872 

.050644 

.050403 

.050133 

.049839 

.049508 

.049149 

19 

20 

1.062036 

1.061813 

1.061575 

1.061310 

1.061023 

1.060699 

1.060346 

1.059960 

20 

21 

.072039 

.071807 

.071546 

.071266 

.070950 

.070605 

.070227 

.069813 

21 

22 

.081196 

.080942 

.080667 

.080359 

.080023 

.079654 

.079251 

.078806 

22 

23 

.089580 

.089313 

.089012 

.088685 

.088327 

.087934 

.087501 

.087030 

23 

24 

.097276 

.096985 

.096665 

.096318 

.095937 

.095516 

.095058 

.094549 

24 

25 

1.104340 

1.104030 

1.103692 

1.103323 

1.102916 

1.102472 

1.101979 

1.101446 

25 

26 

.110835 

.110508 

.110149 

.109756 

.109327 

.108850 

.108334 

.107758 

26 

27 

.116815 

.116469 

.116087 

.115672 

.115213 

.114714 

.114157 

.113549 

27 

28 

.122323 

.121955 

.121553 

.121110 

.120629 

.120093 

.119506 

.118864 

28 

29 

.127397 

.127011 

.126582 

.126119 

.125603 

.125038 

.124419 

.123741 

29 

30 

1.132078 

1.131667 

1.131219 

1.130723 

1.130180 

1.129585 

1.128932 

1.128216 

30 

31 

.136393 

.135963 

.135484 

.134963 

.134392 

.133764 

.133076 

.132325 

31 

32 

.140376 

.139917 

.139415 

.138867 

.138265 

.137605 

.136884 

.136091 

32 

33 

.144045 

.143564 

.143037 

.142461 

.141828 

.141137 

.140376 

.139542 

33 

34 

.147432 

.146928 

.146373 

.145767 

.145106 

.144378 

.143578 

.142706 

34 

35 

1.150557 

1.150026 

1.149445 

1.148812 

1.148116 

1.147351 

1.146516 

1.145601 

35 

36 

.153436 

.152881 

.152275 

.151609 

1  .150878 

.150080 

.149205 

.148247 

36 

37 

.156092 

.155513 

.154875 

.154177 

.153415 

.152579 

.151664 

.150663 

37 

38 

.158540 

.157932 

.157264 

.156536 

.155739 

.154866 

.153910 

.152866 

38 

39 

.160792 

.160155 

.159459 

.158698 

157867 

.156955 

.155959 

.154871 

39 

40 

1.162862 

1.162199 

1.161472 

1.160679 

1.159811 

1.158861 

1.157824 

1.156690 

40 

41 

.164765 

.164073 

.163316 

.162489 

.161585 

.160598 

.159517 

.158343 

41 

42 

.166512 

.165791 

.165002 

.164141 

.163203 

.162174 

.161055 

.159825 

42 

43 

.168113 

.167362 

.166542 

.165649 

.164670 

.163606 

.162435 

.161174 

43 

44 

1 

.169577 

.168798 

.167947 

.167016 

.166005 

.164892 

.163692 

.162381 

44 

18 

19 

20 

21 

22 

23 

24 

25 

Continued  on  Page  *93. 


TABLE    XLTIL 


♦85 


LIFE  AND  TEMPORARY  ANNUITIES.       LOGARITHM  OP  THE    PRESENT  VALUE    OF  ft 
ANNUAL   PAYMENTS  OF  1   AT   THE  BEGINNING  OF  EACH  YEAR. 

6   PER   CENT. 


Pay- 

26 

27 

28 

29 

30 

31 

32 

33 

Pay- 

ments. 
Jl. 

ments.! 
ft. 

1.168055 

1.165920 

1.163661 

1.161274 

1.158757 

1.156097 

1.153290 

1.150327 

1 

0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

1 

2 

.287059 

.287043 

.287025 

.287002 

.286980 

.286955 

.286929 

.286899 

2 

3 

.449323 

.449290 

.449251 

.449207 

.449162 

.449113 

.449058 

.448997 

3 

4 

.560579 

.560526 

.560467 

.560401 

.560333 

.560256 

.560172 

.560076 

4 

5 

0.643948 

0.643876 

0.643796 

0.643708 

0.643614 

0.643509 

0.643393 

0.643263 

5 

6 

.709730 

.709639 

.709538 

.709425 

.709304 

.709170 

.709021 

.708858 

6 

7 

.763421 

.763309 

.763185 

.763046 

.762898 

.762733 

.762552 

.762350 

7 

8 

.808298 

.808165 

.808015 

.807851 

.807674 

.807478 

.807261 

.807023 

8 

9 

.846476 

.846318 

.846146 

.845954 

.845748 

.845518 

.845267 

.844989 

9 

10 

0.879396 

0.879218 

0.879018 

0.878800 

0.878561 

0.878299 

0.878010 

0.877689 

10 

11 

.908093 

.907889 

.907664 

.907415 

.907145 

.906855 

.906518 

.906156 

11 

12 

.933322 

.933094 

.932841 

.932561 

.932266 

.931923 

.931554 

.931148 

12 

13 

.955656 

.955408 

.955125 

.954822 

.954477 

.954104 

.953694 

.953242 

13 

14 

.975561 

.975279 

.974973 

.974624 

.974250 

.973838 

.973385 

.972884 

14 

15 

0.993372 

0.993068 

0.992720 

0.992342 

0.991932 

0.991480 

0.990980 

0.990433 

15 

16 

1.009388 

1.009044 

1.008669 

1.008257 

1.007809 

1.007313 

1.006770 

1.006170 

16 

17 

.023826 

.023456 

.023049 

.022602 

.032113 

.021575 

.020982 

.020330 

17 

18 

.036894 

.036494 

.036054 

.035568 

.035039 

.034454 

.033813 

.033107 

18 

19 

.048751 

.048320 

.047843 

.047324 

.046746 

.046117 

.045424 

.044661 

19 

20 

1.059533 

1.059067 

1.058559 

1.057989 

1.057375 

1.056696 

1.055949 

1.055129 

20 

21 

.069353 

.068858 

.068302 

.067698 

.067037 

.066307 

.065507 

.064628 

21  1 

22 

.078318 

.077778 

.077190 

.076542 

.075832 

.075053 

.074198 

.073257 

22 

23 

.086500 

.085936 

•.085301 

.084606 

.083850 

.083020 

.082105 

.081104 

23 

24 

.093996 

.093381 

.092708 

.091970 

.091166 

.090278 

.089309 

.088243 

24 

25 

1.100846 

1.100196 

1.099482 

1.098699 

1.097840 

1.096902 

1.095871 

1.094736 

25 

26 

.107124 

.106436 

.105679 

.104845 

.103939 

.102943 

.101846 

.100645 

26 

27 

.112880 

.112151 

.111346 

.110468 

.109508 

.108449 

.107291  .106024 

27 

28 

.118156 

.117383 

.116537 

.115607 

.114589 

.113472 

.112252 

.110912 

28 

29 

.122993 

.122180 

,121285 

.120301 

.119228 

.118053 

.116765 

.115353 

29 

30 

1.127430 

1.126571 

1.125625 

1.124591 

1.123462 

1.122224 

1.120868 

1.119385 

30 

31 

.131495 

.130588 

.129596 

.128508 

.127321 

.126019 

.124596 

.123040 

31 

32 

.135216 

.134267 

.133224 

.132081 

.130834 

.129469 

.127978 

.126346 

32 

33 

.138627 

.137629 

.136535 

.135336 

.134029 

.132601 

.131038 

.129332 

33 

34 

.141745 

.140700 

.139553 

.138298 

.136932 

.135436 

.133804 

.132022 

34 

35 

1.144595 

1.143500 

1.142301 

1.140990 

1.139561 

1.138000 

1.136297 

1.134440 

35 

36 

.147195 

.146052 

.144799 

.143430 

.141940 

.140313 

.138539 

.136607 

36 

37 

.149566 

.148372 

.147064 

.145639 

.144086 

.142393 

.140549 

.138540 

37 

38 

.151722 

.150476 

.149117 

.147622 

.146017 

.144258 

.142342 

.140261 

38 

39 

.153678 

.152385 

.150959 

. .149425 

.147749 

.145922 

.143939 

.141784 

39 

40 

1.155454 

1.154097 

1.152635 

1.151034 

1.149295 

1.147406 

1.145353 

1.143127 

40 

41 

.157046 

.155655 

.154131 

.152471 

.150674 

.148719 

.146600 

.144305 

41 

42 

.158496 

.157047 

.155467 

.153754 

.151895 

.149877 

.147695 

.145328 

42 

43 

.159791 

.158290 

.156661 

.154889 

.152970 

.150895 

.148644 

.146216 

43 

44 

.160948 

.159402 

.157717 

.155889 

.153917 

.151777 

.149470 

.146977 

44 

26 

27 

28 

29 

30 

31 

32 

33 

Continued  on  Page  *91. 


*86 


TABLE     XLYIL 


LIFE  AND  TEMPORARY  ANNUITIES.      LOGARITHM  OP  THE  PRESENT  VALUE   OF    n 
ANNUAL  PAYMENTS  OF  1   AT  THE  BEGINNING  OF  EACH  YEAR. 


XXXI  X 

6  PER  CENT. 

Pay- 
ments. 

n. 

a:=34 

35 

36 

37 

38 

39 

40 

41 

Pay- 
ments. 

1.1472001.143903 

1.140434 

1.136773  1 

1.132914 

1.128852 

1.124576 

1.120076 

n. 

1 

0.000000  0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

1 

2 

.286866 

.286826 

.286789 

.286747 

.286697 

.286643 

.286584 

.286522 

2 

3 

.448926 

.448850 

.448773 

.448684 

.448583 

.448475 

.448355 

.448225 

3 

4 

.559971 

.559856 

.559735 

.559598 

.559446 

.559279 

.559096 

.558898 

4 

5 

0.643122 

0.642965 

0,642799 

0.642614 

0.642406  0.642179 

0.641931 

0.641661 

5 

6 

.708676 

.708478 

.708266 

.708028 

.707762 

.707475 

.707159 

.706811 

6 

7 

.762130 

.761888 

.761626 

.761333 

.761011 

.760659 

.760269 

.759846 

7 

8 

.806761 

.806471 

.806158 

.805812 

.805429 

.805007,  .804546 

.804042 

8 

9 

.844681 

.844344 

.843980 

.843577; 

.843127 

.842638'  .842102 

.841512 

9 

10 

0.877337 

0.876951 

0.876533 

0.876067^ 

0.875554 

0.874994 

0.874376 

0.873702 

10 

11 

.905757 

.905320 

.904844 

.904318 

.903737 

.903101 

.902403 

.901637 

11 

12 

.930701 

.930209 

.929677 

.929086; 

.928434 

.927722! 

.926937 

.926080 

12 

13 

.952744 

.952199 

.951605 

.950947; 

.950224 

.949429  .948559 

.947603 

13 

14 

.972336 

.971733 

.971076 

.970351 

.969550 

.968675  .967712 

.966658 

14 

15 

0.989829 

0.989167' 

0.988446 

0.987648^ 

0.986771 

0.985809!o.  984754 

0.983601 

15 

16 

1.005511 

1.0047881.003999 

1.003129  1.002170 

1.001121i  .999973 

.998712 

16 

17 

.019614 

.018827j  .017970 

.017023 

.015983 

.0148461.013596 

1.012227 

17 

18 

.032330 

.031480!  .030550 

.029527 

.028403 

.027171;  .025819 

.024338 

18 

19 

.043824 

.0429051  .041903 

.040802 

.039589 

.038260  .036804 

.035217:  19 

1 

20 

1.054229 

1.0532421.052167 

1.050982 

1.049677 

1.0482511.046694 

1.044982 

20 

21 

.063663 

.062607J  .061453 

.060182 

.058786 

.0572651  .055591 

.053763 

21 

22 

.072227 

.071097!  .069863 

.068505 

.067020 

.065390  .063606 

.061657 

22 

23 

.080005 

.078799  .077483 

.076042 

.074455 

.072721 

.070825 

.068755 

23 

24 

.087072 

.085789  .084395 

.082858 

.081173 

.079334 

.077324 

.075128 

24 

25 

1.093493 

1.0921361.090654 

1.089024 

1.087241 

1.085295^1.083167 

1.080844'  25 

26 

.099333 

.097893 

.096322 

.094602 

.092718 

.090661 

.088414 

.085965  26 

27 

.104634 

.103112 

.101456 

.099641 

.097653  .095484 

.093119 

.090545  27 

28 

.109446 

.107843 

.106098 

.104185 

.102093  .099814 

.097332 

.094629  28 

29 

.113810 

.112125 

.110288 

.108278 

.106081  .103693 

.101091 

.098256  29 

30 

1.117764 

1.115993 

1.114065 

1.111956 

1.109658:1.107157 

1.104432 

1.101474  30 

31 

.121339 

.119482 

.117462 

.115258 

.112854]  .110238 

.107397 

.104311 

31 

32 

.124565!  .122622 

.120512 

.118210 

.115698 

.112974 

.110013 

.106807 

32 

33 

.127470 

.125442 

.123241 

.120837 

.118226 

.115389 

.112316 

.108990 

33 

34 

.130080 

.127967 

.125671 

.123175 

.120457 

.117516 

.114331 

.110885  34 

35 

1.132419 

1.130217 

1.127834 

1.125238 

1.122423 

1.119377 

1.116080 

1.112524  35 

36 

.134503 

.132220 

.129744 

.127057 

.124144 

.120994 

.117594 

.113929  36 

37 

.136359 

.133990 

.131429 

.128650 

.125639'  .122393 

.118892 

.115126 

37 

38 

.138000 

.135551 

.132904 

.130034 

.126934  .123593 

.119998 

.116131 

38 

39 

.139448 

.136919 

.134186 

.131233 

.128044 

.124616 

.120927 

.116975 

39 

40 

1.140717 

1.138107 

1.135297 

1.132261 

1.128991 

1.125476 

1.121707 

1.117669'  40 

41 

.141819 

.139137 

.136250 

.133138J  .129788 

.126197 

.122349 

.118236'  41 

42 

.142775 

.140021 

.137063 

.133877 

.130455 

.126791 

.122873 

.118690  42 

43 

.143595 

.140775 

.137748 

1  .134495 

.131005 

.127276 

.123293 

.119054;  43 

44 

.144295 

.141411 

.13832] 

.135004 

.131454 

.127665 

.123629 

.119335 

44 

34 

35 

36 

37 

38 

39    40 

41 

Continued  on  Page  *90. 


^87 


TABLE    XLYIL 


LIFE  AND  TEMPORARY  ANNUITIES.    LOGARITHM  OF    THE    PRESENT  VALUE    OF    »? 

ANNUAL  PAYMENTS  OF  1  AT  THE  BEGINNING  OF  EACH  YEAR. 

6  PER   CENT. 


Pay- 

42 

43 

44 

45 

46 

47 

48 

49 

Pay- 

ments. 

ments. 

1.115337 

1.110361 

1.1051241.099624 

1.093846 

1.087778 

1.081412 

1.074733 

1 

0.000000 

0.000000 

0.000000  0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

1 

2 

.286448 

.286374 

.286287'  .286192 

.286090 

.285975 

.285852 

.285715 

2 

3 

.448079 

.447923 

.447747  .447556 

.447345 

.447113 

.446859 

.446580 

3 

4 

.558674 

.558434 

.558166 

.557873 

.557551 

.557196 

.556808 

.556380 

4 

5 

0.641356 

0.641030 

0.640665:0.6402671 

0.639830 

0.639347 

0.638819 

0.638237 

5 

6 

.706426 

.706008 

.705544 

.705037 

.704479 

.703865 

.703191 

.702450 

6 

7 

.759374 

.758863 

.758296 

.757675 

.756992 

.756241 

.755417 

.754513 

7 

8 

.803481 

.802873 

.802198!  .801459 

.800647 

.799755 

.798777 

.797703 

8 

9 

.840861 

.840150 

.839364  .838504 

.837558 

.836521 

.835384 

.834132 

9 

10 

0.872953 

0.872139 

0.871238 

0.870252 

0.869171 

0.867982 

0.866678 

0.865245 

10 

11 

.900791 

.899867 

.898848 

.897735 

.896510 

.895165 

.893689 

.892073 

11 

12 

.925129 

.934095 

.922956 

.921708 

.920337 

.918829 

.917182 

.915374 

12 

13 

.946549 

.945402 

.944136 

.942749 

.941224 

.939566 

.937729 

.935723 

13 

14 

.965498 

.964231 

.962834 

.961303 

.959637 

.957791 

.955777 

.953571 

14 

15 

0.982327 

0.980937 

0.979405 

0.977741 

0.975899 

0.973886 

0.971685 

0.969273 

15 

16 

.997323 

.995806 

.994148 

.992319J 

.990321 

.988132 

.985737 

.983119 

16 

17 

L010718 

1.009083 

1.007271 

1.0052951 

1.003131 

1.000761 

.998173  .995338 

17 

18 

.022718 

.020938 

.018988 

.016856 

.014523 

.011972 

1.0091801.006134 

18 

19 

.033462 

.031552 

.029455 

.027166 

.024662 

.021920 

.018931 

.015668 

19 

20 

1.043104 

1.041056 

1.038813 

1.036362 

1.033679 

1.030753 

1.027562 

1.024079 

20 

21 

.051756 

.049571 

.047176 

.044558 

.041702 

.038587 

.035190 

.031487 

21 

22 

.059522 

.057194 

.054643 

.051863 

.048831 

.045523 

.041920 

.037999 

22 

23 

.066485 

.064012 

.061308 

.058363 

.055151 

.051651 

.047845 

.043706 

23 

24 

.072723 

.070106 

.067248 

.064135 

.060743 

.057053 

.053044 

.048690 

24 

25 

1.078304 

1.075544 

1.072529 

1.069247 

1.065678 

1.061798 

1.057589 

1.053028 

25 

26 

,083291 

.080384 

.077210 

.0737641 

.070017 

.065951 

.061548 

.056778 

26 

27 

.087734 

.084677 

.081351 

.077738 

.073818 

.069572 

.064975 

.060005 

27 

28 

.091677 

.088479 

.084996 

.081222 

.077135 

.072708 

.067924 

.062764 

28 

29 

.095172 

.091828 

.088196 

.084265 

.080009 

.075408 

.070448 

.065105 

29 

30 

1.098253 

1.094769 

1.090991 

1.086903 

1.082485 

1.077721 

1.072591 

1.067073 

30 

31 

.100961 

.097341 

.093415i  .0891771 

.084607 

.079685 

.074393 

.068713 

31 

32 

.103329 

.099572 

.095506 

.091126 

.086410 

.081337 

.075895 

.070066 

32 

33 

.105383 

.101497 

.097299 

.092784 

.087927 

.082715 

.077134 

.071165 

33 

34 

.107159 

.103148 

.098825 

.094179 

.089193 

.083851 

.078141 

.072049 

34 

35 

1.108682 

1.104554 

1.100109 

1.095342 

1.090236 

1.084776 

1.078952 

1.072752 

35 

36 

.109978 

.105733 

.101180 

.096302 

.091086 

.085520 

.079596 

.073298 

36 

37 

.111066 

.106724 

.102064 

.097084 

.091770 

.086111 

.^80097 

.073718 

37 

38 

.111980 

.107539 

.102784 

.097713 

.092313 

.086571 

.080481 

.074032 

38 

39 

.112732 

.108203 

.103363 

.098213 

.092736 

.086923 

.080770 

.074263 

39 

40 

1.113345 

1.108737 

1.103824 

1.098602 

1.093059 

1.087189 

1.080982 

1.074429 

40 

41 

.113838 

.109162 

.104182 

.098899 

.093304 

.087383 

.081133 

.074544 

41 

42 

.114231 

.109492 

.104456 

.099125 

.093482 

.087522 

.081239 

.074622 

42 

43 

.114535 

.109745 

.104664 

.099289 

.093610 

.087620 

.081311 

.074669 

43 

44 

.114769  .109937 

,104815 

.099407 

.093700 

.087686 

.081353 

.074698 

44 

42 

43    44 

45 

46 

47 

48 

49 

Cont 

inued  on  F 

•age  *89. 

*88 


TABLE     XLYII. 


LIFE  AND  TEMPORARY  ANNUITIES.      LOGARITHM    OF    THE  PRESENT  VALUE  OF   n 

ANNUAL  PAYMENTS  OF  1  AT  THE  BEGINNING  OF  EACH  YEAR. 

6  PER  CENT. 


Pay- 

x=50 

51 

52 

53. 

54 

55 

56 

57 

Pay. 

ments. 
n. 

ments. 

1.067728 

1.060389 

1.052701 

1.0446521 

1.036227 

1.027411 

1.018200 

1.008575 

n. 

1 

0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

o.ocooco'    1 

2 

.285563 

.285397 

.285214 

.285015 

.284796 

.284553  .284288 

.283991   2 

3 

.446270 

.445932 

.445561 

.445155 

.444709 

.444213  .443670 

.443073   3 

4 

.555907 

.555391 

.554825 

.554205 

.553521 

.552763  .551937 

.551026|   4 

5 

0.637596 

0.636896 

0.636128 

0.635284 

0.634353 

0.633329  0.632207 

0.630974'  5 

6 

.701636 

.700745 

.699766 

.6986881 

.697509 

.696206 

.694781 

.693215   6 

7 

.753519 

.752429 

.751230 

.749920 

.748476 

.746889 

.745152 

.743244   7 

8 

.796521 

.795225 

.793807 

.7922491 

.790537 

.788657 

.786599 

.784343   8 

9 

.832757 

.831254 

.829604 

.827793: 

.825807 

.823625 

.821241 

.818624|  9 

10 

0.863674 

0.861954 

0.860066 

0.857998 

0.855728 

0.853240 

0.850518 

0.847537 

10 

11 

.890299 

.888355 

.886225 

.883890 

.881334 

.878529 

.875466 

.872112 

11 

12 

.913389 

.911218 

.908838 

.906235 

.903382 

.900259 

.896847 

.893117 

12 

13 

.933525 

.931119 

.928488 

.925607 

.922457 

.919007 

.915244 

.9111321  13 

14 

.951153 

.948512 

.945620 

.942461 

.939005 

.935228 

.931109 

.9266151  14 

15 

0.966634 

0.963748 

0.960596 

0.957152 

0.953390 

0.949281 

0. 944806 

0.939930  15 

16 

.980250 

.977121 

.973703 

.969973; 

.965901 

.961460 

.956629 

.951371!  16 

17 

.992243 

.988866 

.985180 

.981160; 

.976779 

.972006 

.966820 

.9611861  17 

18 

1.002807 

.999179 

.995223 

.990914 

.986224 

.981121 

.975587 

.969579'  18 

19 

.012106 

1.008226 

1.004001 

.9994051 

.994408 

.988981 

.983100 

.976731J  19 

20 

1.020281 

1.016150 

1.011657 

1.006776' 

1.001478 

0.995729 

0.989513 

0. 9827921  20 

21 

.027455 

.023074 

.018316 

.013155 

.007558 

1.001499 

.994957 

.987898  21 

22 

.033734 

.029106 

.024088 

.018649 

.012764 

.006404 

.999550 

.992168  22 

23 

.039211 

.034342 

.029065 

.023359 

.017195 

.010546 

1.003394 

.9957071  23  ' 

24 

.043972 

.038862 

.033336 

.027372 

.020941 

.014017 

.006583 

.998615 

24 

25 

1.048085 

1.042744 

1.036979 

1.030767 

1.024082 

1.016898 

1.009206 

1.000974 

25 

26 

.051621 

.046058 

.040064 

.033617 

.026692 

.019269 

.011334 

.002867 

26 

27 

.054642 

.048867 

.042655 

.035986 

.028841 

.021194 

.013043 

.004363 

27 

28 

.057204 

.051227 

.044810 

.037938 

.030585 

.022741 

.014394 

.005528;  28  | 

29 

.059357 

.053191 

.046586 

.0395221 

.031988 

.023964 

.015447 

.006418 

29 

30 

1.061150 

1.054810 

1.048028 

1.040797 

1.033098 

1.024917 

1.016251 

1.007085 

30 

31 

.062629 

.056125 

.049189 

.041806 

.033963 

.025645 

.016853 

.007576 

31 

32 

.063830 

.057183 

.050108 

.042593 

.034624 

.026191 

.017297 

.007928 

32 

33 

.064797 

.058022 

.050824 

.043194 

.035119 

.026593 

.017616 

.008173 

33 

34 

.065564 

.058675 

.051372 

.043644 

.035484 

.026882 

.017837 

.008336 

34 

35 

1.066161 

1.059176 

1.051783 

1.043976 

1.035746 

1.027082 

1.017985 

1.008440l  35 

36 

.066619 

.059551 

.052085 

.044215 

.035928 

.027216 

.018079 

.008503  36 

37 

.066962 

.059827 

.052302 

.044380 

.036049 

.027301 

.018135 

.008539  37 

38 

.0Q7214 

.060025 

.052453 

.044490 

.036127 

.027352 

.018169 

.008558;  38 

39 

.067395 

.060163 

.052554 

.044561 

.036173 

.027383 

.018185 

.008567;  39 

40 

1.067521 

1.060255 

1.052618 

1.044603 

1.036201 

1.027397 

1.018193 

1.008572'  40 

41 

.067606 

.060313 

.052656 

.044629' 

.036214 

.027404 

.018198 

.008575  41 

42 

.067658 

.060348 

.052680 

.044641 

.036220 

.027409 

.018200 

.0085751  42 

43 

.067690 

.060370 

.052691 

.0446461 

.036225 

.027410 

.018200 

.008575  43 

44 

.067710 

.060380 

.052695 

.0446511 

.036226 

.027410 

.018200 

44 

1 

45 

1.067719 

1.060383 

1.052700 

1.044652 

1.036226 

1.027411 

45 

46 

.067722 

.060388 

.052701 

.044652 

.036227 

46 

47 

.067727 

.060389 

.052701 

47 

48 

.067728 

.060389 

48 

49 

.067728 

49 

50 

51 

52 

53 

54 

55 

56 

57 

TABLE    XLYII. 


*89 


LIFE  AND  TEMPORARY  ANNUITIES.     LOGARITHM   OF  THE    PRESENT    VALUE    OF  W 

ANNUAL  PAYMENTS  OF  1   AT  THE  BEGINNINe  OF  EACH  YEAR.  ^ 

6  PER  CENT. 


Pay- 

ments. 

n. 

58 

59 

60 

61 

62 

63 

64 

65 

Pay- 

ments. 

0.998532 

0.988049 

0.977114 

0.965719 

0.953857 

0.941502 

0,928659 

0.915312 

7i. 

1 
2 
3 

4 

0.000000 
.283673 
.442422 
.550033 

0.000000 
.283321 
.441706 
.548939 

0.000000 
.282933 
.440916 
.547736 

0.000000 
.282505 
.440049 
.546419 

0. 000000 
.282040 
.439104 
.544975 

0.000000 
.281525 
.438057 
.543385 

0.000000 
.280960 
.436911 
.541642 

0.000000 
.280338 
.435652 
.539730 

1 

2 
3 

4 

5 
6 

7 
8 
9 

0.629627 
.691504 
.741161 

.781875 
.815767 

0.628145 
.689626 

.738873 
.779171 
.812635 

0.626519 
.687562 
.736365 
.776205 

.809208 

0.  624735 
.685303 
.733616 

.772962 
.805460 

0.  622783 
.682828 
.730611 
.769416 
.801368 

0.620634 
.680110 
.727313 
.765533 
.796893 

0.618282 
.677137 
.723711 
.761293 
.792012 

0.615705 
.673883 

.719772 
.756662 
.786688 

5 
6 

7 
8 
9 

10 
11 
12 
13 
14 

0.844280 
.868454 
.889049 
.906654 
.921727 

0.840718 
.864452 
.884607 
.901771 
.916400 

0.836820 
.860080 
.879762 
.896447 
.910605 

0.832563 
.855314! 

.874480' 
.890658 
.904312 

0.827923 
.850119 

.868737 
.884370 
.897487 

0.822851 
.844455 
.862484 
.877535 
.890083 

0.817329 
.838297 
.855695 
.870129 

.882077 

0.811318 
.831601 
.848329 
.862111 
.873430 

10 
11 
12 
13 
14 

15 
16 
17 
18 
19 

0.934630 
.945665 
.955078 
.963081 
.969852 

0.928866 
.939468 
.948458 
.956050 
.962422 

0.922604 
.932748 
.941293 
.948452 
.954415 

0.915815 
.925476 
.933552 
.940266 
.945802 

0.908466 
.917619 
.925210 
.931459 
.936563 

0.900511 
.909135 
.916220 
.921996 
.926654 

0. 891928 
.900000 
.906567 
.911854 
.916073 

0.882677 
.890181 
.896212 
.901017 
.904792 

15 
16 
17 
18 
19 

20 
21 
22 
23 
24 

0.975546 

.980303 
.984242 
.987476 
.990096 

0.967739 
.972136 
.975742 
.978662 
.981004 

0.959340 
.963374 
.966638 
.969254 
.971319 

0.950331 
.953992 
.956924 
.959236 
.961032 

0.940684 
.943982 
.946579 
.948596 
.950137 

0. 930376 
.933306 
.935580 
.937315 
.938615 

0.919392 
.921966 
.923927 
.925396 
.926471 

0.907716 
.909944 
.911611 
.912831 
.913705 

20 
21 
22 
23 
24 

25 
26 
27 
28 
29 

0.992199 
.993860 
.995153 
.996140 
.996880 

0.982853 
.984291 
.985389 
.986213 
.986818 

0.972923 
.974149 
.975068 
.975742 
.976225 

0.962404 
.963432 
.964185 
.964726 
.965103 

0.951291 
.952135 
.952742 
.953165 
.953445 

0.939565 
.940248 
.940724 
.941040 
.941241 

0.927242 
.927780 
.928137 
.928364 
.928501 

0.914315 
.914720 
.914978 
.915133 
.915222 

25 
26 
27 
28 
29 

30 
31 
32 
33 

34 

0.997425 
.997815 

.998087 
.998266 
.998383 

0.987252 
.987555 

.987754 
.987883 
.988028 

0.976563 
.976785 
.976929 
.977091 
.977065 

0.965352 
.965512 
.965694 
.965665 
.965681 

0. 953624 
.953828 
.953795 
.953813 
.953843 

0.9414710.928580 
.941433  .928623 
.941454  .928641 
.941487  .928655 
.941499  .928660 

0.915271 
.915292 
.915307 
.915313 
.915313 

30 
31 
32 
33 
34 

35 
36 
37 
38 
39 

40 

41 

42 

51 
50 

0.998513 
.998492 
.998503 
.998523 
.998529 

0.998532 
.998532 
.998532 

0.988005 
.988017 
.988039 
.988046 
.988049 

0.988049 
988049 

0.977079 
.977103 
.977111 
.977114 
.977114 

0.977114 

0:965708 
.965717 
.965720 
.965720 
.965719 

0.953853 
.953857 
.953857 
.953857 

0.9415030.928660 

0.915312 

35 

58 
67 
56 
55 

54 
53 
52 
51 
50 

.941503' 
.941502 

.928659 

42 

43 

44 

1.115337 
.115337 
.115337 
.115337 

1.115333 
.115333 
.115328 
.115317 
.115302 

45 

1  OQQfi'Pl 

1.110361 
.110361 
.110361 

1.110361 
.110,357 

46 

1.105124 
,105124 

1.105124 
.105124 

48 

47 

1.093846 
.093846 
.093846 
.093845 
.093841 

1.099624 
.099624 
.099623 
.099619 
.099619 

49 

1.087778 
.087778 
.087778 
.087777 

1.081412 
.081412 
.081412 

.105120'  110.S57 

1.074733 
.074733 

.105120 
.105113 

.110351 
.110340 

49 

48 
47 
46 
45 

1.074733 
.074732 

.074727 
.074725 
.074716 

1.081411 
.081406 
.081405 
.081396 
.081380 

1.087773 
.087772 
.087764 
.087749 

.087725 

1.093840 
.093833 
.093819 
.093797 
.093761 

46 

1.099612 
.099599 
.099579 
.099546 
.099490 

1.105101 
.105083 
.105053 
.105001 
.104924 

1.110323 
.110296 
.110248 
.110176 
.110076 

1.115277 
.115233 
.115167 
.115074 
.114946 

42 

49 
48 
47 
46 
45 

49 

48 

47 

46 

44 

43 

Continued  from  Page  *87. 


*90 


TABLE    XLYII. 


LIFE  AND  TEMPORARY  ANNUITIES.     LOGARITHM    OF  THE    PRESENT  VALUE  OF 
ANNUAL  PAYMENTS  OF  1  AT  THE  BEGINNING  OF  EACH  YEAR. 

6  PER  CENT. 


n 


Pay- 
ments. 

n. 

a:  =  66 

67 

68 

69 

70 

0.840762 

71 

72 

73 

Pay- 
ments. 

0.901459 

0.887078 

0,872181 

0.856733 

0.824241 

0.807180 

0.789571 

n. 
1 

1 

0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

2 

.279660 

.278908 

.278097 

.277190 

.276207 

.275121 

.273936 

.272640 

2 

3 

.434275' 

.432761 

.431109 

.429283 

.427295 

.425110 

.422726 

.420111 

3 

4 

.537641 

.535345 

.532840 

.530080 

.527074 

.523780 

.520183 

.516248 

4 

5 

0.612888 

0.609799  0.606427 

0.602724 

0.598694 

0.594284 

0.589474 

0.584227 

5 

6 

.670330 

.666436  .662192 

.657542 

.652485 

.646959 

.640949 

.634404 

6 

7 

.715472 

.710770  .705653 

.700056 

.693975 

.687351 

.680156 

.672342 

7 

8 

.751614 

.746106 

.740116 

.733580 

.726492 

.718788 

.710440 

.701403 

8 

9 

.780896 

.774584 

.767731 

.760272 

.752199 

.743446 

.733991 

.723764 

9 

10 

0.804784 

0.797679 

0.789981 

0.781623 

0.772595 

0. 762839 

0.752312 

0.741000 

10 

11 

.824339 

.816459 

.807939 

.798712 

.788774 

.778052 

.766548 

.754203 

11 

12 

.840356 

.831725 

.822413 

.812359 

.801549 

.789946 

.777520 

.764238 

12 

13 

.853450 

.844096 

.834033 

.823190 

.811586 

.799157 

.785895 

.771776 

13 

14 

.864109 

.854071 

.843293 

.831734 

.819388 

.806213 

.792208 

.777355 

14 

15 

0.872733 

0.862047 

0.850622 

0.838395 

0.825383 

0.811546 

0.796892 

0.781410 

15 

16 

.879649 

.868376 

.856350 

.843526 

.829923 

.815510 

.800302 

.784295 

16 

17 

.885148 

.873334 

.860770 

.847417 

.833302 

.818401 

.802731 

.786299 

17 

18 

.889463 

.877164 

.864127 

.850318 

.835770 

.820462 

.804421 

.787631 

18 

19 

.892801 

.880078 

.866633 

.852439 

.837531 

.821896 

.805544 

.788473 

19 

20 

0.895343 

0.882254 

0.868466 

0.853952 

0.838757 

0.822850 

0.806255 

0.788982 

20 

21 

.897243 

.883846 

.869774 

.855007 

.839572 

.823454 

.806684 

.789275 

21 

22 

.898633 

.884984 

.870687 

.855708 

.840090 

.823819 

.806931 

.789433 

22 

23 

.899628 

.885779 

.871294 

.856154 

.840402 

.824029 

.807065 

.789500 

23 

24 

.900323 

.886307 

.871680 

.856423 

.840581 

.824143 

.807122 

.789552 

24 

25 

0,900785 

0.886643 

0.871912 

0.856577 

0.840678 

0.824191 

0.807165 

0.789568 

25 

26 

.901078 

.886844 

.872046 

.856660 

.840720 

.824228 

.807179 

.789573 

26 

27 
28 
29 

30 
31 
32 
33 

.901254 
.901356 
.901412 

.886961 
.887024 
.887052 

.872118 
.872150 

.872172 

0.872181 

.872182 
.872181 

.856697 
.856723 

.840751 
.840762 

.824240 
.824243 

.807183 
.807180 

.789571 

27 

34 

.856733 

0.856734 
.856733 

.840764 
0.840762 

.824241 

35 

66 
65 

64 
63 

0.901436  0.887Q71 
.901453  .887079 
.901460  .887079 
.901460  .887078 

36 

1.147200 
.147198 

1.147198 
.147198 

37 

1.140434 
.140433 

1.143903 

1.143902 
.143902 

38 

1.136773 

34 

.901459 

40 

39 

1.132914 

.136773 
.136773 

.140433 
.140433 

.143902 
143901 

.147197 
.147197 

62 
61 

41 

1.128852 

.132913 

1.124576 

.128851 

.132913 

.136773 

.140432 

143901 

147195 

fin 

59 

1.120076 

1.124575 

1.128851 

1.132913 

1.136771 

1.140432 

1.143898 

1.147188  59 

58 

120076 

.124575 

.128851 

.132911 

.136771 

.140428 

.143891 

.147181 

58 

57 

.120076 

.124575 

.128849 

.132911 

.136767 

.140421 

.143883 

.147167 

57 

56 

.120076 

.124572 

.128849 

.132907 

.136760 

.140412 

.143868 

.147142 

56 

65 

.120073 

.124572 

.128844 

.132899 

.136750 

.140397 

.143842 

.147107 

55 

54 

1. 120073 

1.124567 

1.128836 

1.132888 

1.136733 

1.140368 

1.143804 

1.147056 

54 

53 

.120068 

.124558 

.128824 

.132870 

.136702 

.140327 

.143749 

.146987 

53 

52 

.120058 

.124545 

.128804 

.132837 

.136658 

.140268 

.143675 

.146891 

52 

51 

.120044 

.124524 

.128769 

.132790 

.136594 

.140189 

.143570 

.146765 

51 

50 

.120021 

.124486 

.128718 

.132720 

.136509 

.140075 

.143435 

.146599 

50 

49 

1.1199801.124430 

1.128643 

1.132628 

1.136386 

1.139929 

1.143257 

1.146385 

49 

48 

.119919  .124350 

.128543 

.132496 

.136228 

.139737 

.143026 

.146119 

48 

47 

.119833  .124241 

.128401 

.132325 

.136022 

.139489 

.142739 

.145786 

47 

46 

.119715 

.124089 

.128216 

.132103 

.135754 

.139179 

.142381 

.145379 

46 

45 

.119551 

.123889 

.127976 

.131814 

.135420 

.138793 

.141943 

.144886 

45 

41 

40 

39 

38 

37 

36 

36 

34 

Continued  from  Page  *86. 


TABLE    XLYII. 


*91 


LIFE  AND  TEMPORAKY  ANNUITIES.      LOGARITHM  OP  THE  PRESENT  VALUE  OF    fl 
ANNUAL  PAYMENTS  OF  1  AT  THE  BEGINNING  OF  EACH  YEAR. 

6  PER  CENT. 


Pay-  I 
meuts. 


74 


75 


76 


n.    0.771402  0.7527110.733470 


2 
3 

4 

5 
6 

7 
8 
9 

10 
11 
12 
13 
14 

15 
16 
17 
18 
19 

20 
21 
22 
23 
24 

25 
26 


67 
66 
65 

64 
63 
62 
61 
60 

59 
58 
57 
56 
55 

54 
53 
52 
51 
50 

49 

48 
47 
46 
45 


1  :o.  000000 


.271204 
.417238 
.511942 

0.578498 
.627277 
.663864 
.691612 
.712756 

0.728834 
.740985 
.750074 
.756780 
.761642 

0.765097 
.767494 
.769086 
.770092 
.770700 

0.771049 
.771239 
.771319 

.771380 
.771400 


0.000000 
.269646 
,414120 
.507265 

0.572282 
.619569 
.654696 
.681078 
.700933 

0.715826 
.726906 
.735048 
.740935 
.745110 


0.000000 
.267945 
.410707 
.502157 

0.565525 
.611186 
.644789 
.669724 
.688242 

0.701919 
.711919 
.719124 
.724219 

.727744 


0.748002  0.730080 
.749922  .731553 
.751134  .732443 


.751866 

.752287 

0.752515 
.752611 

.752684 
.752708 
.752716 


.732955 
.733232 

0.733348 
.733437 
.733466 
.733476 
.733470 


0.771406  0.752711 
.771402 


33 


32 


1.153290 
1.1503271  .153289 


,150325 
.150325 


.153289 
.153289 


1.1503251.153288 
.150324  .153288 
.150324  .153286 
.150322  .153279 
.150315  .153274 

1.1503091.153262 
.150296|  .153240 
.150273  .153209 
.150240  .153166 
.150193  .r53106 

1.150129,1.153023 
.150039  .152914 
.149922  .152770 
.149769  .152585 
,149569  .152357 

1.1493221.152069 
.149013  .151717 
.148634  .151292 
.148177  .150782 
.147628  .150177 


33 


32 


0.000000 
266064 
406961 
496577 

0.558147 
.602107 
.634083 
.657506 
.674642 

0. 687086 
.696009 
.702298 
.706638 
.709510 

0.711320 
. 712413 
.713040 
.713380 
.713523 


31 


1.156097 
.156096 
.156096 
.156096 
.156095 

1.156095 
.156093 
.156087 
.156082 
.156071 

1.156051 
.156022 
.155982 
.155926 
.155849 

.155747 
.155614 
.155441 
.155229 
.154962 


154634 
154239 
153765 
153202 
152545 

31 


77 


0.713672 


713632 
713667 
713679 
713672 


30 


1.158757 

1.158755 
.158755 
.158755 
.158754 
.158754 

1.158752 
.158747 
.158742 
.158732 
.158714 

1.158686 
.158649 
.158597 
.158525 
.158431 


1. 


158307 
158146: 
157949 
157700 
157395; 

157027 
156586 
156063 
155452 
154737 


30 


78 


0.693356 


0.000000 
.264019 
.402891 
.490520 

0.550179 
.592309 
.622576 
.644426 
.660148 

0.671351 
.679211 
.684619 
.688190 
.690438 

0.691795 
.692572 
.692994 
.693171 
.693306 

0.693350 
.693365 
.693356 


29 


1.161274 
.161272 

1.161272 
.161272 
.161271 
.161271 
.161269 

1.161265 
.161260 
.161251 
.161234 
.161208 

1.161173 
.161125 
.161058 
.160971 
.160855 


,160705 
,160522 
,160290 
,160006 
,159664 

.159254 
.158766 
.158198 
.157533 
.156769 


29 


79 


0.672502 


80 


0.651114 


0.000000  0.000000 
.261782  .259335 
.398447  .393621 
.483943  .476798 

0.541542  0.532205 
.581737  .570351 
.610209  .596956 
.630436  .615521 
.644724  .628364 

0.654689  0.637113 
.661516  .642856 
.666013  .646457 
.668840  .648623 
.670543  .649863 

0.671518  0.650536 
.672048  .650818 
.672270  .651035 
.672440  .651104 
.672495  .651128 

0.672514  0.651114 
.672502 


81 


0.629190 


0.000000 
.256690 
.388367 
.469061 

0.522129 
.558124 
.582800 
.599672 
.611079 

0.618529 
.623185 
.625980 

.627578 
.628445 

0.628809 
.629089 
.629177 
.629208 
.629190 


28 


1.163661 
.163659 
.163659 

1.163659 
.163658 
.163658 
.163657 


27 


26 


1.168055 
.168054 
.168054 


1.165920 
.165918 
.165918  ,168054 
.165918  .168053 


1.165917 

.165917 

.165916 

.165912 

.163653:  .165908 

1.163648ll. 165900 
.163640  .165885 


.163624 
.163599 
.163566 

1.163522 
.163459 
.163378 
.163271 
.163131 

1.162961 
.162744 
.162480 
.162162 
.161780 

1.161326 
.160797 
.160177 
.159467 
.158647 


28 


.165862 
.165831 
.165790 

1.165732 
.165656 
.165557 
.165431 
.165268 

1.165066 
.164820 
.164523 
.164167 
.163745 


163252 
162674 
162013 
161250 
160385 


27 


1.168053 
.168052 
.168049 
.168045 
.168037 

1.168024 
.168002 
.167973 
.167935 
.167881 

1.167810 
.167718 
.167600 
.167448 
.167260 

1.167031 
.166754 
.166422 
.166029 
.165570 

1.165031 
.164416 
.163705 
.162899 
.161983 


26 


Pay- 
ments, 

n. 


1 
2 
3 
4 

5 
6 
7 
8 
9 

10 
11 
12 
13 
14 

15 
16 
17 
18 
19 


74 
73 
72 
71 
70 

69 
68 
67 
66 
65 

64 
63 
62 
61 
60 

59 
58 
57 
56 
55 

54 
53 
52 
51 
50 

49 
48 
47 
46 
45 


Continued  from  Page  *85. 


*9$ 


TABLE    XLYIl 


LIFE  AND  TEMPOKARY  ANNUITIES.      LOGARITHM  OF   THE  PRESENT   VALUE   OP  n 
ANNUAL  PAYMENTS  OF  1   AT  THE  BEGINNING   OF  EACH  YEAR. 

6  PER  CENT. 


Pay    a:=82 

ments.  

n.     0.606694 


83 


1 
2 
3 

4 

5 
6 
7 
8 
9 

10 
11 
12 
13 

14 

15 
16 

17 
18 


75 

74 
73 
72 
71 
70 


52 
51 
50 

49 
48 
47 
46 
45 


0.583647 


84 


0.559909 


85 


0.535453 


o.oooooolo.oooooo 

.253744  .350591 
.382611  .376412 
.460632  .451581 

0.511220,0.499566 
.544974  .530980 
.567662  .551649 
.582833  .564914 
.592671  .573117 

0.598793  0.578007 
602457  .580794 
604549  .582302 


.605683 
.606159 

0.606526 
.606640 
.606681 
.606694 


25 


1.170082 


.582934 
.583423 

0.583574 
.583629 
.583647 


24 


1.171993 
.171993 


1.1700801.171993 
I7OO8O;  .171993 
170080  .171992 


.170079 
.170079 


.171992 
.171991 


69    1.1700781.171988 


.000000 
.247111 
.369650 
.441793 

.487020 
.516032 
.534368 
.545601 
.552261 

.556044 
.558089 
.558944 
.559606 
.559810 

.559885 
.559909 


0.000000 
.243358 
.362393 
.431288 

0.473656 
.499792 
.515579 
.524861 
.530109 

0.532939: 
534121 
535035 
535316 
535420! 

0.535453 


23 


.173803 
,173802 
.173802 

1.173802 
.173802 
.173802 
.173801 
.173798 


22 


68 
67 
66 
65 

64 
63 
62 
61 
60 

59 
58 
57 
56 
55 

54  1.168868 
53   .168558 


.1700751  .171984 
.170071  .171978 
.170064  .171967 
.170052  .171947 

1.170031 
.170004 
.169968 
.169918 
.169852 


1.175513 
.175512 
.175512 
.175512 

1.175512 
.175512 
.175512 
.175509 
.175505 

1.1737941.175499' 


86 


0.510023 


0.000000 
.239313 
.354522 
.420014 

0.458801 
.481703 
.494998 
.502462 
.506472 


87 


0.483173 


88 


0.454503 


89 


0.422455 


0. 000000  0. 000000  0. 000000 
.234793!  .230075  .222029 


.345962 
.406931 

0.441565 
.461257 
.472187 
.478024 
.480948 


508142  0.482321 
509434  .482891 


.509829 
.509977 
.510023 


21 


.171888 
.171842 
.171780 
.171700 

1.171598 
.171466 
.171302 
.171102 


1.169767 
.169657 
.169515 
.169340 
.169126'  .17086;^ 


1.170573 
.170232 
.169833 
.169365 
.168831 

1.168213 
.167513 
.166718 
.165819 
.164816 


.168192 
.167764 
.167262 

1.166689 
.166027 
.165275 
.164422 
.163458 


25 


24 


.173788 

.175490 

.173778 

.175472 

.173759 

.175451 

.173736 

.175421 

1.173704 

1.175381 

.173661 

.175327 

.173604 

.175258 

.173529 

.175168 

.173433 

.175055 

1.173311 

1.174911 

.173157 

.174737 

.172971 

.174528 

.172747 

.174276 

.172477 

.173979 

1.172159 

1.173632 

.171787 

.173226 

.171351 

.172761 

.170853 

.172223 

.170276 

.171615 

1.169624 

1.170924 

.168883 

.170142 

.168045 

.169271 

.167110 

.168294 

.166063 

.167203 

23 

22 

1.177130 
.177128 

.177128 
.177128 
.177128 

1.177128 
.177128 
.177125 
.177122 
.177116 

1.177108 
.177091 
.177071 
.177043 
.177006 

1.176955 
.176891 
.176807 
.176701 
.176567 

1.176405 
.176210 
.175975 
.175698 
.175373 

1.174995 
.174561 
.174059 
.173491 
.172847 

1.172117 
.171305 
.170394 
.169377 
.168260 


.483106 
.483173 


.335400 
.390968 


.320218 
.370386 


0.421437  0.396806 
.438034  .410543 


.446811 
.451185 
.453233 


.417331 
.420496 
.421807 


Pay- 
ments, 


20 


19 


1.180102 
1.178657!  .180101 


1.178656 
.178656 
.178656 
.178656 
.178656 


1.180101 
.180101 
.180101 
.180101 
.180101 


18 


1.181467 
.181466 
.181406 

1.181466 
.181466 
.181466 
.181466 
.181464 

1.181461 
.181457 
.181450 
.181436 
.181420 

1.181396 

.181366 

.181325 

.181273 

1798941  .181205 

1.1784341.1798211.181118 


1.1786561.180099 
.180096 
.180091 
.180084 
.180069 


.178653 
.178650 
.178645 
.178637 

1.178621 
.178603 
.178577 
.178542 
.178494 


1.180052 
.180027 
.179994 
.179950 


.178356 
.178257 
.178132 
.177980 

1.177799 
.177579 
.177321 
.177017 
.176664 

1.176259 
.175791 
.175260 
.174659 
.173979 

1.173221 
.172371 
.171423 
.170381 
.169221 


21 


20 


.179729 
.179612 
.179470 
.179301 

1.179095 
.178855 
.178571 
.178241 
.177863 

1.177426 
.176930 
.176369 
.175735 
.175028 

1.174234 
.173350 
.172378 
.171296 
.170108 


19 


.181009 
.180876 
.180719 
.180526 


1.180302    59 


.180037 
.179729 
.179376 
.178967 

1.178504 
.177980 
.177389 
.176728 
.175988 

1.175163 
.174256 
.173246 
.172138 
.170916 


18 


0.454083  0.422301  10 
.454403'  .422455  11 
.454503 


82 
81 
80 

79 

78 
77 
76 
75 

74 
73 
72 
71 
70 

69 
68 
67 
66 
65 

64 
63 
62 
61 
60 


58 
57 
56 
55 

54 
53 
52 
51 
50 

49 
48 
47 
46 
45 


Continued  from  Page  *84, 


TABLE     XLYII. 


*93 


LIFE  AND  TEMPORARY  ANNUITIES.     LOGARITHM    OF  THE    PRESENT    VALUE    OF   n 
ANNUAL  PAYMENTS  OF  1  AT  THE  BEGINNING  OF  EACH  YEAR. 

6  PER  CENT 


Pay- 
ments. 
n. 

90 

91 

93 

93 

94 

95 

96 

97 

Pay- 
ments. 

0.391855 
0.000000 

0.363938 

0.335983 

0.307090 

0.277673 

0.246844 
0.000000 

0.210226 

0.174939 

n. 

1 

1 

0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

0.000000 

2 

.213204 

.205516 

.197480 

.188212 

.178148 

.167818 

.151126 

.139047 

2 

3 

4 

5 
6 
7 
8 
9 

10 

.304786 
.349841 

0.372540 
.383586 
.388701 
.390812 
.391606 

0.391855 

.290824 
.330929 

0.349933 
.358617 
.362181 
.363519 
.363938 

.276008 
.310990 

0.326562 
.332882 
.335244 
.335983 

.259484 
.289433 

0.301314 
.305714 
.307090 

.242126 
.266205 

0.274956 

.277673 

.222201 
.241074 

0.246844 

.196801 

.174939 

3 

90 

89 
88 
87 
86 
85 

.210226 

10 

11 

12 

1.189964 

1.189962 
.189962 
.189962 
.189962 
.189962 

13 

1.189102 
.189101 
.189101 
.189101 
.189101 

14 

1.188192 
.188191 
.188191 
.188191 

15 

1.187226 
.187225 
.187225 

16 

1.186201 
.186200 

1.185120 

83 

17 

1.183972 
.183972 

1.185118 
.185118 

1.186200 
.186200 

1.187225 

.187225 

1.188191 
.188191 

1.189101 
.189101 

1.189962 
.189962 

84 
83 

1.182755 

82 

.182754 

.183972 

.185118 

.186200 

.187225 

.188191 

.189101 

.189960 

82 

81 

.182754 

.183972 

.185118 

.186200 

.187225 

.188191 

.189099 

.189957 

81 

80 

.182754 

.183972 

.185118 

.186200 

.187225 

.188189 

.189096 

.189952 

80 

79 

1.182754 

1.183972 

1.185118 

1.186200 

1.187222 

1.188186 

1.189091 

1.189945 

79 

78 

.182754 

.183972 

.185118 

.186197 

.187219 

.188181 

.189082 

.189936 

78 

77 

.182754 

.183971 

.185115 

.186194 

.187214 

.188171 

.189073 

.189922 

77 

76 

.182753 

.183968 

.185112 

.186188 

.187203 

.188161 

.189057 

.189905 

76 

75 

.182750 

.183965 

.185105 

.186177 

.187192 

.188144 

.189040 

.189881 

75 

74 

1.182746 

1.183958 

1.185094 

1.186165 

1.187174 

1.188126 

1.189014 

1.189850 

74 

73 

.182739 

.183946 

.185081 

.186146 

.187155 

.188098 

.188981 

.189809 

73 

72 

.182726 

.183932 

.185061 

.186125 

.187125 

.188063 

.188938 

.189760 

72 

71 

.182711 

.183910 

.185038 

.186093 

.187088 

.188017 

.188885 

.189697 

71 

70 

.182688 

.183885 

.185004 

.186054 

.187039 

.187960 

.188817 

.189618 

70 

69 

1.182661 

1.183849 

1.184962 

1.186.001 

1.186977 

1.187887 

1.188733 

1.189527 

69 

68 

.182622 

.183804 

.184905 

.185935 

.186899 

.187798 

.188635 

.189414 

68 

67 

.182574 

.183744 

.184835 

.185852 

.186804 

.187693 

.188515 

.189284 

67 

66 

.182510 

.183668 

.184746 

.185750 

.186692 

.187565 

.188376 

.189129 

66 

65 

.182429 

.183574 

.184637 

.185630 

.186555 

.187416 

.188210 

.188950 

65 

64 

1.182328 

1.183457 

1.184508 

1.185484 

1.186395 

1.187239 

1.188018 

1.188744 

64 

63 

.182203 

.183319 

. 184352 

.185313 

.1862061  .187034 

.187799 

.188506 

63 

62 

.182056 

.183152 

.184169 

.185110 

.1859871  .186799 

.187544 

.188236 

62 

61 

.181876 

.182956 

.183952 

.184876 

.185735 

.186526 

.187255 

.187931 

61 

60 

.181667 

.182724 

.183701 

.184607 

.185444 

.186218 

.186929 

.187588 

60 

59 

1.181419 

1.182455 

1.183414 

1.184295 

1.185114 

1.185869 

1.186562 

1.187204 

59 

58 

.181131 

.182148 

.183080 

.183942 

.184741 

.185476 

.186152 

.186773 

58 

57 

.180802 

.181791 

.182702 

.183543 

.184320 

.185038 

.185691 

.186295 

57 

56 

.180420 

.181386 

.182275 

.183093 

.183851 

.184544 

.185179 

.185769 

56 

55 

.179987 

.180929 

.181794 

.182591 

.183324 

.183996 

.184617 

.185184 

55 

54 

1.179498 

1.180414 

1.181216 

1.182027 

1.182736 

1.183395 

1.183991 

1.184542 

54 

53 

.178946 

.179838 

.180653 

.181398 

.182094 

.182725 

.183304 

.183837 

53 

52 

.178329 

.179193 

.179980 

.180710 

.181377 

.181991 

.182549 

.183063 

52 

51 

.177638 

.178473 

.179243 

.179943 

.180591 

.181183 

.181722 

.182218 

51 

50 

.176868 

.177683 

.178422 

.179101 

.179726'  .180297 

.180817 

.181297 

50 

49 

1.176021 

1.176804 

1.177520 

1.178175 

1.1787771.179328 

1.179831 

1.180293 

49 

48 

.175079 

.175838 

.176528 

.177159 

.177740!  .178272 

.178756 

.179200 

48 

47 

.174045 

.174775 

.175440 

.176049 

.176610|  .177122 

.177585 

.178014 

47 

46 

.172905 

.173609 

.174251 

.174838 

.1753771  .175867 

.176316 

.176727 

46 

45 

.171656 

.172335 

.172953 

.173517 

.174033 
13 

.174508 

.174938 

.175333 

45 

17 

16 

15 

14 

12 

11 

10 

Continued  from  Page  *83. 


*94 


TABLE     XLVIII. 


CONVERSION    TABLE   FROM    ANNUITY    OR  A(l+a)    TO   ANNUAL  PREMIUM  ON   1,000. 

INTEREST    4    PER  CENT, 

Applicable  to  ordinary  Life  and  Endowment  Insurances,  to  Joint  Lives  and  Survivorships,  and  all 
cases  of  the  annexed  Formula,  where  a  denotes  the  Present  Value  of  the  Annuity.  At  4  per  cent.  1—v 
is  .03846154     P  is  theAnnual  Premium. 

For  $1,000  Insured,  P  =  1,000  j  :r^ (1— p)  |  • 

For  a  Bate  of  Interest  other  than  4  per  cent.,  apply  thefollowing  Correction,  1,000(?)— f ')  to  the  Tabular 
result  * 

Fortherateof. .  3  8i  4  4^  5  6  7  8      percent. 

Subtract 4601     P-158     18.142     26.959     35.613 

Add 9.335      4645        p.OOO        • 

Example.  Interest  5  per  cent.  A(l  +  a)  =  0.136820 ;  the  Tabular  result  is  found  to  be  691.306  ;  this, 
less  the  above  Correction  9.158,  leaves  the  Annual  Premium  required  $682.15. 

PROPOBTICNAL   PARTS,   StTBT. 


A(l+a), 


0.00 

0.01 

0.02 

0.03 

0.04 

0.05 

0.06 

0.07 

0.08 

0.09 

0.10 

0.11 

0.12 

0.13 

0.14 

0.15 

0.16 

0.17 


0,5 


0 
5 

0 
5 

0 
5 

0894.79 
5884.11 

0873.55 
5  863.11 


961.54 
950.09 

938.78 
927.59 

916.53 
905.60 


1 
6 

1 
6 

1 
6 

1 
6 

1 
6 

1 
6 

1 
6 

1 
6 

1 
6 

1 
6 

755.87  1 
746.77  6 


852.79 
842.59 

832.50 
822.53 


0812.68 
5  802.93 


793.30 

783.78 

774.37 
765.06 


1,6 


737.79 
728.90 

720.12 
711.43 

702.85 
694.36 

685.97 
677.68 


0669.48 
5  661.38 


959.24 

947.82 

936.53 
925.37 

914.33 
903.43 

892.65 
881.99 

871.45 
861.04 

850.74 
840.56 

830. 50 
820.55 

810.72 
801.00 

791.39 
781.89 

772.50 
763.22 

754.04 
744.97 

736.00 
727.14 

718.37 
709.71 

11701.14 

6692.68 


653.37 
645.45 

637.62 
629.88 

0,5 


684.31 
676.03 

667.86 
659.77 

651.78 
643.88 

636.07 
628.35 


2,7 


956.94 
945.55 

934.29 
923.15 

912.14 
901.26 

890.50 
879.87 
869.36 
858.97 

848.69 
838.54 

828.50 
818.58 

808. 77 
799.07 

789.48 
780.00 

770. 63 
761.37 

752.22 
743.17 
734.22 
725.37 

716.63 
707.99 

699.44 
691.00 

682.65 
674.39 

666.23 
658.17 

650.19 
642.31 

634.52 
626.81 

2,7 


3,8 


4 
9 

4 
9 

4 
9 

4 
9 

4 
9 

846.65  4 
836.52  9 


954.65 
943.29 

932.05 
920.94 

909.96 
899.10 

888.37 
877.76 

867.27 
856.90 


826.51 
816.61 

806.82 
797.14 

787.58 
778.12 


4,9 


768.77  4 
759.53  9 


750.40 
741.37 

732.44 
723.62 

714.89 
706.27 

697.75 
689.32 

680.99 

672.75 

664.61 
656.56 

648.61 
640.74 

632.97 
625.28 

3,8 


952.37 
941.03 

929.82 
918.73 

907.78 
896.94 

886.24 
875.65 

865.19 
854.84 

844.62 
834.51 

824.52 
814.64 

804.87 
795.22 

785.68 
776.24 

766.92 

757.70 

748.58 
739.58 

730.67 
721.86 

713.16 
704.56 

696.05 
687.64 

679.33 
671.12 

662.99 
654.96 

647.03 
639.18 

631.42 
623.76 

4,9 


46j69  92 
45  68  90 


45,67 
44  66 


23 
23 

22 
22 

22 

22 

21 
21 

21 
21 

20 
20 

20  40 
20  39 

2o!39 
19  39 


90 


66 
65 

64 
63 

63 
62 

61 
61 

60 
59 

59 

58 

57 
56 

66 
55 

55 
54 

53 
53 

52 
51 

51 
50 

50 
49 

49 
48 

48 

47 

46 
46 


86 

86 
85 

84 
83 

82 
81 

80 
79 

78 
77 

76 

75 

74 
74 

73 

72 

71 
70 

70 
69 

68 
67 

66 
66 

65 
64 

63 
63 

62 
61 


115 
113 

112 
111 

110 
108 


137160 
136158 


134 
133 

131 
130 


107  128 
106  127 


105 
103 

102 
101 

100 
99 

98 
96 

95 
94 

93 

92 

91 

90 

89 


125 

124 

122 
121 


9 


183 
181 

179 

177 

175 
173 


157 
155 

153 
151 

150  171 
148  169 


206 
204 

202 


146 
144 

143 
141 


167 
165 

163 
161 


120 140 
118138 


117 
116 

114 
113 

112 
110 

109 
108 

107 
105 

87  104 
86  103 


85 
84 

83 

82 

81 
80 

79 

78 

77 

77 


102 
101 

99 

98 

97 
96 

95 
94 

93 
92 


160179 

158177 


137 
135 

133 
132 

130 
129 

127 
126 

124 
123 


199 


197 
195 

192 

190 

188 
186 

184 
182 


156 
154 

152 
151 

149 
147 

146 
144 

142 

140 


122139 
120  137 


119 
117 

116 
115 

113 

112 

111 
110 


136 
134 


176 
173 

171 

169 

168 
165 

164 
162 

160 
158 

156 
154 

153 
151 

133  149 

131 148 


130 
128 

127 
125 


108124 

107122 

i_^ 

7  8 


146 
144 

143 
141^ 

139i 

138j 

9 


TABLE     XLTTII.  *95 

CONVERSION  TABLE   FROM   ANNUITY  OR   X{l  +  (l)    TO  ANNUAL    PREMIUM    ON    1,000. 

INTEREST  4  PER  CENT. 

PROPORTIONAL  PARTS,  SUBT. 


^l+a). 


0.18 
0.19 
0.20 
0.21 
0.22 
0.23 
0.24 
0.25 
0.26 
0.27 
0.28 
0.29 
0.30 
0.31 
0.32 
0.33 
0.34 
0.35 
0.36 
0.37 
0.38 
0.39 
0.40 
0.41 


0,5 


622.23 

614.67 

607.19 
599.80 

592.50 

585.27 


0578.13 
5  571.08 


564.10 
557.20 

550.38 
543.64 

536.98 
530.39 

523.89 
517.44 

511.09 
504.80 

498.57 
492.42 

486.35 
480.34 

0474.40 

468.53 


1,6 


0429 


0418 


462.73 
456.99 

451.32 
445.71 

440.17 
434.69 

27 
423.92 

63 
413.39 

22 
403.12 

398.05 
393.06 

12 
383.24 

378.41 
373.64 

368.93 
364.26 

359.65 
355.10 

350.58 
346.13 

0,5 


0388 
5 

0 
5 

0 


620.71 
613.17 

605.71 
598.33 

591.04 
583.84 

576.72 
569.67 

562.71 
555.83 

549.03 
542.30 

535.66 
529.08 

522.59 
516.16 

509.82 
503.54 

497.34 
491.20 

485.14 
479.15 

473.22 

467.36 

461.57 
455.85 

450.19 
444.60 

439.07 
433.60 

428.20 
422.86 

417.58 
412.36 

407.19 
402.09 

397.05 
392.07 
387.14 
382.27 

377.46 
372.69 

367.98 
363.34 

358.73 
354.18 

349.69 
345.25 


2,7 


3,8 


2i619.20 
7611.67 


604.23 
596.87 

589.60 
582.41 

575.30 

568.27 

561.33 
554.46 

547.68 
540.97 

534.33 

527.78 

521.30 
514.90 

508.55 
502.29 

496.10 
489.98 

483.93 

477.95 

472.04 
466.20 

460.42 

454.71 

449.07 
443.49 

437.97 
432.52 


416.53 
411.32 

406.18 
401.08 


2396.06 
7391.07 


386.16 
381.30 

376.49 
371.74 

367.05 
362.41 

357.82 
353.28 

348.80 
344.36 

2,7 


617.68 
610.17 

602.75 
595.41 

588.15 
580.98 

573.90 
566.89 

559.95 
553.10 

546.33 
539.63 

533.02 

526.48 

520.02 
513.62 

507.30 
501.05 

494.87 

488.77 

482.73  4 

476.77!  9 


4,9 


470.88 
465.04 

459.28 
453.58 

447.95 
442.38 

436.87 
431.43 

426.05 
420.74 

415.48 
410.28 

405.15 
400.08 

395.05 
390.09 

385.18 
380.33 

375.54 
370.81 

366.11 
361.48 

356.91 
352.39 

347.91 
343.48 

3,8 


616.17 
608.68 

601.27 
593.95 

586.71 
579.55 

572.48 
565.49 

558.57 
551.74 

544.98 
538.30 

531.70 
525.18 

518.72 
512.35 

506.04 
499.81 

493.65 

487.56 

481.53 

475.58 

469.70 
463.88 

458.13 
452.45 

446.83 
441.27 

435.78 
430.35 

424.99 
419.68 

414.44 
409.25 

404.13 
399.06 

394.05 
389.10 

384.21 
379.38 

374.59 
369.86 

365.18 
360.56 

356.00 
351.48 

347.02 
342.60 

4,9 


15 
15 

15 
15 

14 
14 

14 
14 

14 

14 

13 
13 

13 
13 

13 
13 

13 
12 

12 
12 

12 


29'44 


1224 


10  21 
10  21 


10 
10 

10 
10 

10 
10 

10 
9 

9 
9 

9 
9 

9 
9 


1928 


60 
60 

59 

58 

58 
57 
56 
56 

55 

55 

54 
53 

53 
52 

52 
51 

50 
50 

49 
49 

48 
48 

47 
46 

46 
45 

45 

44 

44 
43 

43 
42 

42 
41 

41 
41 

40 
40 

39 
39 

38 

38 

37 
37 

36 
36 

36 
35 


5 


76 

75 

74 
73 

72 
71 

71 
70 

69 
68 

67 
67 
66 
65 

65 
64 

63 
62 

62 
61 

60 
59 

59 

58 

57 
57 
56 
55 

55 
54 

54 
53 

52 
52 

51 
51 

50 
49 

49 

48 

48 

47 

47 
46 

46 
45 

45 

44 


6 


35  4:4 

4|5 


91 
90 

89 
88 

87 
86 

85 
84 

83 
82 

81 
80 

79 

78 

77 
76 

75 
75 

74 
73 

72 
71 
70 
70 

69 

68 

67 
66 

66 
65 

64 
63 

63 

62 

61 
61 

60 
59 

59 
58 

57 
57 

56 
55 

55 
54 

53 
53 


106 
105 

103 
102 

101 
100 

99 

98 

97 
95 

94 
93 

92! 
9l| 

90 

89 

88 

87 

86 
85 

84 
83 

82 
81 

80 
79 

79 
78 

77 
76 

75 
74 

73 

72 

71 
71 
70 
69 

68 
68 

67 
66 

65 
65 
64 
63 
62 
62 


8 


121 
120 

118 
117 
116 
114 

113 

112 

110 
109 

108 
107 

105 
104 

103 
102 

101 
100 

98 
97 
96 
95 

94 
93 

92 
91 

90 
89 

88 

87 

86 
85 

84 
83 

82 
81 

80 
79 

78 

77 

76 

76 

75 
74 

73 

72 

71 

70 


9 


136 
135 

133 
131 

130 
129 

127 
126 

124 
123 

121 
120 

119 
117 

116 
114 

113 
112 

111 
109 

108 
107 

106 
104 

103 
102 
101 

100 

99 
98 

96 
95 
94 
93 

92 
91 

90 
89 

88 
87 

86 
'85 

84 
83 
82 
81 

80 
79 


8  9 


96*  .  TABLE     XLYIII. 

CONVERSION  TABLE   FROM   ANNUITY  OR    /(l+r^    TO  ANNUAL    PREMIUM   ON    1,000. 


INTEREST  4  PER  CENT. 


PKOPORTIONAL  PAKTS,  8UBT. 


U(l+«) 


0.42 
0.43 
0.44 
0.45 
0.46 
0.47 
0.48 
0.49 
0.50 
0.51 
0.52 
0.53 
0.54 
0.55 
0.56 
0.57 
0.58 
0.59 
0.60 
0.61 
0.62 
0.63 
0.64 
0.65 


0.5 


Oj341.73 
5  337.38 


1 
6 

1 
6 

324.62  1 
320.46  6 


333.07 

328.82 


0 
5 

0 
5 

0 

5 

0308.28 
5  304.31 


1.6 


316.35 
312.29 


300.38 
296.50 

292.67 
288.88 

285.13 
281.43 

277.77 
274.15 

270.57 
267.03 

263.53 

260.08 


256.66  1 
253.28  6 

249.941 1 
246.64  6 


236.96 
233.81 

230.69 
227.61 

224.57 
221.55 

218.58 
215.64 

212.73 

209.85 

207.01 
204.20 

201.42 

198.68 

195.96 
193.28 

190.63 
188.00 

185.41 
182.85 


340.85 
336.51 

332.22 

327.98 

323.78 
319.63 

315.54 
311.48 

307.48 
303.52 

299.60 
295.73 

291.91 
288.13 

284.39 
280.69 

277.04 
273.43 

269.86 
266.33 

262.84 
259.39 

255.98 
252.61 

249.28 
245.98 

242.73 
239.51 

236.33 
233.18 

230.07 
227.00 

223.96 
220.96 

217.99 
215.05 

212.15 

209.28 

206.44 
203.64 

200.87 
198.13 

195.42 
192.75 

190.10 

187.48 

184.90 
182.34 


2,7 


3,8 


339.98 
335.66 

331.37 
327.13 

322.95 
318.81 

314.72 
310.68 

306.68 
302.73 

298.83 
294.96 


291.15  3290.39 
287.38  8286.63 


283.6513 
279.96  8 


2 

7 

2 

7 

2 

7 

2 

7 

2 

7 

2 

7 

2 

7 

2 

7 

2 

7 

2 

7 

2 

7 

2 

7 

2 

7 

2 

7 

2 

7 

2229.46 
7226.39 


339.11 
334.79 

330.52 
326.29 

322.12 

317.99 

313.91 
309.88 

305.89 
301.95 

298.05 
294.20 


276.31 

272.71 

269.15 
265.63 

262.15 
258.71 

255.30 
251.94 

248.62 
245.33 
242.08 
238.87 
235.70 
232.56 


0,5    1,6 


223.36 
220.36 

217.40 
214.47 

211.57 

208.71 

205.88 
203.08 

200.32 
197.59 

194.88 
192.21 

189.57  j 
186.96 

184.38; 
181.83 

2,7 


282.90 
279.23 

275.59 
271.99 

268.44 
264.93 

261.45 
258.02 

254.63 

251.27 

247.96  4 
244.68 1  9 

241.44  4 
238.23  9 


4,9 


235.07 
231.93 

228.84 

225.78 

222.75 
219.76 

216.81 
213.89 

211.00 
208.14 

205.32 
202.53 

199.77 
197.04 

194.35 
191.68 

189.05 
186.44 


338.24 
333.93 

329.67 
325.45 

321.29 
317.17 
313.10 
309.07 

305.10 
301.16 

297.28 
293.43 

289.63 
285.88 

282.17 
278.50 

274.87 
271.28 

267.73 
264.23 


4  260.77 
9  257.34 


3183.87 
8ll81.32 

3,8 


253.95 
250.61 

247.30 
244.03 

240.79 
237.60 

234.44 
231.31 

228.22 
225.17 
222.15 
219.17 

216.22 
213.31 

210.42 

207.58 

204.76 
201.97 

199.22 
196.50 

193.81 
191.15 

188.53 
185.93 

183.36 
180.82 

4,9 


3  4 


17 
17 

17 
17 

17 
16 

16 
16 

16 
16 

16 
15 

1? 

15 

15 
15 

14 
14 

14 
14 

14 

14 

14 
13 

13 
13 

13 
13 

13 
12 

12 
12 

12 

12 

12 

12 

12 
11 

11 
11 

11 
11  16 

16 
16 

16 

16 

15 
15 


35 
34 

34 
34 

33 
33 

32 
32 

32 
31 

31 
31 

30 
30 

30 

29 

29 

29 

28 
28 

28 

27 

27 
27 
26 
26 

26 

26 

25 
25 

25 
24 

24 
24 

24 
23 

23 
23 

22 
22 

22 
22 

21 
21 

21 

21 

20 
20 


44 
43 

43 
42 

42 
41 

41 
40 

40 
39 

39 
38 

38 
38 

37 
37 

36 
36 

35 
35 

35 
34 

34 
33 

33 
33 

32 
32 

32 
31 

31 
30 

30 
30 

29 
29 

29 

28 

28 
28 

27 
27 

27 
27 

26 
26 

26 
25 


6  7 

52  61 

52  60 1 

51  60 
50  59 

50 '58 
49  58 

49  57 
56 

56 
55 

54 
54 

53 
53 

52 
51 

51 
50 

50 
49 

48 
48 

47 
47 

46 
46 

45 
45 

44 

44 

43 
43 

42 
42 

41 
41 

40 
40 

39 
39 

38 
38 

38 
37 

37 
36 

36 
36 


70  78 


78 

77 
76 

75 
74 

73 

72 

71 

71 

70 
69 

68 
68 

67 
66 

65 
64 

64 
63 

62 
62 

61 
60 

59 
59 


69 

68 
o7 

67 
66 

65 
64 

64 
63 

62 
61 

61 

60 

59 
59 

58 

57 

57 
56 

55 
55 

54 
53 

53 
52 
5258 

51,57 

5057 
50  56 

49,55 
4955 

48:54 
48J53 

47  53 

47152 

46  52 
45  51 

4551 
44  50 


49 
49 

48 
48 

47 

47 

46 
46 


89 


TABLE     XLYIII.  *9r 

CONVERSION   TABLE   FROM    ANNUITY    OR  A(l  +  a)   TO    ANNUAL  PREMIUM  ON  1,000. 

INTEREST    4    PER  CENT. 

PROPORTIONAL   PARTS,   SUBT. 


A(l+a). 

0,5 

1,6 

2,7 

3,8 

4,9 

1 

2 

3 

4 

20 
20 

6 

25 
25 

6 

30 
30 

7 

35 
35 

8 

40 
40 

9 

45 
45 

0.66 

3180.31 

5177.81 

1179.81 
6177.31 

2 

7 

179.31 
176.83 

3 

8 

178.81 
176.32 

4 
9 

178.31 
175.83 

5 
5 

10 
]0 

15 

15 

0.67 

0175.33 

5172.89 

1 
6 

174.84 
172.40 

2 

7 

174.35 
171.92 

3 
8 

173.86 
171.43 

4 
9 

173.37 
170.95 

5 
5 

10 
10 

15 

15 

20 
19 

24 
24 

29 
29 

34 
34 

39 
39 

44 

44 

0.68 

0170.47 
5168.08 

1 
6 

169.99 
167.60 

2 

7 

169.51 
167.13 

3 
8 

169.03 
166.65 

4 
9 

168.55 
166.18 

5 
5 

10 
9 

14 
14 

19 
19 

24 
24 

29 
28 

33 
33 

38 
38 

43 

43 

0.69 

0165.71 
5163.38 

1 
6 

165.24 
162.91 

2 

7 

164.77 
162.45 

3 
8 

164.31 
161.99 

4 
9 

163.84 
161.52 

5 
5 

9 
9 

14 
14 

19 
19 

23 
23 

28 
28 

33 
32 

37 
37 

42 
42 

0.70 

0161.06 

5158.78 

1 
6 

160.61 
158.33 

2 

7 

160.15 
157.87 

3 
8 

159.69 
157.42 

4 
9 

159.24 
156.97 

5 
5 

9 
9 

14 
14 

18 
18 

23 
23 

27 
27 

32 
32 

36 

36 

41 
41 

0.71 

0156.52  jl 
5154.29  6 

156.07 
153.85 

2 

7 

155.63 
153.41 

3 
8 

155.18 
152.96 

4 
9 

154.74 
152.52 

4 
4 

i 

13 
13 

18 
18 

22 
22 

27 

27 

31 
31 

36!  40 
35|40 

0.72 

0152.08 
5149.90 

1 
6 

151.65 
149.47 

2 

7 

151.21 
149.04 

3 

8 

150.77 
148.01 

4 
9 

150.34 
148.18 

4 
4 

9 
9 

13 
13 

17 
17 

22 
22 

26 
26 

31 

30 

35 
34 

39 
39 

0.73  i 

0147.75|1 
5145.62  6 

147.32  2'l46.89 
145.19  7144.77 

3 
8 

146.47 
144.35 

4 
9 

146.04 
143.93 

4 
4 

9 

8 

13 
13 

17 
17 

21 
21 

26 
25 

30 
30 

34 
34 

38 
38 

0.74  ' 

)  143.51  1 
5141.43  6 

143.09 
141.01 

2 

7 

142.67 
140.60 

3 
8 

142.26 
140.19 

4 
9 

141.84 
139.78 

4 

4 

8 
8 

12 
12 

17 
16 

21 
21 

25 
25 

29 
29 

33 
33 

37 
37 

0.75  ' 

3139.37 
5137.33 

1 
6 

138.96 
136.93 

2 

7 

138.55 
136.52 

3 
8 

138.14 
136.12 

4 
9 

137.74 
135.72 

4 
4 

8 
8 

12 

•12 

16 

16 

20 
20 

24 
24 

29 

28 

33 
32 

37 

36 

0.76  < 

)  135.32 
)  133.33 

1 
6 

134.92 
132.93 

2 

7 

134.52 
132.54 

3 
8 

134.12 
132.15 

4 
9 

133.73 
131.75 

4 
4 

8 
8 

12 
12 

16 
16 

20 
20 

24 
24 

28 
28 

32 
32 

36 
35 

0.77  1 

)  131.36 
)  129. 42 

1 
6 

130.97 
129.03 

2 

7 

130.58 
128.65 

3 

8 

130.19 

128.26 

4 
9 

129.81 

127.88 

4 
4 

8 
8 

12 
12 

16 
15 

19 
19 

23 
23 

27 

27 

31 
31 

35 
35 

0.78  ( 

)  127.50  1 
)  125. 60  6 

127.12 
125.22 

2 

7 

126.73  3 
124.84  8 

126.35 
124.47 

4 
9 

125.98 
124.09 

4 
4 

8 
8 

11 
11 

15 
15 

19 
19 

23 
23 

27 
26 

30 
30 

34 
34 

0.79  ( 

) 123. 72  1 
)  121.86  6 

123.35 

121.49 

2 

7 

122.97  3 
121.13  8 

122.60 
120.76 

4 
9 

122.23 
120.39 

4 
4 

7 
7 

11 
11 

15 
15 

19 
18 

22 
22 

26 
26 

30 
29 

33 
33 

0.80  1 

)  120. 03  1 
5118.21  6 

119.66 
117.85 

2 

7 

119.30 

117.49 

3 
8 

118.94 
117.14 

4 
9 

118.57 
116.78 

4 
4 

7 

7 

11 
11 

15 
14 

18 
18 

22 
21 

25 

25 

29 

29 

33 
32 

0.81  1 

)  116.42  1 
5114.65  6 

116.06 
114.30 

2 

7 

115.71 
113.94 

3 

8 

115.35 
113.59 

4 
9 

115.00 
113.24 

4 
4 

7 
7 

11 
11 

14 
14 

18 
18 

21 
21 

25 
25 

28 
28 

32 
32 

0.82 

)112.89  1 
5111.16  6 

112.55 

110.82 

2 

7 

112.20 
110.47 

3 

8 

111.85 
110.13 

4 
9 

111.51 
109.79 

3 
3 

7 
7 

10 
10 

14 

14 

17 
17 

21 
21 

24 
24 

28 

27 

31 
31 

0.83 

}  109. 45  1 
5107.76  6 

109.11 
107.42 

2 

7 

108.77 
107.08 

3 
8 

108.43 
106.75 

4 
9 

108.09 
106.42 

3 
3 

7 

7 

10 
10 

14 
13 

17 
17 

20 
20 

24 
24 

27 
27 

80 
30, 

0.84  ( 

0 106.08 'l 
5104.43  6 

105.75 
104.10 

2 

7 

105.42 
103.77 

3 
8 

105.08 
103.44 

4 
9 

104.76 
103.12 

3 
3 

7 
7 

10 
10 

13 
13 

17 
16 

20 
20 

23 
23 

26 
26 

30  ' 

30 

0.85 

0102.79  1 
5101.18  6 

102.47 
100.85 

2 

7 

102.14 
100.53 

3 
8 

101.82 
100.21 

4 
9 

101.50 
99.80 

3 
3 

6 
6 

10 
10 

13 
13 

16 
16 

19 
19 

28 
22 

26 
26 

29 
29 

0.86 

0  99.58 'l 
5  98.00  6 

99.26 
97.68 

2 

7 

98.94 
97.37 

3 
8 

98.63 
97.06 

4 
9 

98.31 
96.75 

3 
3 

6 
6 

9 
9 

13 
13 

16 
16 

19 

19 

22 
22 

25 
25 

28 
28 

0.87 

0  96.43  1 
5  94.89  6 

96.12 
94.58 

2 

7 

95.82 
94.28 

3 
8 

95.51 
93.97 

4 
9 

95.20 
93.67 

3 
3 

6 
6 

9 
9 

12 

12 

15 
15 

18 
18 

22 
21 

25 
24 

28 
28 

0.88 

0  93.36  1 
5  91.86  6 

93.06 
91.56 

2 

7 

92.76 
91.26 

3 

8 

92.46 
90.96 

4 
9 

92.16 
90.66 

3 
3 

6 

6 

9 

9 

12 

12 

15 
15 

18 
18 

21 
21 

24 
24 

27 

27 

0.89 

0  90.36  1 
5  88.89  6 

90.07 
88.60 

2 

7 

89.77 
88.30 

3 
8 

89.48 
88.01 

4 
9 

89.18 

87.72 

3 
3 

G 
G 

9 
9 

12 

1^ 

15 
15 

18 
18 

21 
20 

24 
23 

26 
26 

0,6  ;   1,6    2,7 

3,8 

4,9 

T 

~2 

¥ 

4 

5 

6 

T 

~S 

9 

'98 


TABLE    XLYIU 


CONVERSION    TABLE   FROM    ANNUITY   OR  A(l+a)    TO  ANNUAL  PREMIUM  ON   1,000. 

INTEREST  4  PER  CENT. 


PROPOBTIONAL 

PAKTS 

,  SUBT. 

A(l+a) 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9    ! 

1 
3 

213 

4 

11 

5 

14 

6 

17 

7 
20 

8 

23 

9 

26 

0.90 

8743 

87.14 

86.85 

86.56 

86.28 

85.99 

85.70 

85.42 

85.13 

84.85 

6 

9 

0.91 

84-57 

84.38 

84.00 

83.72 

83.44 

83.16 

83.88 

82.60 

82.32 

82.04  13 

6 

8 

11 

14 

17 

20 

33 

25 

0.92 

81.77 

81.49 

81.21 

80.94 

80.66 

80.39 

80.13 

79.84 

79.57 

79.30 

3 

5 

8 

11 

14 

16 

19 

22 

25 

0.93 

79.03 

78.76 

78.49 

78.22 

77.95 

77.68 

77.43 

77.15 

76.88 

76.62 

3 

5 

8 

11 

13 

16 

19 

21 

24 

0.94 

76.35 

76.09 

75.83 

75.56 

75.30 

75.04 

74.78 

74.52 

74.26 

74.00 

3 

5 

8 

10 

13 

16 

18 

21 

33 

0.95 

73.74 

73.48 

73.23 

72.97 

72.71 

72.46 

73.30 

71.95 

71.69 

71.44 

3 

5 

8 

10 

13 

15 

18 

20 

33 

0.96 

71.18 

70.93 

70.68 

70.43 

70.18 

69.93 

69.68 

69.43 

69.19 

68.84 

2 

5 

7 

10 

12 

15 

17 

20 

32 

0.97 

68.69 

68.44 

68.30 

67.95 

67-71 

67.46 

67.32 

66.98 

66.73 

66.49 

2 

5 

7 

10 

12 

15 

17 

20 

22 

0.98 

66.25 

66.01 

65.77 

65.53 

65.29 

65.05 

64.81 

64.58 

64.34 

64.10. 

2 

5 

7 

10 

12 

14 

17 

19 

21 

0.99 

63.87 

63.63 

63.40 

63.16 

62.93 

62.69 

63.46 

62.23 

62.00 

61.77 

2 

5 

7 

9 

12 

14 

16 

19 

21 

l.OD 

61.54 

61.31 

61.08 

60.85 

60-62 

60.39 

60.17 

59.94 

59.71 

59.49 

2 

5 

7 

9 

11 

14 

16 

18 

21 

1.01 

59.36 

59.04 

58.81 

58.59 

58-37 

58.14 

57.93 

57.70 

57.48 

57.25 

2 

4 

7 

9 

11 

13 

16 

18 

20 

1.02 

57.04 

56.83 

56.60 

56.38 

56-16 

55.95 

55.73 

55.51 

55.30l55.08 

3 

4 

7 

9 

11 

13 

15 

17 

20 

1.03 

54.86 

54.65 

54.44 

54.22 

54.01 

53.80 

53.58 

53.37 

53.16 

52.95 

2 

4 

6 

8 

11 

13 

15 

17 

19 

1.04 

53.74 

52.53 

52.32 

53.11 

51.90 

51.70 

51.49 

51.28 

51.08 

50.87 

2 

4 

6 

8 

10 

12 

15 

17 

19 

1.05 

50.66 

50.46 

50.25 

50.05 

49.85 

49.64 

49.44 

49.34 

49.04 

48.84 

3 

4 

6 

8 

10 

12 

14 

16 

18 

1.08 

48.64i48.44 

48.24 

48.04 

47.84 

47.64 

47.44 

47.34 

47.05 

46.85 

3 

4 

6 

8 

10 

12 

14 

16 

18 

1.07 

46.65|46.46 

46.26 

46.07 

45.87 

45.68 

45.49 

45.39 

45.10 

44.91 

2 

4 

6 

8 

10 

12 

14 

15 

17 

1.08 

44.73  44.53 

44.33 

44.14 

43.95 

43.76 

43.57 

43.39 

43.20 

43.01 

2 

4 

6 

8 

10 

11 

13 

15 

17 

1.09 

43.83 

43.64 

42.45 

42.26 

42.08 

41.89 

41.71 

41.53 

41.34 

41.15 

3 

4 

6 

7 

9 

11 

13 

15 

17 

1.10 

40.97 

40.79 

40.61 

40.43 

40.24 

40.06 

39.88 

39.70 

39.52 

39.34 

3 

4 

5 

7 

9 

11 

13 

14 

16 

1.11 

39.16 

38.99 

38.81 

38.63 

38.45 

38.28 

38.10 

37.93 

37.75 

37.57 

3 

4 

5 

7 

9 

11 

13 

14 

16 

1.12 

37.40 

37.33 

37.05 

36.87 

36.70 

36.53 

36.36 

36.18 

36.01 

35.84 

3 

3 

5 

7 

9 

10 

13 

14 

16 

1.13 

35.67 

35.50 

35.33 

35.16 

34.99 

34.82 

34.65 

34.48 

34.32 

34.15 

2 

3 

5 

7 

8 

10 

12 

14 

15 

1.14 

33.98 

33.83 

33.65 

33.48 

33.32 

33.15 

32.99 

33.83 

32.66 

32.50 

2 

3 

5 

7 

8 

10 

12 

13 

15 

1.15 

33.33 

32.17 

33.01 

31.85 

31.68 

31.52 

31.36 

31.30 

31.04 

30.88 

2 

3 

5 

6 

8 

10 

11 

13 

14 

1.16 

30.73 

30.56 

30.40 

30.25 

30.09 

29.93 

29.77 

39.63 

29.46 

29.30 

2 

3 

5 

6 

8 

9 

11 

13 

14 

1.17 

39.15 

38.99 

28.84 

28.68 

28.53 

38.37 

28.22 

28.07 

27.91 

27.76 

2 

3 

5 

6 

8 

9 

11 

12 

14 

1.18 

37.61 

37.46 

27.30 

27.15 

27.00 

36.85 

26.70 

26.55 

36.40 

26.25 

2 

3 

5 

6 

8 

9 

11 

12 

14 

1.19 

36.10 

25.96 

25.81 

25.66 

25.51 

35.37 

25.22 

25.07 

24.93 

24.78 

3 

4 

6 

7 

9 

10 

12 

13 

1.20 

34.63 

24.49 

24.34 

24.20 

24.06 

33.91 

23.77 

23.63 

23.48 

23.34 

3 

4 

6 

7 

9 

10 

11 

13 

1.21 

33.30 

23.06 

22.91 

33.77 

22.63 

33.49 

32.35 

22.21 

22.07 

21.93 

3 

4 

6 

7 

8 

10 

11 

13 

1.22 

31.79  31.66 

21.52 

31.38 

21.24 

31.10 

20.97 

20.83 

20.69 

20.56 

3 

4 

5 

7 

8 

10 

11 

12 

1.23 

30.4330.39 

20.15 

30.03 

19.88 

19.75 

19.61 

19.48 

19.35 

19.33 

3 

4 

5 

7 

8 

9 

11 

12 

1.24 

19.08  18.95 

18.82 

18.89 

18.55 

18.43 

18.29 

18.16 

18.03 

17.90 

3 

4 

5 

7 

8 

9 

10 

12 

1.25 

17.77 

17.64 

17.51 

17.39 

17.26 

17.13 

17.00 

16.87 

16.75 

16.63 

3 

4 

5 

6 

8 

9 

10 

12 

1.26 

16.49 

16.37 

1-6.24 

16.11 

15.99 

15.86 

15.74 

15.61 

15.49 

15.37 

3 

4 

5 

6 

8 

9 

10 

11 

1.27 

15.34 

15.12 

14.99 

14.87  14.751 

14.63 

14.50 

14.38 

14.26 

14.14 

2 

4 

5 

6 

7 

9 

10 

11 

1.28 

14.03 

13.90 

13.78 

13.66 

13.54 

13.43 

13.30 

13.18 

13.06 

13.94 

2 

4 

5 

6 

7 

8 

10 

11 

1.29 

13.83 

12.71 

12.59 

12.47 

12.35 

13.34 

12.12 

12.00 

11.89 

11.77 

3 

3 

5 

6 

7 

8 

9 

10 

1.30 

11.66 

11.54 

11.43 

11.31 

11.20 

11.08 

10.97 

10.86 

10.74 

10.63 

3 

3 

5 

6 

7 

8 

9 

10 

1.31 

10.53 

10.40 

10.29 

10.1810.07 

9.96 

9.84 

9.73 

9.62 

9.51 

2 

3 

4 

6 

7 

8 

9 

10 

1.32 

9.40 

9.29 

9.18 

9.071  8.96 

8.85 

8.74 

8.64 

8.53 

8.42 

2 

3 

4 

5 

•7 

8 

9 

10 

1.33 

8.31 

8.20 

8.10 

7.99    7.88 

7.78 

7.67 

7.56 

7.46 

7.35 

2 

3 

4 

5 

6 

7 

8 

10 

1.34 

7.35 

7.14 

7.04 

6.93 

6.83 

6.73 

6.62 

6.52 

6.41 

6.31 

2 

3 

4 

5 

6 

7 

8 

9 

1.35 

6.31 

6.10 

6.00 

5.90 

5.80 

5.70 

5.59 

5.49 

5.39 

5.29 

2 

3 

4 

5 

6 

7 

8 

9 

1.36 

5.19 

5.09 

4.99 

4.89.  4.79 

4.69 

4.59 

4.49 

4.39 

4.39 

2 

3 

4 

5 

6 

7 

8 

9 

1.37 

4.30 

4.10 

4.00 

3.90 

3.81 

3.71 

3.61 

3.51 

3.42 

3.33 

2 

3 

4 

5 

6 

7 

8 

9 

1.38 

3.33 

3.13 

3.03 

2.94 

2.84 

3.75 

2.65 

2.56 

2.46 

2.37 

2 

3 

4 

5 

6 

7 

8 

9 

1.39 

2.38 

2.18 

2.09 

2.00 

1.90 

1.81 

1.72 

1.63 

1.53 

1.44 

T 

2 
2 

3 
3 

4 
4 

5 

6 
~6 

7 

7 

7 



8 

0 

1 

2 

3 

4 

5 

6 

7 

"s^ 

9 

TABLE     XLIX. 


*99 


CONVERSION   TABLE   FROM   ANNUITY   OR  A(l-f«)  TO   SINGLE   PREMIUM  ON    1,000. 

INTEREST    4    PER  CENT. 

Applicable  to  ordinary  Life  and  Endowment  Insurance,  to  Joint  Lives  and  Survivorships,  and  all 
cases  under  the  annexed  Formula : 

For  $1,000  Insured,  A  =  1,000  ^  -  (1— »)  (1  +ffl)j . 
For  other  Bates  of  Interest :  Before  entering  the  Table,  correct  /l(l  +  a)  by  }-{\~v')  —  A(l— ■»),  thus: 
For  the  rate  of.  3  3^  4  4.V  5  6  7  8      percent. 

Subtract 0.120743    .055899    .000000     ...'. 

Add 049070.093754    .167819.230688.284640 

Example.    Interest  3  per  cent.  A(l  +  a)  =  0.368943.    Subtracting  0.120743.  leaves  0.248200.     With 
this,  the  Table  gives  the  required  Single  Premium  93189. 


X{\+a). 

0 

1 

2 

8 

4 

6 

6 

7 

8 

9 

*Ref. 

0.00 

961.54 

961.45 

961.36 

961.27 

961.18 

961.09 

961.00 

960.91 

960.83 

960.73 

1.39 

0.01 

960.64 

960.55 

960.46 

960.37 

960.28 

960.19 

960.09 

960.00 

959.91 

959.82 

1.39 

0.02 

959.73 

959.63 

959.54 

959.45 

959.35 

959.36 

959.17 

959.07 

958.98 

958.88 

1.38 

0.03 

958.79 

958.69 

958.60 

958.50 

958.41 

958.31 

958.21 

958.12 

958.02 

957.93 

1.37 

0.04 

957.83 

957.73 

957.63 

957.54 

957.44 

957.34 

957.24 

957.14 

957.04 

556.94 

1.36 

0.05 

956.85 

956.75 

956.65 

956.55 

956.45 

956.35 

956.25 

956.14 

956.04 

955.94 

1.35 

0.06 

955.84 

955.74 

955.64 

955.53 

955.43 

955.33 

955.23 

955.13 

955.02 

954.93 

1.34 

0.07 

954.81 

954.71 

954.60 

954.50 

954.39 

954.29 

954.18 

954.08 

953.97 

953.87 

1.33 

0.08 

953.76 

953.65 

953.55 

953.44 

953.33 

953.22 

953.12 

953.01 

952.90 

953.79 

1.32 

0.09 

952.68 

952.57 

952.46 

952.35 

952.24 

952.13 

952.02 

951.91 

951.80 

951.69 

1.31 

0.10 

951.58 

951.47 

951.36 

951.24 

951.13 

951.02 

950.91 

950.79 

950.68 

950.57 

1.30 

0.11 

950.45 

950.34 

950.22 

950.11 

949.99 

949.88 

949.76 

949.65 

949.53 

949.41 

1.29 

0.12 

949.30 

949.18 

949.06 

948.95 

948.83 

948.71 

948.59 

948.47 

948.36 

948.24 

1.28 

0.13 

948.12 

948.00 

947.88 

947.76 

947.64 

947.52 

947.39 

947.27 

947.15 

947.03 

1.27 

0.14 

946.91 

946.79 

946.66 

946.54 

946.42 

946.29 

946.17 

946.05 

945.93 

945.80 

1.26 

0.15 

945.67 

945.55 

945.42 

945.29 

945.17 

945.04  944.92 

944.79 

944.66 

944.53 

1.35 

0,16 

944.41 

944.28 

944.15 

944.02 

943.89 

943.76  943.63 

943.50 

943.37 

943.24 

1.24 

0.17 

943.11 

942.98 

942.85 

942.72 

942.58 

942.45  942.32 

943.19 

943.05 

941.92 

1.23 

0.18 

941.79 

941.65 

941.52 

941.38 

941.25 

941.11  940.98 

940.84 

940.70 

840.57 

1.33 

0.19 

940.43 

940.29 

940.16 

940.02 

939.88 

939.74  939.60 

939.46 

939.33 

939.18 

1.31 

0.20 

939.04 

938.90 

938.76 

938.62 

938.48 

938.34 

938.19 

938.05 

937.91 

937.77 

1.20 

0.21 

937.63 

937.48 

•937.33 

937.19 

937.05 

936.90 

936.75 

936.61 

936.46 

936.32 

1.19 

0.22 

936.17 

936.02 

935.88 

935.73 

935.58 

935.43 

935.28 

935.13 

934.98 

934.83 

1.18 

0.23 

934.68 

934.53 

934.38 

934.23 

934.08 

933.93 

933.77 

933.62 

933.47 

933.33 

1.17 

0.24 

933.16 

933.01 

932.85 

932.70 

933.54 

932.39 

932.33 

932.08 

931.93 

931.76 

1.16 

0.25 

931.60 

931.45 

931.29 

931.13 

930.97 

930.81 

930.65 

930.49 

930.33 

930.17 

1.15 

0.26 

930.01 

929.85 

929.69 

929.53 

939.36 

929.201  929.04 

938.87 

938.71 

938.55 

1.14 

0.27 

928.38 

928.22 

928.05 

927.88 

937.73 

927.55|  927.38 

927.22 

927.05 

936.88 

1.13 

0.28 

926.71 

926.54 

926.37 

926.21 

926.03 

925.86 

935.69 

925.53 

925.35 

925.18 

1.12 

0.29 

925.01 

924.83 

924.66 

924.49 

924.31 

924.14 

933.96 

933.79 

923.61 

933.44 

1.11 

0.30 

923.26 

923.08 

922.90 

922.73 

932.55 

922.37 

933.19 

932.01 

921.83 

931.65 

1.10 

0.31 

921.47 

921.29 

921.11 

920.93 

920.74 

930.56 

930.38 

920.20 

920.01 

919.83 

1.09 

0.32 

919.64 

919.46 

919.27 

919.09 

918.90 

918.71 

918.53 

918.34 

918.15 

917.96 

1.08 

0.33 

917.77 

917.581  917.39 

917.30 

917.01 

916.83 

916.63 

916.43 

916.24 

916.05 

1.07 

0.34 

915.86 

915.66 

915.47 

915.27 

915.08 

914.88 

914.68 

914.49 

914.39 

914.09 

1.06 

0.35 

913.90 

913.70 

913.50  913.30 

913.10 

912.90 

913.70 

913.50 

913.29 

912.09 

1.05 

0.36 

911.89 

911.69 

911.48  911.28 

911.07 

910.87 

910.66 

910.46 

910.25 

910.04 

1.04 

0.37 

909.84 

909.63 

909.42i  909.21 

909.00 

908.79 

908.58 

908.37 

908.16 

907.95  1 

1.03- 

0.38 

907.74 

907.52 

907.31 

907.10 

906.88 

906.67 

906.45 

906.24 

906.02 

905.81 

1.02 

0.39 

905.59 

905.37 

905.15 

904.93 

904.71 

904.49 

904.27 

904.05 

903.83 

903.61 

1.01 

0.40 

903.39 

903.17 

902.94 

902.72 

902.50 

902.27 

902.04 

901.82 

901.59 

901.37 

1.00 

0.41 

901.14 

900.91 

900.68 

900.45 

900.22 

899.99 

899.76 

899.53 

899.30 

899.07 

1.00 

0.42 

898.84 

898.60 

898.37 

898.13 

897.90 

897.66 

897.43 

897.19 

896.96 

896.72 

0.99 

0 

1 

2 

3 

4 

6 

6 

7 

8 

9 

* 

Ref,     1 

■"his  refe] 

PS  to  Prc 

)PORTIOI 

TAL  PaB 

Ta,  comi 

non  to  b 

oth,  on  t 

he  prece 

ding  Pag 

e. 

*100 


TABLE     XLIX. 


CONVERSION  TABLE    FROM   ANNUITY  OR   ?i{l-\-a)    TO    SINGLE    PREMIUM    ON    l.OOa 

INTEREST  4  PER  CENT. 

PROPOBTIONAL,  PARTS,  8TJBT. 


X{l  +  a). 


0.43 

0.44 

0.45 

0.46 

0.47 

0.48 

0.49 

0.50 

0.51 

0.52 

0.53 

0.54 

0.55 

0.56 

0.57 

0.58 

0.59 

0.60 

0.61 

0.62 

0.63 

0.64 

0.65 

0.66 


0,5 


0896.48 
5895.38 

0894.07 
5  892.84 

0891.60  1 
5890.35  6 

1 
6 


1,6 


889.08 

887.79 

886.49 
885.18 

883.85 

5J882.50 

0:881.14 

5|879.77 


0878.37  1 
5;876.97  6 

o!875.54 
5J874.10 

0872.6411 
5871.17  6 


869.6811 

868.171  6 

866.64  1 
865.101 

863.531 1 
861.9516 


896.24 
895.04 

893.82 
892.59 

891.35 
890.09 

888.82 
887.53 

886.23 
884.91 

883.58 
882.23 

880.87 
879.49 

878.09 
876.68 

1875.25 
6873.81 

872.35 

870.87 

869.37 
867.86, 


2,7 


3,8 


860.35 
858. 74 

857.10 
855.45 

853.77 
852.08 

850.37 
848.63 

846.88 
845.11 

843.32 

841.50 

839.67 
837.81 

835.93 
834.03 

832.11 
830.17 

828.20 
826.21 

824.20 
822.16 

oj" 


860.03 
858.41 

856.77 
855.11 

853.44 
851.74 

850.02 
848.29 

846.53 
844. 75 

842.95 
841.14 

839.30 
837.44 

835.55 
833. 65 

831.72 

829.77 

827.80 
825.81 

823.79 
821.75 


2896.00 
7894.80 


2 

7 

2 

7 

2 

7 

866.3312 
864. 78  7 

863. 22 1  2 
861.63   7 


893.58 
892.35 

891.10 ' 
889.841 

888.56 

887.27, 

885.97 
884.^65  J 

883.31 ! 
881.96 

880.59 
879.21 

877.81 
876.40 

874.97 
873.52 

872.05 
870.57 

869.07 
867.56 

866.02  3 
864.47  8 
862.9013 
861.32  8 


859.71 
858.09 

856.44 
854. 78 

853.10 
851.40 
849. 68 
847.94 

846.18 
844.39 

842.59 
840. 77 

838.93 
837.06 

835.17 
833.27 
831.33 
829.38 

827.41 
825.41 

823.39 
821.34 

2,7    I 


895.76 
894.55 


4,9 


893.33  4 
892.10  9 


890.85 
889.59 

888.31 
887.01 

885.71 
884.38 

883.04 
881.69 

880.32 
878.93 

877.53 
876.11 

874.68 
873.23 


3871.76 
8870.27 

868.77 
867.25 


865.72 
864.16 


859.39 
857.76 
856.11 
854.45 
852.76 
851.05 

849.33 
847.59 

845.82 
844.04 


842.23 
840.40 

838.55 
836.68 

834.79 

832.88 

830.95 
828.99 

3|827.01 
8825.00 
3|822.98|4 
8|820.93  9 

3.8 


895.52 
894.31 

893.09 
891.85 

890.60 
889.33 

888.05 
886.75 

885.44 
884.12 

882.77 
881.42 

880.04 
878.65 

877.25 
875.83 

874.39 

872.93 


871.46 
869.98 

4868.47 
9  866.95 


862.59  4 
861.00  9 


865.41 

863.85 

862.27 
860.68 

859.06 

857.43 

855.78 
854.11 

852.42 
850. 71 

848.98 
847.23 

845.47 
843.68 

841.87 
840.03 

838.18 
836.31 

834.41 
832.50 

830.56 
828.59 

826.61 
824.60 

822.57 
820.52 

4,9 


9 

9 

9 

9 
9 

9 
9 

9 
9 

9 
10 

10 
10 

10 
10 

10 
10 

10 
11 

11 
11 

11 
11 

11 
11 

11 

12 

12 
12 

12 
12 

12 
12 


10 
10 

10 
10 

10 
10 

10 
10 

10 
11 

11 
11 

8|ll 
11 

11 
11 

12 
12 

12 
12 

12 
12 

12 
13 

13 
13 

13 
13 

13 
13 

14 
14 

14 
14 

14 
14 

15 
15 

15 
15 

15 
15 

16 
16 

16 
16 

16 
16 


3   4 


12 
12 

12 
12 

13 
13 

13 
13 

13 
13 

14 
14 

14 
14 

14 
14 

14 
15 

15 
15 

15 
15 

15 
16 

16 
16 

16 
16 

17 
17 

17 
17 

17 
18 

18 
18 

18 
18 

19 
19 

19 
19 

19 
20 

20 
20 

20 
21 


6    7    8   9 


14 
15 

15 
15 

15 
15 

15 
16 

16 
16 

16 
16 

16 
17 

17 
17 

17 
18 

18 

18 

18 
18 

18 
19 

19 
19 

19 
20 

20 
20 

20 
21 

21 
21 

21 
21 

22 
22 

22 
23 

23 
23 

23 
24, 

24 
24 

24 
25 

6^ 


17 
17 

17 

17 

18 
18 

18 
18 

18 
19 

19 
19 

19 
20 

20 
20 

20 
20 

21 
21 

21 
21 

22 
22 

22 
22 

23 
23 

23 

24 

24 
24 

24 

25 

25 
25 

25 
26 

26 
26 

27 

27 

27 
28 

28 
28 

29 


19 
19 

20 
20 

20 
20 

21 

21 

21 
21 

22 
22 

22 
22 

22 
23 

23 
23 

24 
24 

24 
24 

25 
25 

25 
26 


22 

22 

22 
22 

23 
23 

23 
23 

24 
24 

24 
24 

25 

25 

25 
26 

26 
26 

26 

27 

27 
28 

28 
28 

28 
29 


26  29 
26  30 


2731 
28  31 


29  33  37 


32|36 
3337 


8 


9 


TABLE     XLIX. 


*101 


CONVEKSION  TABLE    FROM   ANNUITY  OR   X{l-\-a)    TO    SINGLE    PREMIUM    ON    1,000. 

INTEREST  4  PER  CENT. 

PROPORTIONAL  PARTS,  SUBT. 


A(l  +  «). 


0.67 
0.68 
0.69 
0.70 
0.71 
0.72 
0.73 
0.74 
0.75 
0.76 
0.77 
0.78 
0.79 
0.80 
0.81 
0.82 
0.83 
0.84 
0.85 
0.86 
0.87 
0.88 
0.89 
0.90 


0,5 


0820.10 
5  818.03 


815.91 
813.78 

811.62 


1,6 


5  809.44 

Oj807.24 
5j805.00 

0802.75 
5  800.46 


798.15 
795.81 

793.45 

791.06 

788.64 
786.19 

783.71 
781.21 

778.68 
776.11 

773.52 
770.90 

768.25 
765.56 

762.85 
760.10 

757.32 
754.51 

751.67 
748.80 

745.89 
742.94 

739.97 
736.96 

733.91 
730.83 

727.71 
724.56 

721.37 

718.14 

714.88 
711.58 

708.24 
704.86 

701.44 
697.99 

694.49 
690.95 

0,5 


819.69 
817.60 

815.49 
813.35 

811.19 
809.00 

806.79 
804.55 

802.29 
800.00 

797.69 
795.34 

792.97 
790.58 

788.15 
785.70 

783.22 

780.71 

778.17 
775.60 

773.00 

770.37 

767.71 
765.02 

762.30 
759.55 

756.76 
753.95 
751.10 

748.22 

745.30 
742.35 

739.37 
736.35 

733.30 

730.21 

727.09 
723.93 

720.73 

717.49 

714.22 
710.91 

707.57 
704.18 

700.76 
697.29 

693.78 
690.24 


2,7 


819.27 
817.18 

815.06 
813.92 


810.75 
808.56 

2|806.35 
7804.10 


801.84 
799.54 

797.33 
794.87 

793.50 
790.09 

787.66 
785.30 

783.73 
780.30 

777.66 
775.08 

772.48 
769.84 

767.18 

764.48 

761.75 
758.99 

756.30 
753.38 
750.53 
747.64 

744.71 
741.76 

738.77 

735.74 

733.68 
729.59 

726.46 
723.29 

730.08 
716.84 

713.56 
710.35 

706.89 
703.50 

700.07 
696.59 

693.08 
689.53 

2,7 


3,8 


818.85 
816.76 

814.64 
813.49 

810.33 
808.13 

805.90 
803.65 

801.38 
799.08 

796.75 
794.40 

793.03 
789.61 

787.17 
784.71 

783.33 
779.69 

777.14 
774.56 

771.95 
769.31 

766.64 
763.94 

761.20 

758.44 

755.64 
753.81 

749.95 
747.05 

744.13 

741.16 

738.17 
735.13 

733.07 
728.96 

725.83 
722.65 

719.44 
716.19 

712.90 
709.58 

706.33 

703.83 

699.37 
695.89 


3  692.37 
8  688.81 

3,8 


4,9 


818.44 
816.33 

814.21 
812.06 

809.88 
807.68 

805.45 
803.20 

800.93 

798.63 

796.28 
793.92 

791.54 
789.13 

786.68 
784.31 

781.71 
779.19 

776.63 
774.04 

771.43 
768.78 

766.10 
763.39 

760.65 

757.88 

755.08 
753.34 

749.37 

746.47 

743.54 
740.57 
737.56 
734.53 

731.45 
738.34 

735.19 
733.01 

718.79 
715.54 

713.24 

708.91 

705.54 
702.13 

698.68 
695.19 

691.66, 
688.09 

4,9 


9 
9 

9 
9 

9 
9 

9 
9 

9 
9 

10 
10 

10 
10 

10 
10 

10 
10 

10 
11 

11 
11 

11 
11 

11 
11 

11 
13 

13 

13 

13 
13 

13 

12 

13 
13 

13 

13 

13 
13 

14 
14 

14 
14 

14 

14 

2 


16  31 
16  31 


33  37 
33  27 


6 

35 
35 

26 
26 

26 
36 

37 
37 

37 
38 

38 
38 

39 
39 

39 
30 

30 
30 

31 
31 

31 
33 

32 
33 

33 
33 

34 
34 

34 
35 

35 

36 

36 
37 

37 
37 

38 
38 

39 
39 

40 
40 

41 
41 

41 
42 

43 
43 


8 

33 
34 

34 
35 

35 
35 

36 

36  41 

37  41 

37143 

37:43 
38|43 

38  43 

39  44 

39  44 

40  45 


39 
30 

30 
30 

31 
31 

31 
33 

33 
32 

33 
33 

33 
34 

34 
35 

35 
35 

36 
36 

37 
37 

38  43  48 
38  43  49 


♦102  TABLE     XL  IX. 

CONVERSION    TABLE    FROM    ANNUITY    OR  A(l  +  a)    TO    SINGLE    PREMIUM    ON    1,000 

PROPORTIONAL   PARTS,   8UBT. 


INTEREST    4    PER   CENT. 


A(l+a). 


0.91 
0.92 
0.93 
0.94 
0.95 
0.96 
0.97 
0.98 
0.99 
1.00 
1.01 
1.02 
1.03 
1.04 
1.05 
1.06 
1.07 
l.OB 
1.09 
1.10 
1.11 
1.12 
1.13 
1.14 


0.5 


687.37 
683.75 

680.09 
376.39 

673.64 
668.85 

665.01 
661.13 
657.21 
653.24 

649.23 
645.16 

641.06 
636.90 

0  632.70 

5  628.44 

0  624.14 

5  619.79 

615.38 
610.93 

606.43 
601.87 

597.26 
592.59 

587.88 
583.10 

578.28 
573.39 

568.45 
563.46 

558.40 
553.29 

548.12 

542.88 

537.59 
532.24 

526.82 
521.34 

0515.80 
5510.19 


1,6 


504.52 

498. 78 

492.98 
487.11 

481.17 
475.16 

469.08 
462.94 


686.65 
683.02 

679.35 

675.64 

671.88 
668.09 

664.24 
660.35 

656.42 
652.44 

648.42 

644.35 

l|640.23 

61636.06 

631.85 
6  627.59 

623.27 
618.91 

614.50 
610.03 

605.52 
600.95 

596.33 
591.66 

586.93 
582.14 

577.31 
572.41 

567.46 
562.45 

557.38 
552.26 

547.07 
541.83 

536.52 
531.16 

525.73 
520.24 

514.68 
509.06 

503.38 
497.63 

491.81 
485.92 

479.97 
473.95 


2,7 


467.86 
461.70 


0,6  1,6 


685.93 
682.29 

678.61 
674.89 
671.13 
667.32 


663.47 
659.57 
655.63 
651.64 
647.61 
643.53 

2639.40 
7635.22 

2631.00 

71626.73 

2622.40 


618.03 

613.61 
609.14 

604.61 
600.03 

595.40 
590.71 

585.97 
581.18 

576.33 
571.43 

566.46 
561.44 

556.36 
551.23 

546.03 
540. 77 

535.46 
530.08 

524.64 
519.13 

513.56 
507.93 

502.23 
496.47 

490.64 
7'484.74 


478.77 
472.74 

466.63 
460.46 

2?r" 


3,8 


685.21 
681.56 

677.87 
674.14 

670.37 
666.55 

662.69 

658.79 

654.83 
650.84 
646.80 
642.71 

638.57 
634.38 

630.15 

625.87 

621.53 
617.15 

612.72 
608.23 

603.70 
599.11 

594.47 

589.77 

585.02 

580.22 

575.35 

8  570.44 

3565.46 
8560.43 


555.34 
550.19 

544.98 
539.72 

534.39 
528.99 

523.54 
518.02 

512.44 
506.80 

501.08 
495.31 


4,9 


4:684.48 
9680.83 


489.46 
483.55 

477.57 
471.52 

465.40 
459.21 

3^8" 


677.13 
673.39 

669.61 
665,78 
661.91 
658.00 

654.04 
650.03 
645.98 
641.88 

637.73 
633.54 

629.30 
625.00 

620.66 
616.27 

4611.83 
9'607.33 


602.78 
598.18 

593.53 

588.82 


4584.06 


579.25 

574.38 
569.45 

564.46 
559.42 

554.32 
549.16 

543.94 

538.65 

533.31 
527.91 

522.44 
516.91 

511.32 
505.66 

499.93 
494.14 

488.29 
482.36 

476.37 
470.30 

464.17 

457.97 

4^ 


1|2 

14 

15 

15 

15 
15 
15 
16 
16 

16 
16 

16 
16 

17 
17 

17 
17 

17 
18 

18 
18 

18 
18 

19 
19 

19 
19 

20 
20 

20 
20 

20 
21 

21 
21 

21 
22 


8 

8 
8 

9 
9 

9 
9 

9 
9 

9 
9 

b 

9 

10 
10 

10 
10 

10 
10 

10 
10 

10 
11 

11 
11 

11 
11 

11 
11 

11 

12 

12 
12 

12 
12 

12 
12 


22 
22 
22 
23 

23 
23 

23 
24 

24 

24j32 

2433 
25J33 

25^33 
25'34 

26  34 
26134 

2635 
26|35 

27  36 


28  38 


30,40 
30140 

31  ki 

41 


22 
22 

22|34 

23'34 

23134 

23 

23 


42 
42 

43 
43 

44 
44 

45 
45 

46 
46 

47 
48 

48 
49 

49 
50 


36 
37 

37 
38 

38 
38 
39 
39 
40 
40 
41 
41 

42 

42 

43 
43 

44 

44 

45 
45 

46 
46 

47 
47 

48 
48 

49 
49 

50 
51 

51 

52 

52 
53 

54 

54 

65 
55 

56 

57 

57 
58 

59 
59 

60 
61 

61 
62 


8 


56  65 

67|66 

5767 

58  67 

59  68 
69 


63  73 

74 


6  16 


58 
69 

59 
60 

61 
61 

62 
63 

64 
64 

65 
66 

67 
67 

68 
69 

70 
71 

71 

72 

73 

74 

76 

76 

76 

77 

78 
79 

80 
81 

82 
83 

84 
86 

86 

87 

88 
89 

90 
91 

92 
93 

94 

96 

96 
97 

98 
100 

~8~ 


9 

65 
66 

67 
68 

68 
69 
70 
71 

71 

72 

73 

74 
75 
76 

77 
77 

78 
79 

80 
81 

82 
83 

84 
85 

86 

87 

88 
89 

90 
91 

92 
93 

94 
96 

96 
98 

99 
100 

101 
102- 

103 
104 

106 
107 

108 
109 

111 
112 


TABLE     XLIX.  *103 

CONVERSION  TABLE    PROM  ANNUITY  OR  ^l+a)    TO    SINGLE    PREMIUM    ON    1,000. 

INTEREST  4  PER  CENT. 

PROPORTIONAL  PARTS,  SUBT. 


Hl  +  a). 


1.15 

1.16 

1.17 

1.18 

1.19 

1.20 

1.21 

1.22 

1.23 

1.24 

1.25 

1.26 

1.27 

).28 

1.29 

1.30 

1.31 

1.32 

1.33 

1.34 

1.35 

1.36 

1.37 

1.38 


0,5 


0456.72 
5  450.43 


444.06 
437.62 

431.11 
424.52 


1,6 


0417.86  1 
5411.12  6 


0404.30 
5  397.40 

0390.43 
5  383.37 


376.23 
369.00 


0361.70 
5354.31 

0346.83 
5  339.27 
0331.61 
5  323.87 


455.46 
449.16 

442.78 
436.33 

429.80 
423.20 

416.52 
409.76 

402.93 
396.01 

389.02 
381.95 

374.79 
367.55 

360.23 
352.82 

345.32 
337.74 


2,7 


1330.07  2 
6322.32  7 


2 

7 

2 

7 

2 

7 

2 

7 

2401.55  3 
7394.62  8 


454.21 

447.89 

441.50 
435.03 
428.49 
421.87 

415.17 
408.40 


316.05 
308.13  6 


1 
6 

1 
6 

1 
6 

1 
6 

1 
6 

1 
6 

1 
6 

1 
6 

1 
6 

1 
6 

1 
6 

1 
6 

77.37  1 
66.6916 


300.11 
292.01 

283.81 
275.52 

267.13 
258.64 

250.06 
241.38 

232.59 
223.71 

214.72 
205.62 

196.42 
187.12 

177.71 
168.18 

158.55 
148.81 

138.95 
128.98 

118.90 
108.69 

98.37 
87.93 


0,6 


314.47 
306.53 

298.50 
290.38 

282.16 
273.85 

265.44 
256.93 

248.33 
239.63 

230.82 
221.92 

212.91 
203.79 

194.57 
185.25 

175.81 
166.27 
156.61 
146.85 

136.97 
126.97 

116.87 
106.64 

96.29 
85.83 

75.24 
64.54 

1,6 


3,8 


4,9 


452.95  4 
446.62  9 

440.21 
433.73 


387.61 
380.52 

373.35 
366.09 

358.75 
351.33 

343.81 
336.22 

328.53 
320. 75 

312.89 
304.93 

296.88 
288.74 

280.51 
272.17 
263.75 
255.22 

246.60 

237.87 

229.05 
220.12 

211.09 
201.96 

192.71 
183.37 
173.91 
164.35 

154.67 
144.88 

134.98 
124. 96i 

114.83 
104.58 

94.21 

83.72 

73.11 
62.38 

2/7~ 


427.17 
420.54 

413.83 
407.04 

400.17 
393.23 

386.^ 
379.09 

371.90 
364.63 

357.27 
349.83 


342.30  4 
334.69  9 


326.98 
319.19 


311.30  4 
303.33  9 


3295.26 
8287.10 


278.85 
270.50 

262.05 
253.50 

244.86 
236.12 

227.27 
218.32 

209.27 
200. 12 

190.85 
181.48 

172.01 
162.42 

152.72 
142.91 

132.98 
122.94 

112.79 
102.52 

92.12 
81.61 


451.69 
445.34 

438.92 
432.42 

425.85 
419.20 

412.47 
405.67 

398.79 
391.83 

384.79 
377.66 

370.45 
363.16 

355.79 
348.33 

340.79 
333.15 

325.43 
317.62 

309.72 
301.72 

293.64 
285.46 

^77.19 
268.82 

260.35 
251.78 

243.12 
234.36 

225.49 
216.52 

207.45 
198.27 
188.99 
179.60 

170.10 
160.49 

150.77 
140.93 

4|l30.99 
9120.92 


70.98  4 
60.22  9 


110.74 
100.45 

90.03 
79.49 

68.83 
58.05 


3,8  I  4,9 


13 
13 

13 
13 

13 
13 

13 
14 

14 
14 

14 
14 

14 
15 

15 
15 

15 
15 

15 
16 

16 
16 

16 
16 

17 
17 

17 
17 

17 

18 

18 
18 

18 
18 

19 


32148 


19 

19 
19 

19 
20 

20 

20 

20 
21 

21 
21 

21 
22 


32 
33 

33 
34 

34 
34 

35 
35 

36 
36 

36 
37 

37 

38 

38 
39 

39 
39 

40 
40 

41 
41 

42 
42 

43 
43 

2 


49 
49 

50 
50 

51 
51 

52 
53 

53 
54 

55 
55 

56 
56 

57 
58 

58 
59 

60 
60 

61 
62 

63 
63 

64 
65 


50 
61 

52 
52 

53 
53 

54 
55 

55 
56 

56 

57 

58 

58 

59 
60 

60 
61 

62 
63 

63 
64 

65 
66 

66 
67 
68 
69 

69 
70 

71 

72 

73 

74 

74 
75 

76 
77 
78 
79 

80 
81 

82 
83 

84 

85 

85 
86 


63 
64 

64 
65 

66 
67 

67 
68 

69 
70 

71 
71 

72 
73 

74 
75 

76 

77 

77 
78 

79 
80 

81 
82 

83 

84 

85 
86 

87 
88 

89 
90 

91 
92 

93 
94 

95 
96 

97 
99 

100 
101 

102 
103 

104 

106 

107 
108 


6 

75 
76 

77 
78 

79 
80 

81 

82 

83 
84 

85 
86 

87 

88 

89 
90 

91 
92 

93 
94 

95 
96 

97 
98 

99 
101 

102 
103 

104 
105 

107 
108 

109 
110 

112 
113 

114 
116 

117 


89 

90 
91 

92 
93 

94 
95 

97 
98 

99 
100 

101 
102 

103 
105 

106 
107 

108 
109 

111 
112 

113 
115 

116 
117 

119 
120 

122 
123 

124 
126 

127 

129 

130 
132 

133 
135 

136 


8 

101 
102 

103 
104 

105 
107 

108 
109 

110 
112 

113 
114 

116 
117 

118 
120 

121 
123 

124 

125 

127 
128 

130 
131 

133 
134 

136 
137 

139 
141 

142 
144 


9 

113 
115 

116 
117 

119 
120 

121 
123 

124 

125 

127 

129 

130 
131 

133 

135 

136 
138 

139 
141 

143 
144 

146 
148 

149 
151 

153 

154 

156 
158 

160 
162 


146164 
147166 


118138 
120  140 


121 

123 
124 

125 
127 

128 
130 

6 


141 

143 
144 

146 
148 

150 
J51 


149 
151 

152 
154 

156 

158 

160 
161 

163 
165 

167 
169 

171 
173 

8~ 


167 
169 

172 

173 

175 

177 

179 
181 

184 
186 

188 
190 

192 
195 

9 


*104 


TABLE    L. 


SINGLE    PREMIUM    OR    RESERVE    BY    MONTHS,    ON    PAID-UP    INSURANCE    OF    1,000 

FOR  THE    WHOLE  LIFE. 

4  PER  CENT. 


AGE. 

X+n. 

Om. 

|m. 

l|m. 

3im. 

3im. 

Hm. 

5^m. 

AGE. 

x-\-n. 

*Dec. 

Nov. 

Oct. 

Sept. 

Aug. 

July. 

10 

202.630 

303.753 

203.000 

303.346 

303.493 

303.739 

303.986 

10 

11 

205.587 

305.716 

205.972 

306.338 

306.485 

306.741 

306.997 

11 

12 

208.665 

308.799 

209.067 

309.334 

209.603 

209.869 

210.137 

12 

13 

211.878 

313.017 

213.396 

313.575 

213.854 

213.133 

313.413 

13 

14 

215.224 

315.369 

315.658 

315.948 

316.338 

216.538 

316.817 

14 

15 

218.699 

218.850 

319.153 

319.454 

319.755 

330.057 

330.359 

15 

16 

223.321 

333.478 

333.793 

333.107 

333.433 

333. 736 

334.051 

16 

17 

226.095 

336.358 

336.586 

336.913 

337.339 

337.566 

337.894 

17 

18 

230.019 

330.189 

330.539 

330.  §69 

331.310 

331.550 

331.890 

18 

19 

234.101 

334.378 

234.633 

334.986 

335.340 

335.694 

336.048 

19 

20 

238.349 

338.533 

338.901 

339.369 

339.636 

340.004 

340.373 

20 

21 

242.763 

343.954 

343.336 

343.718 

344.100 

344.482 

344.864 

21 

22 

247.348 

347.547 

347.944 

348.341 

348.739 

349.136 

349.533 

22 

23 

252.116 

353.333 

353.735 

353.147 

353.560 

353.973 

354.385 

23 

24 

257.065 

257.379 

357.707 

358.135 

358.564 

358.993 

259.430 

24 

25 

262.203 

363.435 

363.870 

263.315 

363.759 

364.304 

364.649 

25 

26 

267.540 

367.771 

368.331 

368.693 

369.153 

369.614 

370.074 

26 

27 

273.069 

373.308 

373.786 

374.364 

374.743 

375.330 

375.698 

27 

28 

278.806 

379.054 

379.550 

380.046 

380.541 

381.037 

381.533 

28 

29 

284.756 

285.012 

385.535 

386.038 

386.551 

387.064 

387.577 

29 

30 

290.909 

291.175 

391.706 

393.337 

292.768 

393.399 

393.830 

30 

31 

297.284 

397.559 

398.109 

398.659 

399.310 

399.760 

300.310 

31 

32 

303.886 

304.171 

304.739 

305.308 

305.878 

306.447 

307.015 

32 

33 

310.714 

311.008 

311.596 

313.185 

313.773 

313.361 

313.949 

33 

34 

317.773 

318.077 

318.685 

319.392 

319.901 

330.508 

331.116 

3^ 

35 

335.066 

335.379 

336.006 

336.633 

337.360 

^37.887 

338.514 

35 

36 

333.588 

333.913 

333.559 

334.307 

334.854 

335.503 

336.149 

36 

37 

340.359 

340.693 

341.361 

343.029 

343.696 

343.364 

344.033 

37 

38 

348.373 

348.717 

349.405 

350.093 

350.783 

351.470 

353.158 

38 

39 

356.630 

356.984 

.357.693 

358.403 

359.110 

359.819 

360.538 

39 

40 

365.134 

365.498 

366.337 

366.956 

367.684 

368.413 

369.143 

40 

41 

373.879 

374.354 

375.004 

375.754 

376.504 

377.354 

378.004 

41 

42 

383.879 

383.364 

384.034 

384.804 

385.574 

386.344 

387.114 

42 

43 

393.119 

393.514 

393.305 

394.096 

394.887 

395.678 

396.469 

43 

44 

401.608 

403.013 

403.824 

403.635 

404.446 

405.257 

406.068 

44 

45 

411.338 

411.753 

413.584 

413.415 

414.346 

415.077 

415.908 

45 

46 

431.309 

431.734 

433.585 

433.435 

434.387 

435.137 

435.988 

46 

47 

431.516 

431.951 

433.831 

433.690 

434.560 

435.439 

436.399 

47 

48 

441.953 

443.397 

443.386 

444.175 

445.064 

445.953 

446.843 

48 

49 

453.618 

453.071 

453.978 

454.885 

455.792 

456.699 

457.606 

49 

50 

463.500 

463.963 

464.887 

465.811 

466.736 

467.660 

468.585 

50 

51 

474.594 

475.065 

476.006 

476.947 

477.888 

478.839 

479.770 

51 

52 

485.889 

486.368 

487.335 

488.383 

489.240 

490.197 

491.154 

52 

53 

497.376 

497.863 

498.835 

499.807 

500.780 

501.753 

503.735 

53 

54 

509.046 

509.539 

510.536 

511.514 

513.500 

513.488 

514.475 

54 

*  Months  of  Entry  for  Annual  Valuation  Dec.  31. 


♦105 


TABLE    L. 


SINGLE   PREMIUM    OR    RESERVE    BY    MONTHS,  ON   PAID-UP    INSURAJ^CE    OF    1,000 

FOR  THE  WHOLE  LIFE. 

4  PER  CENT. 


AGE. 

6m. 

6|m. 

7im. 

8im. 

9^m. 

lO^m. 

IHm. 

AGE, 

x-\-n. 
10 

June. 

May. 

April. 

March. 

Feb. 

Jan. 

10 

204.109 

204.232 

204.479 

204.725 

204.971 

205.217 

205.464 

11 

207.126 

207.255 

207.511 

207.767 

208.024 

208.280 

208.536 

11 

12 

210.271 

210.405 

210.673 

210.940 

211.209 

211.476 

211.744 

12 

13 

213.551 

213.690 

213.969 

214.248 

214.527 

214.806 

215.085 

13 

14 

216.962 

217.107 

217.396 

217.686 

217.975 

218.265 

218.554 

14 

15 

220.510 

220.661 

220.963 

221.265 

221.566 

221.868 

222.170 

15 

16 

224.208 

224.365 

224.680 

224.994 

225.309 

225.623 

225.938 

16 

17 

228.057 

228.220 

228.548 

228.875 

229.201 

229.528 

229.856 

17 

18 

232.060 

232.2.30 

232.570 

232.910 

233.251 

233.591 

233.931 

18 

19 

236.225 

236.402 

236.756 

237.110 

237.464 

237.818 

238.172 

19 

20 

240.556 

240.740 

241.108 

241.476 

241.843 

242.211 

242.579 

20 

21 

245.055 

245.246 

245.628 

246.010 

246.393 

246.775 

247.157 

21 

22 

249.732 

249.931 

250.328 

250.725 

251.123 

251.520 

251.917 

22 

23 

254.591 

254.797 

255.210 

255. 622 

256.034 

256.446 

256.859 

23 

24 

259.634 

259.848 

260.276 

260. 704 

261.133 

261.561 

261.989 

24 

25 

264.871 

265.093 

265.538 

265.983 

266.428 

266.873 

267.318 

25 

26 

270.305 

270.536 

270.996 

271.457 

271.917 

272.378 

272.838 

26 

27 

275.937 

276.176 

276.654 

277.132 

277.611 

278.089 

278.567 

27 

28 

281.781 

282.029 

282.525 

283.021 

283.516 

284.012 

284.508 

28 

29 

287.833 

288.089 

288.602 

289.115 

289.627 

290.140 

290.653 

29 

30 

294.096 

294.362 

294.893 

295.424 

295.956 

296.487 

297.018 

30 

31 

300.585 

300.860 

301.410 

301.960 

302.511 

303.061 

303.611 

31 

32 

307.300 

307.585 

308.153 

308.722 

309.292 

309.861 

310.429 

32 

33 

314.243 

314.537 

315.125 

315.714 

316.302 

316.891 

317.479 

33 

34 

321.420 

32L724 

322.332 

322.939 

323.547 

324.154 

324.762 

34 

35 

828.827 

329.140 

329.767 

330.394 

331.021 

331.648 

332.275 

35 

36 

336.473 

336.797 

337.444 

338.092 

338.740 

339.388 

340.035 

36 

37 

344.366 

344.700 

345.368 

346.036 

346.703 

347.371 

348.039 

37 

38 

352.502 

352.846 

353.534 

354.222 

354.910 

355.598 

356.286 

38 

39 

360.882 

361.236 

361.945 

362.654 

363.362 

364.071 

364.780 

39 

40 

369.506 

369.870 

370.599 

371.328 

372.057 

372.786 

373.515 

40 

41 

378.379 

378.754 

379.504 

380.254 

381.004 

381.754 

382.504 

41 

42 

387.499 

387.884 

388.654 

389.424 

390.194 

390.964 

391.734 

42 

43 

396.864 

397.259 

398.050 

398.841 

399.631 

400.422 

401.213 

43 

44 

406.473 

406.878 

407.689 

408.500 

409.311 

410.122 

410.933 

44 

45 

416.323 

416.738 

417.569 

418.400 

419.232 

420.063 

420.894 

45 

46 

426.413 

426.838 

427.689 

428.539 

429.390 

430.240 

431.091 

46 

47 

436.734 

437.169 

438.039 

438.908 

439.779 

440.648 

441.518 

47 

48 

447.286 

447.730 

448.619 

449.508 

450.396 

451.285 

452.174 

48 

49 

458.059 

458.512 

459.419 

460.326 

461.233 

462.140 

.463.047 

49 

50 

469.047 

469.509 

470.434 

471.358 

472.283 

473.207 

474.132 

50 

51 

480.241 

480.712 

481.653 

482.594 

483.536 

484.477 

485.418 

51 

52 

491.633 

492.112 

493.069 

494.026 

494.983 

495.940 

496.897 

52 

53 

503.211 

503.697 

504.670 

505.642 

506.615 

507.587 

508.560 

53 

54 

514.968 

515.461 

516.448 

517.436 

518.422 

519.410 

520.397 

54 

*106^ 


TABLE     L. 


SINGLE    PREMIUM    OR   RESERVE    BY  MONTHS,    ON    PAID-UP    INSURANCE    OP    1.000 

FOR    THE    WHOLE    LIFE. 

4  PER  CENT. 


ACtE. 

x+n. 

Cm. 

W- 

l^m. 

2^m. 

S^m. 

^m. 

5|m. 

AGE. 

x  +  n. 

*Dec. 

Nov. 

Oct. 

Sept. 

Aug. 

July. 

55 

520.890 

521.390 

522.389 

523.388 

524.388 

525.387 

526.386 

55 

56 

532.882 

533.388 

534.399 

535.411 

536.421 

537.433 

538.444 

56 

57 

545.019 

545.530 

546.551 

547.573 

548.594 

549.616 

550.637 

57 

58 

557.277 

557.792 

558.823 

559.853 

560.884 

561.914 

562.945 

58 

59 

569.642 

570.161 

571.200 

572.238 

573.276 

574.314 

575.353 

59 

60 

582.103 

582.625 

583.670 

584.714 

585.759 

586.803 

587.848 

60 

61 

594.636 

595.160 

596.208 

597.256 

598.305 

599.353 

600.401 

61 

62 

607.214 

607.740 

608.791 

609.842 

610.893 

611.944 

612.995 

62 

63 

619.829 

620.355 

621.408 

622.460 

623.513 

624.565 

625.618 

63 

64 

632.458 

632.983 

634.034 

635.085 

636.136 

637.187 

638.238 

64 

65 

645.069 

645.593 

646.641 

647.689 

648.736 

649.784 

650.832 

65 

66 

657.643 

658.165 

659.208 

660.251 

661.295 

662.338 

663.381 

66 

67 

670.162 

670.680 

671.716 

672.753 

673.789 

674.826 

675.862 

67 

68 

682.598 

683.112 

684.141 

685.169 

686.198 

687.226 

688.255 

68 

69 

694.941 

695.450 

696.467 

697.484 

698.502 

699.519 

700.536 

69 

70 

707.148 

707.651 

708.656 

709.661 

710.666 

711.671 

712.676 

70 

71 

719.211 

719.706 

720.697 

721.688 

722.678 

723.669 

724.660 

71 

72 

731.099 

731.586 

732.561 

733.536 

734.510 

735.485 

736.460 

72 

73 

742.795 

743.274 

744.232 

745.189 

746.148 

747.105 

748.063 

73 

74 

754.288 

754.757 

755.694 

756.631 

757.568 

758.505 

759.442 

74 

75 

765.535 

765.994 

766.910 

767.828 

768.744 

769.662 

770.578 

75 

76 

776.539 

776.987 

777.882 

778.778 

779.673 

780.569 

781.464 

76 

77 

787.285 

787.721 

788.592 

789.464 

790.335 

791.207 

792.078 

77 

78 

797.743 

798.167 

799.014 

799.862 

800.710 

801.558 

802.405 

78 

79 

807.914 

808.325 

809.148 

809.970 

810.792 

811.614 

812.437 

79 

80 

817.783 

818.181 

818.978 

819.775 

820.573 

821.370 

822.167 

80 

81 

827.346 

827.732 

828.,505 

829.277 

830.049 

830.821 

831.594 

81 

82 

836.614 

836.987 

837.733 

838.480 

839.225 

839.972 

840.718 

82 

83 

845.569 

845.931 

846.655 

847.379 

848.103 

848.827 

849.551 

83 

84 

854.256 

854.607 

855.309 

856.010 

856.712 

857.413 

858.115 

84 

85 

862.677 

863.019 

863.704 

864.389 

865.073 

865.758 

866.443 

85 

86 

870.893 

871.231 

871.908 

872.584 

873.262 

873.938 

874.615 

86 

87 

879.012 

879.349 

880.022 

880.695 

881.367 

882.040 

882.713 

87 

88 

887.089 

887.437 

888.132 

888.827 

889.523 

890.218 

890.913 

88 

89 

895.433 

895.740 

896.354 

896.969 

897.583 

898.198 

898.812 

89 

90 

902.805 

903.066 

903.589 

904.111 

904.635 

905.157 

905.680 

90 

91 

909.076 

909.321 

909.811 

910.301 

910.792 

911.282 

911.772 

91 

92 

914.958 

915.194 

915.665 

916.137 

916.608 

917.080 

917.551 

92 

93 

920.617 

920.841 

921.288 

921.735 

922.183 

922.630 

923.077 

93 

94 

925.985 

926.203 

926.639 

927.075 

927.512 

927.948 

928.384 

94 

95 

931.219 

931.457 

931.934 

932.410 

932.887 

933.363 

933.840 

95 

96 

936.936 

537.147 

937.570 

937.992 

938.414 

938.836 

939.259 

96 

97 

942.005 

942.305 

942.906 

943.506 

944.108 

944.708 

945.309 

97 

98 

949.212 

949.726 

950.758 

951.780 

952.806 

953.833 

954.860 

98 

99 

1  961.537 

1 

963.140 

966.345 

969.550 

972.756 

975.961 

979.166 

99 

Months  of  Entry  for  Annual  Valuation  Dec.  31. 


♦lO-? 


TABLE     L. 


SINGLE    PREMIUM    OR    RESERVE    BY    MONTHS,    ON    PAID-UP    INSURANCE    OF    1,000 

FOR    THE    WHOLE    LIFE. 

4  PER    CENT. 


AGE. 
x-\-n. 

6m. 

6im. 

7im. 

8im. 

9|^m. 

10|m. 

11  |m. 

AGE. 

X-\-7l. 

June. 

May. 

April. 

March. 

Feb. 

Jan. 

55 

526.886 

627.386 

528.385 

529.384 

530.384 

531.383 

532.382 

55 

56 

538.950 

539.456 

540.467 

541.479 

542.490 

543.502 

544.513 

56 

57 

551.148 

551.659 

552.680 

553.702 

554.723 

555.745 

556.766 

57 

58 

563.460 

563.975 

565.006 

566.036 

567.066 

568.096 

569.127 

58 

59 

575.872 

576.391 

577.430 

578.468 

579.507 

580.545 

581.584 

59 

60 

588.370 

588.892 

589.937 

590.981 

592.025 

593.069 

594.114 

60 

61 

600.925 

601.449 

602.497 

603.545 

604.594 

605.642 

606.690 

61 

62 

613.521 

614.047 

615.098 

616.149 

617.201 

618.252 

619.303 

62 

63 

626.144 

626.670 

627.723 

628.775 

629.827 

630.879 

631.932 

63 

64 

638.763 

639.288 

640.339 

641.390 

642.442 

643.493 

644.544 

64 

65 

651.356 

651.880 

652.928 

653.976 

655.023 

656.071 

657.119 

65 

66 

663.903 

664.425 

665.468 

666.511 

667.554 

668.597 

669.640 

66 

67 

676.380 

676.898 

677.934 

678.971 

680.007 

681.044 

682.080 

67 

68 

688.769 

689.283 

690.312 

691.340 

692.370 

693.398 

694.427 

68 

69 

701.045 

701.554 

702.571 

703.588 

704.605 

705.622 

706.639 

69 

70 

713.179 

713.682 

714.687 

715.692 

716.698 

717.703 

718.708 

70 

71 

725.155 

725.650 

726.641 

727.632 

728.622 

729.613 

730.604 

71 

72 

736.947 

737.434 

738.409 

739.384 

740.358 

741.333 

742.308 

72 

73 

748.542 

749.021 

749.979 

750.936 

751.894 

752.851 

753.809 

73 

74 

759.911 

'760.380 

761.317 

762.254 

763.192 

764.129 

765.066 

74 

75 

771.037 

771.496 

772.412 

773.330 

774.246 

775.164 

776.080 

75 

76 

781.912 

782.360 

783.255 

784.151 

785.046 

785.942 

786.837 

76 

77 

792.514 

792.950 

793.821 

794.693 

795.564 

796.436 

797.307 

77 

78 

802.829 

803.253 

804.100 

804.948 

805.795 

806.643 

807.490 

78 

79 

812.848 

813.259 

814.082 

814.904 

815.727 

816.549 

817.372 

79 

80 

822.565 

822.963 

823.760 

824.557 

825.354 

826.151 

826.948 

80 

81 

831.980 

832.366 

833.139 

833.911 

834.683 

835.455 

836.228 

81 

82 

841.091 

841.464 

842.210 

842.957 

843.703 

844.450 

845.196 

82 

83 

849.913 

850.275 

850.999 

851.723 

852.446 

853.170 

853.894 

83 

84 

858.466 

858.817 

859.519 

860.220 

860.923 

861.624 

862.326 

84 

85 

866.785 

867.127 

867.812 

868.497 

869.181 

869.866 

870.551 

85 

86 

874.953 

875.291 

875.968 

876.644 

877.321 

877.997 

878.674 

86 

87 

883.050 

883.387 

884.060 

884.733 

885.406 

886.079 

886.752 

87 

88 

891.261 

891.609 

892.304 

892.999 

893.695 

894.390 

895.085 

88 

89 

899.119 

899.426 

900.040 

900.655 

901.269 

901.884 

902.498 

89 

90 

905.941 

906.202 

906.725 

907.247 

907.770 

908.292 

908.815 

90 

91 

912.017 

912.262 

912.752 

913.242 

913.733 

914.223 

914.713 

91 

92 

917.787 

918.023 

918.494 

918.966 

919.438 

919.910 

920.381 

92 

93 

923.301 

923.525 

923.972 

924.419 

924.867 

925.314 

925.761 

93 

94 

928.602 

928.820 

929.256 

929.692 

930.129 

930.565 

931.001 

94 

95 

934.078 

934.316 

934.793 

935.269 

935.745 

936.221 

936.698 

95 

96 

939.470 

939.681 

940.104 

940.526 

940.949 

941.371 

941.794 

96 

97 

945.609 

945.909 

946.510 

947.110 

947.711 

948.311 

948.912 

97 

98 

955.374 

955.888 

956.915 

957.942 

958.969 

959.996 

961.023 

98 

99 

980.769 

982.372 

985.577 

988.782 

991.987 

995.192 

998.397 

99 

♦108 


TABLE     LI. 


LOGARITHM    OF   THE    SINGLE    PREMIUM    BY    MONTHS,    ON    1  INSURED    FOR    THE 

WHOLE    LIFE. 

4  PER  CENT. 


AGE. 

Om. 

^m. 

l^m. 

2^m. 

3^m. 

4im. 

5Jm. 

AGE 

x-\-n. 

♦Dec. 

Nov. 

Oct. 

Sept. 

Aug. 

July. 

10 

1.306703 

1.306967 

1.307496 

1.308022 

1.308549 

1.309074 

1.309601 

10 

11 

.312996 

.313267 

.313808 

.314348 

.314889 

.315427 

.315964 

11 

12 

.319450 

.319728 

.320286 

.320839 

.321395 

.321948 

.322503 

12 

13 

.326086 

.326371 

.326942 

.327512 

.328082 

.328651 

.329219 

13 

14 

.332890 

.333183 

.333766 

.334349 

.334932 

.335514 

.336093 

14 

15 

1.339847 

1.340147 

1.340745 

1.341344 

"1.341939 

T.  342535 

1.343131 

15 

16 

.346980 

.347287 

.347902 

.348513 

.349126 

.349736 

.350347 

16 

17 

.354290 

.354604 

.355233 

.355860 

.356483 

.357107 

.357733 

17 

18 

.361763 

.362084 

.362725 

.363366 

.364007 

.364645 

.365282 

18 

19 

.369403 

.369731 

.370388 

.371042 

.371696 

.372349 

.373000 

19 

20 

1.377213 

1.377548 

1.378218 

1.378886 

1.379552 

1.380218 

1.380884 

20 

21 

.385182 

.385524 

.386207 

.386887 

.387568 

.388247 

.388925 

21 

22 

.393309 

.393658 

.394354 

.395049 

.395744 

.396436 

.397128 

22 

23 

.401601 

.401955 

.402666 

.403373 

.404081 

.404786 

.405492 

23 

24 

.410042 

.410404 

.411126 

.411847 

.412568 

.413286 

.414003 

24 

25 

1.418637 

1.419005 

T.  419741 

i.  420476 

T.421207 

1.421939 

1.422670 

25 

26 

.427389 

.427764 

.428509 

.429255 

.429999 

.430742 

.431482 

26 

27 

.436272 

.436653 

.437412 

.438168 

.438925 

.439680 

.440434 

27 

28 

.445303 

.445688 

.446459 

.447230 

.447997 

.448764 

.449530 

28 

29 

.454473 

.454863 

.455645 

.456424 

.457202 

.457979 

.458754 

29 

30 

T.  463757 

i. 464155 

1.464945 

1.465736 

1.466524 

1.467311 

i.468096 

30 

31 

.473172 

.473573 

.474376 

.475176 

.475976 

.476774 

.477570 

31 

32 

.482711 

.483118 

.483928 

.484738 

.485548 

.486356 

.487160 

32 

33 

.492361 

.492771 

.493592 

.494412 

.495228 

.496045 

.496859 

33 

34 

.502117 

.502532 

.503362 

.504188 

.505015 

.505839 

.506662 

34 

35 

1.511971 

1.512390 

1.513226 

1.514060 

1.514893 

T.  515724 

1.516554 

35 

36 

.521906 

.522330 

.523173 

.524015 

.524855 

.525695 

.526532 

36 

37 

.531937 

.532363 

.533214 

.534063 

.534909 

.535755 

.536599 

37 

38 

.542045 

.542473 

.543329 

.544184 

.545037 

.545888 

.546738 

38 

39 

.552218 

.552649 

.553511 

.554370 

.555227 

.556084 

.556939 

39 

40 

T.  562452 

1.562885 

1.563750 

T.564614 

1.565475 

1.566335 

1.567193 

40 

41 

.572731 

.573166 

.574036 

.574904 

.575770 

.576634 

.577496 

41 

42 

.583062 

.583498 

.584369 

.585239 

.586107 

.586974 

.587839 

42 

43 

.593418 

.593855 

.594730 

.595602 

.596473 

.597342 

.598209 

43 

44 

.603802 

.604240 

.605115 

.605989 

.606861 

.607731 

.608599 

44 

45 

1.614199 

T.  614637 

1.615512 

1.616386 

1.617259 

1.618129 

1.618997 

45 

46 

.624601 

.625038 

.625914 

.626787 

.627660 

.628529 

.629397 

46 

47 

.634997 

.635434 

.636308 

\    .637179 

.638050 

.638917 

.639784 

47 

48 

.645376 

.645812 

.646684 

1  .647554 

.648423 

.649289 

.650154 

48 

49 

.655732 

.656166 

.657035 

1  .657901 

.658767 

.659630 

.660492 

49 

50 

1.666050 

1.666483 

1.667347 

1.668210 

T.  669071 

1.669930 

1.670789 

50 

51 

.676322 

.676753 

.677612 

.678470 

.679326 

.680180 

.681033 

51 

52 

.686537 

.686965 

.687819 

.688671 

.689522 

.690370 

.691218 

52 

53 

.696685 

.697109 

.697957 

.698802 

.699647 

.700489 

.701331 

53 

54 

.706757 

1 

.707177 

.708018 

.708858 

.709694 

.710530 

.711364 

54 

*  Moutha  of  Entry  for  Annual  Valuation  Dec.  31. 


♦109 


TABLE     LI. 


LOGARITHM    OF   THE    SINGLE    PREMIUM    BY    MONTHS,    ON    1    INSURED    FOR    THE 

WHOLE  LIFE. 

4  PER  CENT. 


AGE. 

x-\-n. 

10 

6m. 

6^m. 

7ini.  . 

8^in. 

9im. 

lO^m. 

ll^m. 

AGE. 

x-\-n. 

10 

June. 

May. 

April. 

March. 

Feb. 

Jan. 

1.309862 

1.310124 

1.310649 

1.311171 

i.311692 

1.312214 

1.312735 

11 

.316235 

.316505 

.317041 

.317577 

.318113 

.318648 

.319181 

11 

12 

.322779 

.323056 

.323609 

.324159 

.324712 

.325261 

.325811 

12 

13 

.329502 

.329784 

.330351 

o330917 

.331482 

.332046 

.332610 

13 

14 

.336384 

.336674 

.337252 

.337830 

.338407 

.338984 

.339559 

14 

15 

1.343428 

1.343726 

1.344320 

T.344913 

1.345503 

1.346095 

1.346685 

16 

16 

.350651 

.350955 

.351564 

.352171 

.352778 

.353384 

.353989 

16 

17 

.358043 

.358354 

.358977 

.359599 

.360217 

.360835 

.361456 

17 

18 

.365600 

.365918 

.366544 

.367188 

.367824 

.368456 

.369088 

18 

19 

.373326 

.373651 

.374301 

.374950 

.375598 

.376244 

.376891 

19 

20 

1.381216 

T.381548 

1.382211 

1.382874 

1.383533 

1.384194 

1.384853 

20 

21 

.389264 

.389602 

.390278 

.390953 

.391628 

.392301 

.392973 

21 

22 

.397474 

.397820 

.398510 

.399198 

.399886 

.400573 

.401258 

22 

23 

.405843 

.406194 

.406898 

.407598 

.408298 

.408996 

.409694 

23 

24 

.414362 

.414720 

.415434 

.416148 

.416862 

.417573 

.418283 

24 

25 

T.  423035 

1.423398 

1.424127 

1.424854 

1.425580 

1.426305 

1.427028 

25 

26 

.431854 

.432225 

.432963 

.433701 

.434436 

.435172 

.435905 

26 

27 

.440810 

.441186 

.441937 

.442687 

.443437 

.444184 

.444930 

27 

28 

.449912 

.450294 

.451057 

.451819 

.452578 

.453337 

.454095 

28 

29 

.459141 

.459527 

.460299 

.461071 

.461840 

.462608 

.463375 

29 

30 

T.  468489 

1.468882 

1.469665 

1.470446 

1.471227 

T.  472006 

1.472783 

30 

31 

.477967 

.478364 

.479158 

.479949 

.480741 

.481530 

.482317 

31 

32 

.487563 

.487965 

.488766 

.489568 

.490369 

.491167 

.491963 

32 

33 

.497265 

.497672 

.498483 

.499294 

.500102 

.500910 

.501715 

33 

34 

.507073 

.507484 

.508304 

.509121 

.509937 

.510751 

.511566 

34 

35 

L516967 

1.517381 

1.518207 

1.519032 

1.519855 

T.  520677 

T.  521498 

35 

36 

.526950 

.527368 

.528202 

.529035 

.529866 

.530696 

.531524 

36 

37 

.537020 

.537441 

.538282 

.539121 

.539958 

.540793 

.541628 

37 

38 

.547161 

.547585 

.548431 

.549275 

.550118 

.550960 

.551799 

38 

39 

.557365 

.557791 

.558643 

.559493 

.560339 

.561186 

.562031 

39 

40 

1.567621 

1.568049 

1.568904 

1.569758 

r.  570609 

T.571460 

T.  572308 

40 

41 

.577927 

.578357 

.579216 

.580074 

.580929 

.581783 

.582636 

41 

42 

.588271 

.588702 

.589563 

.590422 

.591280 

.592136 

.592991 

42 

43 

.598641 

.599074 

.599938 

.600800 

.601659 

.602518 

.603375 

43 

44 

.609031 

.609464 

.610329 

.611192 

.612053 

.612913 

.613771 

44 

45 

1.619430 

1.619863 

1.620728 

1.621592 

1.622454 

1.623314 

1.624173 

45 

46 

.629830 

.630263 

.631128 

.631990 

.632852 

.633711 

.634569 

46 

47 

.640217 

.640649 

.641513 

.642373 

.643234 

.644092 

.644948 

47 

48 

.650585 

.651016 

.651878 

.652737 

.653594 

.654451 

.655306 

48 

49 

.660921 

.661351 

.662209 

.663065 

.663921 

.664774 

.665625 

49 

50 

1.671216 

1.671644 

1.672499 

1.673351 

1.674203 

1.675051 

1.675899 

50 

51 

.681459 

.681885 

.682735 

.683582 

.684428 

.685273 

.686116 

51 

52 

.691641 

.692064 

.692908 

.693750 

.694590 

.695429 

.696266 

52 

53 

.701750 

.702169 

.703007 

.703843 

.704678 

.705511 

.706342 

53 

54 

.711780 

.712196 

.713026 

.713857 

.714684 

.715510 

.716335 

54 

*110 


TABLE     LI. 


LOGARITHM    OF   THE    SINGLE    PREMIUM    BY    MONTHS,    ON    1   INSURED    FOR    THE 

WHOLE    LIFE. 

4  PER  CENT. 


AGE 

x-\-n. 

55 

Om. 

|m. 

lim. 

2^in. 

3im. 

4im. 

5|m. 

AGE. 
x-\-n. 

*Dec. 

Nov. 

Oct. 

Sept. 

Aug. 

July. 

T.  716746 

1.717163 

1.717994 

1.718823 

T.  719652 

T.  720480 

1.721304 

55 

56 

.726631 

.727043 

.727865 

.728687 

.729506 

.730324 

.731140 

56 

57 

.736412 

.736819 

.737631 

.738442 

.739251 

.740060 

.740866 

57 

58 

.746071 

.746473 

.747274 

.748074 

.748873 

.749670 

.750466 

58 

59 

.755602 

•  .755998 

.756788 

.757577 

.758364 

.759149 

.759934 

59 

60 

T.  765000 

T.  765389 

1.766167 

1.766944 

1.767719 

1.768492 

T.  769265 

60 

61 

.774251 

.774634 

.775398 

.776160 

.776923 

.777683 

.778442 

61 

62 

.783342 

.783718 

.784469 

.785217 

.785965 

.786712 

.787457 

62 

63 

.792272 

.792641 

.793377 

.794111 

.794845 

.795578 

.796310 

63 

64 

.801032 

.801392 

.802113 

.802832 

.803550 

.804267 

.804983 

64 

65 

1.809606 

1.809959 

T.  810664 

1.811366 

1.812068 

1.812769 

1.813469 

65 

66 

.817990 

.818335 

.819023 

.819709 

.820396 

.821080 

.821763 

66 

67 

.836180 

.826515 

.827186 

.827856 

.828524 

.829192 

.829858 

67 

68 

.834165 

.834492 

.835146 

.835797 

.836450 

.837100 

.837750 

68 

69 

.841948 

.842266 

.842900 

.843534 

.844167 

.844799 

.845431 

69 

70 

T.  849510 

T.  849820 

1.850436 

1.851051 

T.851666 

1.852280 

1.852892 

70 

71 

.856856 

.857156 

.857753 

.858350 

.858945 

.859540 

.860134 

71 

72 

.863976 

.864266 

.864844 

.865422 

.865998 

.866574 

.867149 

72 

73 

.870869 

.871149 

.871708 

.872266 

.872825 

.873382 

.873938 

73 

74 

.877537 

.877807 

.878346 

.878885 

.879422 

.879959 

.880494 

74 

75 

1.883965 

T.  884225 

T.  884744 

1.885264 

1.885781 

T.  886300 

1.886817 

75 

76 

.890163 

.890414 

.890914 

.891414 

.891913 

.892411 

.892909 

76 

77 

.896132 

.896373 

.896852 

.897332 

.897811 

.898290 

.898768 

77 

78 

.901863, 

.902094 

.902554 

.903015 

.903475 

.903935 

.904394 

78 

79 

.907365 

.907586 

.908028 

.908469 

.908909 

.909349 

.909790 

79 

80 

1.912638 

T.  912850 

1.913272 

T.  913695 

1.914118 

T.  914539 

1.914960 

80 

81 

.917687 

.917890 

.918296 

.918700 

.919104 

.919508 

.919911 

81 

82 

.922525 

.922719 

.923106 

.923493 

.923879 

.924265 

.924650 

82 

83 

.927149 

.927335 

.927707 

.928078 

.928449 

.928820 

.929190 

83 

84 

.931588 

.931767 

.932123 

.932479 

.932835 

.933191 

.933546 

84 

85 

1.935848 

1.936021 

1.936365 

1.936710 

1.937053 

1.937397 

1.937740 

85 

86 

.939965 

.940134 

.940471 

.940807 

.941145 

.941481 

.941817 

86 

87 

.943995 

.944162 

.944494 

.944826 

.945157 

.945488 

.945820 

87 

88 

.947967 

.948138 

.948478 

.948818 

.949158 

.949496 

.949836 

88 

89 

.952033 

.952182 

.952480 

.952778 

.953075 

.953372 

.953669 

89 

90 

L 955594 

1.955719 

1.955971 

1.956222 

T.  956474 

T.  956724 

1.956975 

90 

91 

.958600 

.958718 

.958951 

.959185 

.959419 

.959653 

.959886 

91 

92 

.961401 

.961513 

.961737 

.961961 

.962184 

.962407 

.962630 

92 

93 

.964079 

.964185 

.964395 

.964606 

.964817 

.965028 

.965238 

93 

94 

.966604 

.966706 

.966911 

.967115 

.967320 

.967524 

.967728 

94 

95 

1.969052 

T.969163 

T.  969385 

T.  969607 

1.969829 

T.  970051 

T.  970272 

95 

96 

.971710 

.971808 

.972004 

.972119 

.972395 

.972590 

.972786 

96 

97 

.974053 

.974191 

.974468 

.974745 

.975022 

.975298 

.975574 

97 

98 

.977363 

.977598 

.978068 

.978537 

.979004 

.979473 

.979940 

98 

99 



.982986 

.983689 

.985132 

.986570 

.988004 

.989432 

.990856 

99 

*  Months  of  Entry  for  Annual  Valuation  Dec.  31. 


TABLE    LI. 


♦Ill 


LOGARITHM    OF    THE    SINGLE    PREMIUM    BY    MONTHS,    ON    1    INSURED    FOR    THE 

WHOLE  LIFE. 

4  PER  CENT. 


A&E, 
x-\-n. 

6m. 

6|m. 

7iin. 

8^in. 

9^in. 

lOim. 

llim. 

AGE. 
x-\-n. 

June. 

May. 

April. 

March. 

Feb. 

Jan. 

55 

1.721717 

T.  722129 

T.  722951 

T.  723771 

1.724590 

1.725407 

1.726224 

55 

56 

.731548 

.731956 

.732770 

'.733581 

.734392 

.735202 

.736008 

56 

57 

.741368 

.741670 

.742474 

.743276 

.744076 

.744876 

.745673 

57 

58 

.750863 

.751260 

.752053 

.752844 

.753634 

.754422 

.755209 

58 

59 

.760326 

.760717 

.761499 

.762279 

.763059 

.763836 

.764612 

59 

60 

T.  769651 

T.  770036 

T.  770806 

T.  771574 

1.772340 

1.773105 

1.773870 

60 

61 

.778821 

.779199 

.779955 

.780710 

.781464 

.782216 

.782967 

61 

62 

.787830 

,  .788202 

.788945 

.789685 

.790427 

.791165 

.791903 

62 

63 

.796674 

.797039 

.797768 

.798496 

.799221 

.799946 

.800670 

63 

64 

.805340 

.805697 

.806410 

.807122 

.807834 

.808544 

.809253 

64 

65 

1.813818 

T.  814168 

T.  814866 

T.  815562 

T.816257 

T.  816951 

T.  81 7644 

65 

66 

.822105 

.822446 

.823127 

.823808 

.824486 

.825164 

.825841 

66 

67 

.830191 

.830524 

.831187 

.831852 

.832513 

.833175 

.833835 

67 

68 

.838073 

.838398 

..839045 

.839692 

.840338 

.840983 

.841626 

68 

69 

.845746 

.846061 

.846691 

.847319 

.847946 

.848572 

.849197 

69 

70 

T.  853198 

1.853505 

1.854116 

1.854726 

1.855336 

T.  855945 

T.  856553 

70 

71 

.860431 

.860727 

.861320 

.861912 

.862502 

.863093 

.863682 

71 

72 

.867436 

.867723 

.868297 

.868870 

.869442 

.870014 

.870584 

72 

73 

.874216 

.874494 

.875049 

.875603 

.876156 

.876709 

.877261 

73 

74 

.880763 

.881031 

.881666 

.882099 

.882634 

.883167 

.883699 

74 

75 

1.887075 

1.887334 

T.  887849 

T.  888365 

T.  888879 

T.  889393 

T.  889906 

75 

76 

.893158 

.893407 

.893903 

.894400 

.894895 

.895390 

.895885 

76 

77 

.899007 

.899246 

.899723 

.900200 

.900675 

.901151 

.901626 

77 

78 

.904623 

.904853 

.905310 

.905768 

.906225 

.906682 

.907137 

78 

79 

.910009 

.910229 

.910668 

.911106 

.911545 

.911982 

.912420 

79 

80 

T.  915171 

T.  915381 

T.915801 

T.  916221 

T.  916640 

T.  917060 

1.917478 

80 

81 

.920113 

.920314 

.920718 

.921120 

.921522 

.921923 

.922325 

81 

82 

.924843 

.925035 

.925420 

.925806 

.926190 

.926574 

.926957 

82 

83 

.929375 

.929560 

.929929 

.930299 

.930667 

.931036 

.931404 

83 

84 

.933723 

.933901 

.934256 

.934610 

.934965 

.935318 

.935671 

84 

85 

T.  937912 

1.938083 

1.938426 

1.938769 

1.939111 

1.939452 

1.939795 

85 

86 

.941985 

.942153 

.942488 

.942823 

.943159 

.943494 

.943828 

86 

87 

.945985 

.946151 

.946482 

.946813 

.947142 

.947473 

•  .947802 

87 

88 

.950005 

.950175 

.950513 

.950851 

.951190 

.951527 

.951865 

88 

89 

.953818 

.953965 

.954262 

.954559 

.954855 

.955151 

.955446 

89 

90 

1.957100 

T.  957225 

T.  957476 

T.  957726 

T.  957976 

T.  968226 

T.  958476 

90 

91 

.960003 

.960120 

.960353 

.960586 

.960820 

.961052 

.961285 

91 

92 

.962742 

.962854 

.963076 

.963299 

.963522 

.963745 

.963968 

92 

93 

.965344 

.965449 

.965659 

.965869 

.966080 

.966289 

.966499 

93 

94 

.967830 

.967932 

.968135 

.968339 

.968544 

.968747 

.968950 

94 

95 

1.970383 

T.  970494 

T.970716 

T.  970937 

T.  971158 

T.  971379 

T.  971600 

95 

96 

.972883 

.972981 

.973176 

.973371 

.973567 

.973761 

.973956 

96 

97 

.975712 

.975850 

.976125 

.976400 

.976676 

.976951 

.977226 

97 

98 

.980174 

.980407 

.980874 

.981339 

.981805 

.982269 

.982734 

98 

99 

.991567 

.992276 

.993691 

.995101 

.996506 

.997907 

.999304 

99 

*112 


TABLE      LII. 


SINGLE    PREMIUM   OR    RESERVE     (A),    FOR  TEMPORARY    INSURANCE    OF  1,000    CON- 
TINUING  m  YEARS  FROM  THE  PRESENT   AGE. 

m  the  order  oi  time,  a;  denotes  the  Age  of  Entry;  x  +  n  the  Present  Age ;  m  the  unexpired  Policy 
Years;  and  ?i+wi  the  whole  Period  of  Insurance.  a   PFR  CFNT 

PRESEUT 
AGE. 


L 


15 
16 
17 
18 
19 

20 
21 
22 
23 
24 

25 
26 
27 
28 
29 

30 
31 
32 
33 
34 

35 
36 
37 
38 
39 

40 
41 
42 
43 
44 

45 
46 
47 
48 
49 

50 
51 
52 
53 
54 

55 
56 
57 
58 
59 

60 
61 
62 
63 
64 
65* 


m  =1. 


6.339 
6.361 
6.393 
6.426 
6.459 

6.502 
6.547 
6.591 
6.647 
6.704 

6.762 
6.842 
6.913 
6.995 
7.101 

7.198 
7.308 
7.431 
7.568 
7.719 

7,896 
8.065 
8.262 
8.486 
8.728 

8.999 
9.277 
9.612 
9.955 
10.346 

10.773 
11.239 
11.758 
12.321 
12.943 

13.628 
14.381 
15.206 
16.108 
17.095 

18.202 
19.396 
20.731 
22.175 

23.756 

25.506 
27.432 
29.521 
31.833 
34.366 
37.154 


1^.  jim.d. 


9.376 
9.414 
9.462 
9.510 
9.564 

9.628 
9.694 
9.765 
9.848 
9.933 

10.028 
10.142 
10.251 
10.385 
10.536 

10.685 
10.853 
11.042 
11.249 
11.485 

11.741 
12.004 
12.307 
12.645 
13.015 

13.417 
13.854 
14.350 

14.877 
15.470 

16.115 

16.826 
17.609 
18.463 
19.407 

20.444 

21.582 
*22.828 
24.189 
25.691 

27.350 
29.162 
31.162 
33.333 
35.715 

38.345 
41.219 
44.356 

47.808 
51.590 

55.727 


.253 
.254 
.256 

.257 
.259 

.261 
.262 
.265 
.267 
.269 

.272 
.275 
.278 
.283 
.286 

.291 
.295 
.301 
.307 
.314 

.320 
.328 
.337 
.347 
.357 

.368 
.381 
.395 
.410 

.427 

.445 
.466 
.488 
.512 
.539 

.568 
.600 
.635 
.673 
.716 

.762 
.814 
.869 
.930 
.997 

1.070 
1.149 
1.236 
1.331 
1.435 
1.548 


2. 


2i.  -J^m.d. 


12.414 
12.467 
12.530 
12.594 
12.669 

12.755 
12.841 
12.939 
13.049 
13.161 

13.295 
13.441 
13.590 
13.774 
13.971 

14.172 
14.399 
14.652 
14.931 
15.250 

15.587 
15.943 
16.351 
16.804 
17.302 

17.836 
18.430 
19.088 
19.800 
20.593 

21.458 
22.412 
23.460 
24.606 
25.870 

27.260 
28.783 
30.450 
32.271 
34.286 

36.499 
38.928 
41.593 
44.490 

47.675 

51.183 '64.089 
55.007  168.864 
59.190  I  74.079 
63.783  79.796 
68.814 1  86.034 
74. 300 192.841 


15.330 
15.398 
15.476 
15.560 
15.655 

15.760 
15.873 
15.996 
16.132 
16.279 

16.445 
16.629 
16.826 
17.052 
17.300 

17.556 
17.844 
18.164 
18.524 
18.918 

19.343 
19.799 
20.316 
20.890 
21.512 

22.196 
22.942 
23.774 
24.676 
25.674 

26.770 
27.972 
29.294 
30.741 
32.336 

34.086 
36.002 
38.097 
40.397 
42.926 

45.711 
48.756 
52.090 
55.724 
59.715 


.243 
.244 
.246 
.247 
.249 

.250 
.253 
.255 

.257 
.260 

.263 
.266 
.270 
.273 

.277 
.282 
.287 
.293 
.299 
.306 

.313 
.321 
.330 
.341 
.351 

.363 
.376 
.391 
.406 
.423 

.443 
.463 
'.486 
.511 
.539 

.569 
.602 
.637 

.677 
.720 

.768 

.819 

.875 

936 

1.003 

1.076 
1.155 
1.241 
1.334 
1.435 
1.545 


18.247 
18.329 
18.422 
18.526 
18.640 

18.766 
18.904 
19.053 
19.215 
19.398 

19.595 
19.817 
20.061 
20.331 
20.628 

20.940 
21.289 
21.677 
22.116 
22.586 

23.099 
23.656 
24.281 
24.976 
25.722 

26.555 
27.455 
28.460 
29.551 
30.756 

32.081 
33.532 

35.128 
36.877 
38.801 

40.912 
43.221 

45.744 
48.523 
51.566 

54.924 
58.583 
62.587 
66.959 
71.754 

76.995 
82.721 
88.968 
95.809 
103.254 
111.382 


3i. 


21.047 
21.143 
21.255 
21.377 
21.511 

21.661 
21.823 
21.997 
22.193 
22.406 

22.639 
22.905 
23.192 
23.508 
23.857 

24.228 
24.641 
25.104 
25.616 
26.169 

26.777 
27.436 
28.176 
28.988 
29.876 

30.853 
31.917 
33.101 
34.387 
35.808 

37.368 
39.076 
40.956 
43.014 
45.276 

47.755 
50.464 
53.435 
56.692 
60.266 

64.195 
68.472 
73.157 

78.268 
83.857 

89.966 
96.629 
103.892 
111.819 
120.445 
129.816 


^m.  d. 

PEESENT 

AGE. 

.233 

15 

.235 

16 

.236 

17 

.238 

18 

.239 

19 

.241 

20 

.243 

21 

.245 

22 

.248 

23 

.251 

24 

.254 

25 

.257 

26 

.261 

27 

.265 

28 

.269 

29 

.274 

30 

.279 

31 

.286 

32 

.292 

33 

.299 

34 

.307 

35 

.315 

36 

.325 

37 

.334 

38 

.346 

39 

.358 

40 

.372 

41 

.387 

42 

.403 

43 

.421 

44 

.441 

45 

.462 

46 

.486 

47 

.511 

48 

.540 

49 

.570 

50 

.604 

51 

.641 

52 

.681 

53 

.725 

54 

.773 

55 

.824 

56 

.881 

57 

.942 

58 

1.009 

69 

1.081 

60 

1.159 

61 

1.244 

62 

1.334 

63 

1.433 

64 

1.536 

65 

Ages,  66,  67, continued  on  Page  *117. 


Formula,  Ax+»  =  1,000 


Ma;+n  — Ma 


TABLE     LII. 


*n3 


SINGLE  PREMIUM  OR  RESERVE  (A),  FOR  TEMPORARY  INSURANCE  OF  1,000  CONTINU- 
ING m  YEARS  FROM  THE  PRESENT   AGE. 

4  PER  CENT. 


PRESENT 
AOE. 

4. 

4i. 

Ym.d.* 

5. 

bh 

^m.d. 

6. 

6i. 

|m.d. 

PEE8ENT 
AQE. 

15 

23.847 

26.535 

.224 

29.223 

31.808 

.215 

34.392 

36.877 

.207 

15 

16 

23.957 

26.663 

.226 

29.369 

31.970 

.217 

34.572 

37.073 

.208 

16 

17 

24.088 

26.811 

.227 

29.535 

32.154 

.218 

34.773 

37.296 

.210 

17 

18 

24.229 

26.971 

.229: 

29.713 

32.354 

.220 

34.994 

37.537 

.212 

18 

19 

24.382 

27.147 

.230 

29.911 

32.574 

.222 

35.237 

37.801 

.214 

19 

20 

24.556 

27.344 

.232 

30.132 

32.816 

.224 

35.501 

38.095 

.216 

20 

21 

24.742 

27.553 

.234 

30.364 

33.080 

.226 

35.796 

38.416 

.218 

21 

22 

24.940 

27.784 

.237 

30.628 

33.371 

.229 

36.114 

38.764 

.221 

22 

23 

25.171 

28.043 

.239 

30.916 

33.691 

.231 

36.466 

39.155 

.224 

23 

24 

25.415 

28.321 

.242 

31.227 

34.043 

.235 

36.859 

39.583 

.227 

24 

25 

25.682 

28.632 

.246 

31.581 

34.434 

.238 

37.287 

40,051 

.230 

25 

26 

25.994 

28.982 

.249 

31.971 

34.867 

.241 

37.762 

40.572 

.234 

26 

27 

26.322 

29.355 

.253 

32.387 

35.330 

.245 

38.273 

41.132 

.238 

27 

28 

26.685 

29.768 

.257 

32.851 

35.846 

.250 

38.841 

41.755 

.243 

28 

29 

27.087 

30.225 

.262 

33.363 

36.416 

.254 

39.469 

42.448 

.248 

29 

30 

27.515 

30.714 

.267  1 

33.913 

37.034 

.260 

40.156 

43.196 

.253 

30 

31 

27.993 

31.263 

.273 

34.534 

37.720 

.266 

40.906 

44.018 

.259 

31 

32 

28.532 

31.871 

.278 

35.210 

38.471 

.272 

41.731 

44.924 

.266 

32 

33 

29.115 

32.533 

.285 

35.950 

39.296 

.279 

42.643 

45.923 

.273 

33 

34 

29.752 

33.260 

.292 

36.768 

40.206 

.287 

43.644 

47.022 

.282 

.  34 

35 

30.455 

34.060 

.300 

37.665 

41.207 

.295 

44.748 

48.226 

.290 

35 

36 

31.216 

34.930 

.310  1 

38.644 

42.291 

.304 

45.938 

49.536 

.300 

36 

37 

32.071 

35.896 

.319  1 

39.721 

43.494 

.314 

47.268 

50.989 

.310 

37 

38 

33.001 

36.959 

.330 

40.918 

44.821 

.325 

48.724 

52.583 

.322 

38 

39 

34.029 

38.124 

.341 

42.219 

46.269 

.338 

50.319 

54.330 

.334 

39 

40 

35.151 

39.401 

.354 

43.651 

47.861 

.351 

52.071 

56.247 

.348 

40 

41 

36.379 

40.799 

.368  1 

45.218 

49.602 

.365 

53.985 

58.343 

.363 

41 

42 

37.742 

42.345 

.384 

46.949 

51.525 

.381 

56.102 

60.657 

.380 

42 

43 

39.223 

44.031 

.401 

48.838 

53.623 

.399 

58.408 

63.179 

.398 

43 

44 

40.861 

45.889 

.419 

50.918 

55.932 

.418 

60.946 

65.954 

.417 

44 

45 

42.654 

47.926 

.439 

53.197 

58.462 

.439 

63.727 

68.994 

.439 

45 

46 

44.621 

50.159 

.462 

55.697 

61.236 

.462 

66.775 

72.322 

.462 

46 

47 

46.783 

52.612 

.486 

58.441 

64.279 

.487 

70.116 

75.968 

.488 

47 

48 

49. 151 

55.297 

.512 

61.444 

67.605 

.513 

73.767 

79.950 

.515 

48 

49 

51.751 

58.243 

.541 

64.734 

71.247 

.543 

77.760 

84.309 

546 

49 

50 

54.598 

61.464 

.572 

68.330 

75.235 

.575 

82.139 

89.080 

.578 

50 

51 

57.708 

64.992 

.607 

72.276 

79.597 

.610 

86.919 

94.292 

.614 

51 

52 

61.125 

68.855 

.644 

76.586 

84.370 

.649 

92.154 

99.987 

.653 

52 

53 

64.861 

73.087 

.686 

81.312 

89.590 

.690 

97.868 

106.198 

.694 

53 

54 

68.967 

77.723 

.730 

86.479 

95.290 

.734 

104.101 

112.973 

.739 

54 

55 

73.465 

82.794 

.777 

92.124 

101.518 

.783: 

110.912 

120.368 

.788 

55 

56 

78.362 

88.320 

.830 

98.278 

108.303 

.835 

118.327 

128.405 

.840 

56 

57 

83.726 

94.367 

.887 

105.007 

115.703 

.891 

126.399 

137.148 

.896 

57 

58 

89.578 

100.947 

.947 

112.316 

123.742 

.952 

135.168 

146.636 

.956 

58 

59 

95.960 

108.123 

1.014! 

120.287 

132.495 

1.017 

144.704 

156.942 

1.020 

59 

60 

102.936 

115.954 

1.085 

128.972 

142.022  1.088 

155.071 

168.117 

1.087 

60 

61 

110.537 

124.479 

1.162 

138.420 

152.358  1.162 

166.296 

180.211 

1.160 

61 

62 

118.817 

133.738 

1.243 

148.660 

163.556  1.241 

178.452 

193.262 

1.234 

62 

63 

127.829 

143.812 

1.332 

159.794 

175.684  1.324 

191.574 

207.348 

1.315 

63 

64 

137.636 

154.727 

1.424 

171.819 

188.7861.4141 

205.754 

222.516 

1.397 

64 

65 

148.250 

166.550 

1.525 

184.850 

202.929  1.507  i 

221.007 

238.801 

1.483 

65 

*  Note  that  J  m,  d.  is  ^^  of  the  diflference  of  tlie  integer  or  m  columns,  5  —  4,  etc. 


*1U 


TABLE     LII. 


SINGLE    PREMIUM  OR    RESERVE    (A),    FOR  TEMPORARY    INSURANCE    OF  1,000    CON- 
TINUING  m  YEARS  FROM  THE  PRESENT  AGE. 


4 

PER 

CENT. 

PEE8ENI 
AaE. 

m  =  7.  7i. 

^m.d. 

8. 

8i. 

ym.d. 

9. 

9i. 

|^m.d. 

PEESENT 
AGE. 

15 

39.362  41.751 

.199 

44.141 

46.442 

.192 

48.743 

50.959 

.185 

15 

16 

39.575,  41.985 

.201 

44.394 

46.714 

.193 

49.034 

51.269 

.186 

16 

17 

39.818 

42.247 

.202 

44.676 

47.015 

.195 

49.354 

51.614 

.188 

17 

18 

40.081 

42.530 

.204 

44.979 

47.345 

.197 

49.711 

51.993 

.190 

18 

19 

40.365 

42.842 

.206 

45.320 

47.709 

.199 

50.099 

52,407 

.192 

19 

20 

40.689  43.191 

.209 

1  45.693 

48.110 

.201 

50.526 

52.868 

.195 

20 

21 

41.035j  43.566 

.211 

46.097 

48.549 

.204 

51.001 

53.373 

.198 

21 

22 

41.414  43.982 

.214 

46.550 

49.034 

.207 

51.518 

53.925 

.201 

22 

23 

41.844'  44.445,  .217 

47.046 

49.566 

.210 

52.087 

54.533 

.204 

23 

24 

42.307,  44.947  .220 

47.587 

50.148 

.213 

52.709 

55.198 

.207 

24 

25 

42.816 

45.4991  .224 

48.181 

50.788 

.217 

53.394 

55.930 

.211 

25 

26 

43.381 

46.110  .227 

48.840 

51.496 

.221 

54.153 

56.744 

.216 

26 

27 

43.991 

46.774  .232 

49.556 

52.271 

.226 

54.985 

57.630 

.220 

27 

28 

44.670 

47.513 

.237 

50.357 

53.127 

.231 

55.897 

58.602 

.225 

28 

29 

45.427 

48.329 

.242 

51.231 

54.065 

.236 

56.899 

59.675 

.231 

29 

30 

46.236 

49.206 

.248 

52.175 

55.083 

.242 

57.991 

60.841 

.238 

30 

31 

47.129 

50.176 

.254 

53.223 

56.209 

.249 

59.195 

62.129 

.245 

31 

32 

48.117 

51.246 

.261 

54.376 

57.451 

.256 

60.526 

63.545 

.252 

32 

33 

49.203 

52.426 

.269 

55.649 

58.813 

.264 

61.978 

65.100 

.260 

33 

34 

50.401 

53.718 

.276 

57.035 

60.308 

.273 

63.581 

66.808 

.269 

34 

35 

51.704 

55.135 

.286 

58.566 

61.949 

.282 

65.332 

68.677 

.279 

35 

36 

53.134 

56.681 

.296 

60.228 

63.737 

.292 

67.245 

70.720 

.290 

36 

37 

54.709 

58.388 

.307 

62.067 

65.711 

.304 

69.356 

72.970 

.301 

37 

38 

56.443 

60.266 

.319 

64.088 

67.880 

.316 

71.672 

75.442 

.314 

38 

39 

58.341 

62.319 

.332 

66.298 

70.254 

.330 

74.209 

78.145 

.328 

39 

40 

60.422 

64.573 

.346 

68.724 

72.856 

.344 

76.988 

81.108 

.343 

40 

41 

62.701 

67.039 

.362 

71.376 

75.701 

.360 

80.026 

84.346 

.360 

41 

42 

65.212 

69.753 

.378 

74.295 

78.832 

.378 

83.369 

87.906 

.378 

42 

43 

67.951 

72.717 

.397 

77.482 

82.249 

.397 

87.016 

91.790 

.398 

43 

44 

70.962 

75.971 

.417 

80.981 

85.998 

.418 

91.015 

96.045 

.419 

44 

45 

74.260 

79.535 

.440 

84.809 

90.096 

.441 

95.384 

100.689 

.442 

45 

46 

77.870 

83.431 

.463 

88.993 

94.573 

.465 

100.153 

105.764 

.468 

46 

47 

81.820 

87.692 

.489 

93.564 

99.469 

,.492 

105.374 

111.309 

.495 

'  47 

48 

86.132 

92.349 

.518 

98.566 

L  04. 816 

.521 

111.065 

117.358 

.524 

48 

49 

90.859 

97.443 

.549 

104.027 

L10.656 

.552 

117.286 

123.957 

.556 

49 

50 

96.020 

103.009 

.582 

109.998 

117.031 

.586 

124.064 

131.142 

.590 

50 

51 

101.665 

109.085 

.618 

116.504 

L23.971 

.622 

131.438 

138.956 

.627 

51 

52 

107.821 

115.704 

.657 

123.588 

131.526 

.662 

139.463 

147.453 

.666 

52 

53 

114.528 

122.916 

.699 

131.304 

139. 748 

.704 

148.192 

156.680 

.707 

53 

54 

121.844 

130.776 

.744 

139.707 

148.685 

.748 

157.663 

166.686 

.752 

54  1 

55 

129.825 

139.331 

.792 

148.837 

158.391 

.796 

167.945 

177.534 

.799 

56 

56 

138.482 

148.609 

.844 

158.737 

168.902 

.847 

179.067 

189.257 

.849 

56 

57 

147.898 

158.687 

.899 

169.476 

180.291 

.901 

191.106 

201.919 

.901 

57 

58 

158.104 

169.600 

.958 

181.095 

192.588 

.958 

204.081 

215.554 

.956 

58 

59 

169.179 

181.413 

1.020 

193.648 

205.862 

1.018 

218.076 

230.220 

1.012 

6& 

60 

181.164 

194.189 

1.085 

207.213 

220.162 

1.079 

233.111 

245.966 

1.071 

60 

61 

194.125 

207.959 

1.153 

221.793 

235.526 

1.144 

249.259 

262.8261.131 

61 

62 

208.072 

222.774 

1.225 

237.476 

252.000 

1.210 

266.524 

280.8201.191 

62 

63 

223.123 

238.706 

1.299 

254.290 

269.629 

1.278 

284.968 

299.9891 

1.252  ! 

63 

64 

239.277 

255.776 

1.375 

272.275 

288.432 

1.346 

304.590 

320.325 

1.311 

64 
65 

65* 

256.596 

274.023 

1.452 

291.450 

308.421 

1.414 

325.392 

341.837 

1.370  j 

*  Ages 

66,  67,  . . . 

.  continu< 

jd  on  Pa 

ge  *117. 

TABLE     LII. 


*115 


SINGLE    PREMIUM    OR    RESERVE    (A),  FOR    TEMPORARY    INSURANCE  OF  1,000    CON- 
TINUINe^  m  YEARS  FROM   THE  PRESENT  AGE, 

4  PER  CENT. 


PRESENT 
A&E, 

10. 

loi 

iin.d. 

11. 

Hi. 

Jm.d. 

12. 

12i. 

Jm.d. 

PRESENT 
AGE. 

15 

53.176 

55.310 

.178 

57.444 

59.506 

.172 

61.568 

63.557 

.166 

15 

16 

53.503 

55.661 

.180 

57.820 

59.902 

.174 

61.984 

63.995 

.168 

16 

17 

53.874 

56.054 

.182 

58.234 

60.340 

.176 

62.446 

64.487 

.170 

17 

18 

54.275 

56.480 

.184 

58.685 

60.821 

.178 

62.958 

65.024 

.172 

18 

19 

54.715 

56.952 

.186 

59.189 

61.353 

.180 

63.517 

65.614 

.175 

19 

20 

55.210 

57.476 

.189 

59.742 

61.937 

.183 

64.132 

66.262 

.178 

20 

21 

55.746 

58.045 

.192 

60.343 

62.574 

.186 

64.804 

66.971 

.181 

21 

22 

56.332 

58.667 

.195 

61.003 

63.272 

.189 

65.542 

67.750 

.184 

22 

23 

56.979 

59.356 

.198 

61.732 

64.044 

.193 

66.356 

68.612,  .188 

23 

24 

57.686 

60.107 

.202 

62.529 

64.892 

.197 

67.255 

69.557 

.192 

24 

25 

58.466 

60.941 

.206 

63.415 

65.825 

.201 

68.235 

70.589 

.196 

25 

26 

59.336 

61.860 

.210 

64.385 

66.851 

.206 

69.316 

71.730 

.201 

26 

27 

60.274 

62.857 

.215 

65.439 

67.968 

.211 

70.497 

72.976 

.207 

27 

28 

61.308 

63.957 

.221 

66.606 

69.202 

.216 

71.799 

74.350 

.213 

28 

29 

62.450 

65.170 

.227 

67.890 

70.563 

.223 

73.235 

75.859 

.219 

29 

30 

63.691 

66.491 

.233 

69.291 

72.040 

.229 

74.790 

77.503 

.226 

30 

31 

65.063 

67.944 

.240 

70.826 

73.669 

.237 

76.511 

79.313 

.234 

31 

32 

66.565 

69.544 

.248 

72.522 

75.459 

.245 

78.396 

81.301 

.242 

32 

33 

68.222 

71.300 

.257 

74.378 

77.422 

.254 

80.467 

83.482 

.251 

33 

34 

70.034 

73.225 

.266 

76.416 

79.577 

.263 

82.737 

85.872 

.261 

34 

.35 

72.023 

75.336 

.276 

78.650 

81.937 

.274 

85.224 

88.491 

.272 

35 

36 

74.194 

77.641 

.287 

81.087 

84.513 

.286 

87.939 

91.350 

.284 

36 

37 

76.585 

80.178 

.299 

83.772 

87.348 

.298 

90.925 

94.491 

.297 

37 

38 

79.211 

82.963 

.313 

86.715 

90.456 

.312 

94.197 

97.934 

.311 

38 

39 

82.082 

86.008 

.327 

89.933 

93.854 

.327 

97.775 

101.696 

.327 

39 

40 

85.227 

89.342 

.343 

93.457 

97.573 

.343 

101.689 

105.812 

.344 

40 

41 

88.666 

92.987 

.360 

97.308 

101.636 

.361 

105.964 

110.302 

.362 

41 

42 

92.444 

96.988 

.379 

101.533 

106.089 

.380 

110.645 

115.216'  .381 

42 

43 

96.564 

101.350 

.399 

106.136 

110.938 

.400 

115.740 

120.569,  .402 

43 

44 

101.074 

106.121 

.421 

111.167 

116.242 

.423 

121.316 

126.417 

.425 

44 

45 

105.994 

111.329 

.445 

116.665 

122.027 

.447 

127.390 

132.791 

.450 

45 

46 

111.375 

117.016 

.470 

122.657 

128.337 

.473 

134.016 

139.732 

.476 

46 

47 

117.245 

123.222 

.498 

129.199 

135.213 

.501 

141.228 

147.281 

.504 

47 

48 

123.650 

129.983 

.528 

136.316 

142.689 

.531 

149.062 

155.479 

.535 

48 

49 

130.629 

137.343 

.560 

144.057 

150.817 

.563 

157.577 

164.382 

.567 

49 

50 

138.219145.346 

.594 

152.472 

159.647 

.598 

166.821 

174.033 

.601 

50 

51 

146.474154.042 

.631 

161.611 

169.219 

.634 

176.827 

184.473 

.637 

51 

52 

155.4441163.477 

.669 

171.509 

179.582 

.673 

187.655 

195.757 

.675 

52 

53 

165.168:173.698 

.711 

182.229 

190.791 

.714 

199.353 

207.936 

.715 

53 

54 

175.709184.765 

.755 

193.821 

202.899 

.757 

211.977 

221.053 

.756 

54 

55 

187.123196.735 

.801 

206.347 

215.956 

.801 

225.566 

235.159 

.799 

55 

56 

199.446209.633 

.849 

219.820 

229.990 

.848 

240.159 

250.270 

.843 

56 

57 

212.732  223.526 

.900 

234.320 

245.052 

.894 

255.784 

266.438 

.888 

57 

58 

227.028  238.435 

.951 

249.842 

261.166 

.944 

272.490 

283.677 

.932 

58 

59 

242.363j254.418 

1.005 

266.473 

278.382 

.992 

290.291 

302.013 

.977 

59 

60 

1258.821  271. 52C 

1.058 

284.219 

296.719 

1.042 

309.219 

321.461 

1.020 

60 

61 

!276. 393:289. 74? 

1.113 

303.102 

316.180 

1.090 

329.258 

341.994 

1.061 

61 

62 

1295.116:309.117 

1.167 

323.118 

336.752 

1.136 

350.387 

363.598 

1.101 

62 

63 

,315.011  329. 640  1.219 

344.269 

358.445 

1.181 

372.620 

386.250 

1.136 

63 

64 

336.060  351.3071.271 

366.555 

381.215 

1.222 

395.876 

409.865 

1.166 

64 

65 

:358.282  374.094  1.318 

389.906 

404.994 

1.257 

420.081 

434.369 

1.191 

65 

*116 


TABLE     LII. 


SINGLE    PREMIUM  OR    RESERVE    (A),    FOR  TEMPORARY    INSURANCE   OF    1,000    CON. 
TINUING  m  YEARS  FROM  THE  PRESENT   AGE. 

4  PER   CENT. 


PRESENT 
AGE. 

m—lZ, 

13i. 

im.d. 

14. 

14i. 

|m.d. 

15. 

15i. 

^m.d. 

PB,ERENT 
A&E. 

15 

65.546 

67.467 

.160 

69.389 

71.250 

.155 

73.112 

74.913 

.150 

15 

16 

6.6.007 

67.956 

.162 

69.905 

71.791 

.157 

73.677 

75.504 

.152 

16 

17 

66.527 

68.501 

.165 

70.475 

72.388 

.159 

74.300 

76.156 

.155 

17 

18 

67.091 

69.094 

.167 

71.096 

73.039 

.162 

74.983 

76.871 

.157 

18 

19 

67.710 

69.744 

.170 

71.779 

73.756 

.165 

75.732 

77.656 

.160 

19 

20 

68.393 

70.463 

.173 

72.532 

74.546 

.168 

76.560 

78.525 

.164 

20 

21 

69.138 

71.247 

.176 

73.356 

75.413 

.171 

77.471 

79.475 

.167 

21 

22 

69.958 

72.112 

.180 

74.267 

76.366 

.175 

78.464 

80.514 

.171 

22 

23 

70.868 

73.066 

.183 

75.264 

77.410 

.179 

79.557 

81.658 

.175 

23 

24 

71.858 

74.106 

.187 

76.353 

78.554 

.183 

80.755 

82.912 

.180 

24 

25 

72.943 

75.248 

.192 

77.554 

79.813 

.188 

82.072 

84.292 

.185 

25 

26 

74.145 

76.512 

.197 

78.878 

81.203 

.194 

83.527 

85.811 

.190 

26 

27 

75.454 

77.889 

.203 

80.324 

82.715 

.199 

85.107 

87.466 

.197 

27 

28 

76.901 

79.406 

.209 

81.911 

84.383 

.206 

86.854 

89.291 

.203 

28 

29 

78.484 

81.073 

.216 

83.662 

86.214 

.213 

88.767 

91.292 

.210 

29 

30 

80.215 

82.890 

.223 

85.565 

88.210 

.220 

90.854 

93.474 

'.218 

30 

31 

82.116 

84.887 

.231 

87.659 

90.404 

.229 

93.149 

95.871 

.227 

31 

32 

84.205 

87.082 

.240 

89.958 

92.811 

.238 

95.665 

98.502 

.236 

32 

33 

86.497 

89.487 

.249 

92.478 

95.451 

.248 

98.424 

101.383 

.247 

33 

34 

89.007 

92.124 

.260 

95.240 

98.342 

.259 

101.444 

104.537 

.258 

34 

35 

91.759 

95.011 

.271 

98.263 

101.506 

.270 

104.748 

107.987 

.270 

35 

36 

94.760 

98.160 

.283 

101.560 

104.956 

.283 

108.353 

111.750 

.283 

36. 

37 

98.058 

101.620 

.297 

105.182 

108.745 

.297 

112.308 

115.876 

.297 

37 

38 

101.670 

105.408 

.312 

109.146 

112.889 

.312 

116.632 

120.385 

.313 

38 

39 

105.618 

109.545 

.327 

113.473 

117.411 

.328 

121.348 

125.299 

.329 

39 

40 

109.934 

114.067 

.344 

118.199 

122.345 

.346 

126.491 

130.661 

.348 

40 

41 

114.641 

118.993 

.363 

123.346 

127.723 

.365 

132.101 

136.501 

.367 

41 

42 

119.787 

124.384 

.383 

128.981 

133.602 

.385 

138.222 

142.875 

.388 

42 

43 

125.398 

130.252 

.405 

135.106 

139.994 

.407 

144.882 

149.801 

.410 

43 

44 

131.518 

136.655 

.428 

141.792 

146.961 

.431 

152.130 

157.332 

.433 

44 

45 

138.191 

143.626 

.453 

149.060 

154.528 

.456 

159.997 

165.504 

.459 

45 

1?/ 

145.448 

151.200 

.479 

156.952 

162.744 

.483 

168.536 

174.366 

.486 

46 

153.334 

159.428 

.508 

165.523 

171.659 

.511 

177.7941 183.962 

.514 

47 

48 

161.896 

168.356 

.538 

174.815 

181.309 

.541 

187.803 

194.329 

.544 

48 

49 

171.188 

178.029 

.570 

184.870 

191.745 

.573 

198.621 

205.522 

.575 

49 

50 

181.244 

188.492 

.604 

195.740 

203.015 

.606 

210.290 

217.582 

.608 

50 

51 

192.119 

199.793 

.640 

207.468 

215.161 

.641 

222.854 

230.545 

.641 

51 

52 

203.860 

211.982 

.677 

220.104 

228.225 

.677 

236.345 

244.451 

.676 

52 

53 

216.518 

225.099 

.715 

233.680 

242.246 

.714 

250.812' 259.328 

.710 

53 

54 

230.129 

239.190 

.755 

248.250 

257.258 

.751 

266.266 

275.209 

.745 

54 

55 

244.753 

254.291 

.795 

263.830 

273.298 

.789 

282.767 

292.121 

.779 

55 

56 

260.381 

270.419 

.837 

280.456 

290.372 

.826 

300.288  310.048 

.813 

56 

57 

277.091 

287.616 

.877 

298.141 

308.501 

.863 

318.860  329.006 

.846 

57 

58 

294.864 

305.875 

.918 

316.887 

327.671 

.899 

338.455  348.957 

.875 

58 

59 

313.736 

325.216 

.957 

336.696 

347.875 

.932 

359.055  369.888 

.903 

59 

60 

333.702 

345.624 

.994 

357.545 

369.097 

.963 

380.648  391.755 

.926 

60 

61 

354.730 

367.071 

1.028 

379.413 

391.279 

.989 

403.145  414.468 

.944 

61 

62 

376.810 

389.514 

1.059 

402.217 

414.338 

1.010 

426.459  437.938 

.957 

62 

63 

399.880 

412.885 

1.084 

425.890 

438.206 

1.026 

450.523  462.071 

.962 

63 

64 

423.853 

437.100 

1.104 

450.348 

462.770 

1.035 

475.192  486.720 

.961 

64 

65* 

448.657 

462.055 

1.117 

475.452 

487.886 

1.036 

500.319  511.728 

.951 

65 

Ages  66,  67, continued  on  Page  *117. 


TABLE     LII. 


*117 


SINGLE    PREMIUM  OR    RESERVE    (A),    FOR  TEMPORARY    INSURANCE  OF    1,000    CON. 
TINUING  m  YEARS  FROM  THE  PRESENT   AGE. 


4  PER  CENT. 

PBESENT 
AGE. 

W=:l. 

2. 

3. 

4. 

5. 

6. 

7     PEESENT 
'  •      AGE. 

66 

40.184 

80.300 

120.184 

159.777 

198.892 

237.392 

275.097 

66 

67 

43.540 

86.829 

129.802 

172.255 

214.042 

254.965 

294.818 

67 

68 

47.155 

93.967 

140.213 

185.732 

230.311 

273.724 

315.790 

68 

69 

51.195 

101.770 

151.552 

200.305 

247.783 

293.788 

338.024 

69 

70 

55.557 

110.241 

163.796 

215.949 

266.485 

315.078 

361.442 

70 

71 

60.360 

119.471 

177.037 

232.818 

286.453 

337.628 

386.094 

71 

72 

65.594 

129.472 

191.369 

250.886 

307.673 

361.453 

411.880 

72 

73 

71.297 

140.383 

206.812 

270.195 

330.221 

386.505 

438.740 

73 

74 

77.604 

152.223 

223.420 

290.846 

354.069 

412.745 

466.583 

74 

75 

84.417 

164.963 

241.243 

312.767 

379.147 

440.055 

495.220 

75 

76 

91.830 

178.796 

260.341 

336.020 

405.461 

468.353 

524.567 

76 

77 

99.995 

193.756 

280.772 

360.616 

432.931 

497.565 

554.382 

77 

78 

108.829 

209.830 

302.505 

386.441 

461.463 

527.411 

584.471 

78 

79 

118.447 

227.130 

325.565 

413.546 

490.885 

557.801 

614.568 

79 

80 

128.910 

245.665 

350.020 

441.753 

521.122 

588.455 

644.371 

80 

81 

140.224 

265.556 

375.719 

471.043 

551.910 

619.066 

673.718 

81 

82 

152.600 

286.742 

402.805 

501.266 

583.033 

649.575 

702.195 

82 

83 

165.825 

309.300 

431.016 

532.095 

614.353 

679.402 

731.612 

83 

84 

180.310 

333.275 

460.305 

563.681 

645.430 

711.044 

761.097 

84 

85 

195.801 

358.404 

490.730 

595.372 

679.361 

743.431 

788.654 

85 

PEESENT 
AGE. 

m=8. 

9. 

10. 

11. 

12. 

13. 

14. 

PEESENT 
AGE. 

66 

311.816 

347.395 

381.607 

414.250 

445.163 

474.150 

501.052 

66 

67 

333.435 

370.566 

405.995 

439.548 

471.009 

500.207 

526.998 

67 

68 

356.239 

394.832 

431.382 

465.653 

497.459 

526.643 

553.076 

68 

69 

380.231 

420.203 

457.683 

492.467 

524.384 

553.291 

579.128 

69 

70 

405.351 

446.522 

484.732 

519.792 

551.547 

579.928 

604.877 

70 

71 

431.538 

473.713 

512.411 

547.460 

578.788 

606.326 

630.152 

71 

72 

458.680 

501.622 

540.515 

575.278 

605.835 

632.275 

654.704 

72 

73 

486.669 

530.079 

568.879 

602.986 

632.496 

657.530 

678.320 

73 

74 

515.345 

558.929 

597.240 

630.389 

658.509 

681.863 

700.867 

74 

75 

544.526 

587.868 

625.369 

657.183 

683.602 

705.102 

722.104 

75 

76 

573.981 

616.735 

653.006 

683.126 

707.638 

727.022 

742.581 

76 

77 

603.542 

645.245 

679.879 

708.063 

730.351 

748.240 

761.886 

77 

78 

632.877 

673.076 

705.800 

731.669 

752.433 

768.263 

779.443 

78 

79 

661.711 

700.075 

730.413 

754.764 

773.339 

786.450 

795.241 

79 

80 

689.875 

725.860 

754.742 

776.775 

792.326 

802.752 

809.424 

80 

81 

716.936 

751.624 

778.085 

796.763 

809.285 

817.298 

822.118 

81 

82 

744.430 

776.649 

799.389 

814.636 

824.392 

830.261 

833.541 

82 

83 

771.440 

799.552 

818.399 

830.460 

837.715 

841.770 

843.949 

83 

84 

796.426 

820.113 

835.270 

844.388 

849.484 

852.222 

853.469 

84 

85 

818.973 

838.374 

850.046 

856.569 

860.073 

861.670 

862.352 

85 

ni8  TABLE    LIII. 

ANNUAL  PREMIUM  (P)  OF  TEMPORARY  INSURANCE  OF  1000  FOR  m  TEARS. 

4  PER  CENT. 


ALSO    A(7r  — P).* 


AQE. 
X. 

m=l. 

2. 

3. 

4. 

AGE. 
X. 

P. 

Hjr-n 

P. 

A(7r-P). 

P. 

A(7r-P). 

P.   A(7r-P). 

15 

6.339 

0.646159 

6.349 

0.645088 

6.363 

0.643740 

6.378  0.642295 

15 

16 

6.361 

.666022 

6.377 

.664539 

6.392 

.663059 

6.408  .661562 

16 

17 

6.393 

.685150 

6.409 

.683844 

6.425 

.682346 

6.443 i  .680708 

17 

18 

6.426 

.704502 

6.442 

.703069 

6.461 

.701461 

6.481 

.699713 

18 

19 

6.459 

.724063 

6.480 

.722280 

6.501 

.720520 

6.622 

.718763 

19 

20 

6.502 

0.743023 

6.524 

0.741335 

6.545 

0.739587 

6.569 

0.737749 

20 

21 

6.547 

.762213 

6.568 

.760500 

6.594 

.758675 

6.619 

.756706 

21 

22 

6.591 

.781648 

6.619 

.779692 

6.646 

.777720 

6.673 

.775721 

22 

23 

6.647 

.800593 

6.675 

.798740 

6.703 

.796760 

6.735 

.794541 

23 

24 

6.704 

.819800 

6.733 

.817846 

6.767 

.815632! 

6.801 

.813358 

24 

25 

6,762 

0.839277 

6.801 

0.836814 

6.836 

0.834539' 

6.873 

0.832U88 

25 

26 

6.842 

.857724 

6.876 

.855689 

6.914 

.853366: 

6.958 

.850718 

26 

27 

6.913 

.877101 

6.953 

.874716 

7.000 

.872014; 

7.046 

.869338 

27 

28 

6.995 

.896179 

7.047 

.893342 

7.095 

.890663 

7.145 

.887858 

28 

29 

7.101 

.914412 

7.148 

.911939 

7.199 

.909193 

7.253 

.906320 

29 

30 

7.198 

0.933538 

7.252 

0.930807 

7.309 

0.927915 

7.369 

0.924798 

30 

31 

7.308 

.952468 

7.368 

.949558 

7.432 

.946425 

7.498 

.943141 

31 

32 

7.431 

.971234 

7.498 

.968128 

7.568 

.964853 

7.644 

.961235 

32 

33 

7.568 

.989881 

7.641 

.986585 

7.722 

.982942 

7.802 

.979305 

33 

34 

7.719 

1.008430 

7.805 

1.004747 

7.888 

1.001140 

7.975 

.997379 

34 

35 

7.896 

1.026460 

7.979 

1.023012 

8.068 

1.019327 

8.166 

1.015296 

35 

36 

8.065 

.045362 

8.161 

.041571 

8.264 

.037507 

8.372 

.033181 

36 

37 

8.262 

.063840 

8.371 

.059760 

8.485 

.055417 

8.604 

.050823 

37 

38 

8.486 

.081934 

8.604 

.077663 

8.730 

.073089 

8.857 

.068422 

38 

39 

8.728 

.100102 

8.860 

.095477 

8.993 

.090880 

9.136 

.085754 

39 

40 

8.999 

1.117984 

9.135 

1.113515 

9.286 

1.108366 

9.442 

1.103102 

40 

41 

9.277 

.136381 

9.440 

.131161 

9.604 

.125917 

9.776 

.120288 

41 

42 

9.612 

.153845 

9.779 

.148674 

9.959 

.143115 

10.147 

.137178 

42 

43 

9.955 

.171864 

10.146 

.166291 

10.344 

.160342 

10.551 

.154077 

43 

44 

10.346 

.189423 

10.554 

.183514 

10.771 

.177300 

10.999 

.170673 

44 

45 

10.773 

1.206904 

11.000 

1.200718 

11.240 

1.194123 

11.489 

1.187120 

45 

46 

11.239 

.224347 

11.492 

.217759 

11.754 

.210787 

12.028 

.203401 

46 

47 

11.758 

.241475 

12.032 

.234588 

12.320 

.227262 

1  12.622 

.219402 

47 

48 

12.321 

.258627 

12.624 

.251332 

12.941 

.243507 

13.273 

.235204 

48 

49 

12.943 

.275547 

13.276 

.267802 

13.625 

.259532 

13.989 

.250767 

49 

50 

13.628 

1.292263 

13.995 

1.284037 

14.377 

1.275337 

14.775 

1.266078 

50 

51 

14.381 

.308803 

14.782 

.300163 

15.200 

.290977 

;  15.635 

.281179 

51 

52 

15.206 

.325195 

15.645 

.316105 

16.101 

.306388 

16.583 

.295944 

52 

53 

16.108 

.341466 

16.588 

.331851 

17.095 

.321472  1  17.622 

.310432 

53 

54 

17.095 

.357628 

17.633 

.347236 

18.187 

.336294 

18.768 

.324502 

54 

55 

18.202 

1.373155 

18.781 

1.362382 

19.393 

1.350687 

20.027 

1.338234 

55 

56 

19.396 

.388816 

20.044 

.377181 

20.711 

.364847 

21.404 

.351666 

56 

57 

20.731 

.403844 

21.431 

.391695 

22.158 

.378680 

22.918 

.364650 

57 

58 

22.175 

.418941 

22.940 

.406085 

23.742 

.392188 

1  24.577 

.377242 

58 

59 

23.756 

.433834 

24.603 

.420046 

25.485 

.405246 

26.395 

.389423 

59 

60 

25.506 

1.448213 

26.437. 

1.433548 

27.397 

1.417933 

28.394 

1.401053 

60 

61 

27.432 

.462217 

28.441 

.446845 

29.494 

.430164 

30.584 

.412207 

61 

62 

29.521 

.476214 

30.637 

.459719 

31.791 

.441965 

32.988 

.422773 

62 

63 

31.833 

.489607 

33.054 

.472085 

34.319 

.453137 

35.622 

.432525 

63 

64 

34.366 

.502669 

35.708 

.483974 

37.085 

.463577 

38.511 

.442041 

64 

65 

37.154 

.515179 

38.610 

.495002 

40.122 

.473918 

41.668 

.450779 

65 

Formula,    P^=  1000 


Ma;  —  Ma;+wi . 

-Nx -Nx  +  TO 


TTa-  = 


1000  Ma 


TABLE     LIII. 

ANNUAL  PREMIUM  (P)  OF  TEMPORARY  INSURANCE  OF  1.000  FOR  m  YEARS. 

ALSO  A  (tt—P).* 


*119 


4  PER  CENT. 


AGE. 

X. 

5. 

6. 

7. 

8. 

AGE. 

X. 

P. 

6.393 

A(:r-P). 

P. 

A  (tt-P). 

P. 

A(7T-P). 

0.637504 

P. 

6.443 

A  (TT-P). 

15 

0.640832 

6.409 

0.639220 

6.426 

0.635731 

15 

16 

6.425 

.669952 

6.443 

.658221 

6.461 

.656452 

6.481 

.654585 

16 

17 

6.462 

.678969 

6.481 

.677201 

6.502 

.675334 

6.523 

.673364 

17 

18 

6.501 

.697950 

6.523 

.696094 

6.545 

.694120 

6.568 

.692079 

18 

19 

6.545 

.716909 

6.569 

.714943 

6.593 

.712909 

6.619 

.710715 

19 

20 

6.594 

0.735785 

6.619 

0.733765 

6.646 

0.731583 

6.675 

0.729294 

20 

21 

6.645 

.754701 

6.674 

.752516 

6.704 

.750229 

6.735 

.747838 

21 

22 

6.704 

.773521 

6.735 

.771232 

6.767 

.768846 

6.802 

.766238 

22 

23 

6.768 

.792264 

6.801 

.789893 

6.838 

.787280 

6.876 

.784583 

23 

24 

6.836 

.810996 

6.876 

.808378 

6.915 

.805678 

6.957 

.802847 

24 

25 

6.915 

0.829545 

6.957 

0.826847 

7.000 

0.824014 

7.046 

0.821056 

25 

26 

7.002 

.848043 

7.047 

.845218 

7.094 

.842270 

7.144 

.839126 

26 

27 

7.094 

.866511 

7.144 

.863582 

7.196 

.860440 

7.251 

.857136 

27 

28 

7.197 

.884938 

7.252 

.881811 

7.309 

.878511 

7.371 

.874936 

28 

29 

7.310 

.903209 

7.371 

.899934 

7.436 

.896365 

7.502 

.892676 

29 

30 

7.433 

0.921515 

7.501 

0.917931 

7.571 

0.914245 

7.644 

0.910386 

30 

31 

7.571 

.939550 

7.644 

.935869 

7.720 

.932026 

7.801 

.927918 

31 

32 

7.721 

.957574 

7.801 

.953739 

7.885 

.949646 

7.974 

.945294 

32 

33 

7.886 

.975510 

7.974 

.971437 

8.067 

.967094 

8.165 

.962484 

33 

34 

8.068 

.993329 

8.165 

.988999 

8.268 

.984402 

8.374 

.979615 

34 

35 

8.267 

1.010988 

8.375 

1.006399 

8.486 

1.001641 

8.604 

0.996488 

35 

36 

8.486 

.028590 

8.602 

.023843 

8.727 

.018690 

8.855 

1.013311 

36 

37 

8.726 

.046103 

8.856 

.040956 

8.991 

.035596 

9.133 

.029884 

37 

38 

8.993 

.063290 

9.135 

.057964 

9.284 

.052274 

9.439 

.046233 

38 

-  39 

9.284 

.080462 

9.440 

.074798 

9.604 

.068780 

9.774 

.062407 

39 

40 

9.605 

1.097463 

9.776 

1.091462 

9.955 

1.085120 

10.143 

1.078367 

40 

41 

9.956 

.114305 

10.144 

.107983 

10.341 

.101252 

10.547 

.094105 

41 

42 

10.345 

.130901 

10.551 

.124215 

10.767 

.117103 

10.993 

.109558 

42 

43 

10.769 

.147405 

10.996 

.140321 

11.233 

.132806 

11.481 

.124785 

43 

44 

11.237 

.163630 

11.486 

.156159 

11.747 

.148180 

12.019 

.139689 

44 

45 

11.751 

1.179693 

12.025 

1.171750 

12.311 

1.163306 

12.610 

1.154311 

45 

46 

12.316 

.195498 

12.617 

.187096 

12.930 

.178153 

13.257 

.168630 

46 

47 

12.937 

.211053 

13.267 

.202162 

13.610 

.192696 

13.968 

.182614 

47 

48 

13.619 

.226367 

13.980 

.216961 

14.356 

.206942 

14.749 

.196212 

48 

49 

14.368 

.241427 

14.763 

.231474 

15.176 

.220813 

15.606 

.209439 

49 

50 

15.189 

1.256204 

15.624 

1.245613 

16.076 

1.234321 

16.548 

1.222199 

50 

51 

16.093 

.270661 

16.568 

.259449 

17.065 

.247406 

17.581 

.234542 

51 

52 

17.083 

.284815 

17.606 

.272856 

18.150 

.260083 

18.713 

.246429 

52 

53 

18.174 

.298553 

18.746 

.285880 

19.339 

.272329 

19.955 

.257783 

53 

54 

19.370 

.311934 

19.995 

.298493 

20.645 

.284063 

21.319 

.268563 

54 

55 

20.685 

1.324922 

21.369 

1.310618 

22.080 

1.295250 

22.814 

1.278781 

55 

56 

22.125 

.337489 

22.875 

.322259 

23.649 

.305935 

24.452 

.288353 

56 

57 

23.708 

.349562 

24.526 

.333402 

25.372 

.315984 

26.247 

.297240 

57 

58 

25.439 

.361242 

26.334 

.343990 

27.258 

.325424 

28.212 

.305386 

58  1 

59 

27.339 

.372347 

28.317 

.353971 

29.326 

.334127  ; 

30.362 

.312640 

59 

60 

29.426 

1.382882 

30.494 

1.363248 

31.591 

1.341971 

32.720 

1.319205 

60 

61 

31.715 

.392792. 

32.876 

.371730 

34.072 

.349229 

35.294 

.324817 

61 

62 

34.218 

.401931 

35.486 

.379712 

36.782 

.355582 

38.110 

.329362 

62 

63 

36.967 

.410631 

38.341 

.386804 

39.752 

.360895 

41.188 

.332839 

63 

64 

39.969 

.418541 

41.470 

.392957 

42.996 

.365247 

44.549 

.335136 

64 

65 

43.262 

.425541 

44.887 

.398203 

46.541 

.368478 

48.217 

.336167 

65 

*  In  valuing  Term  Polidea  by  Table  LXIII,  {n — P)  Bf  will  be  suUractive. 


^120 


TABLE    LIIl. 


ANNUAL  PREMIUM  (P)  OF  TExMPORARY   INSURANCE  OP   1000  FOR  m   YEARS. 

ALSO  A(7T— P).* 

4   PER    CENT. 


AQE. 

X. 

w=9. 

10. 

11. 

12. 

AGE. 

X, 

P. 

A(Tr_P). 

P. 

6.482 

A(7r-P)- 

P. 

A(77  — P). 

P. 

A(Tr-P). 

15 

6.462 

0.633870 

0.631890 

6.502 

0.629841 

6.523 

0.627645 

15 

16 

6.501 

.652608 

6.522 

.650560 

6.545 

.648358 

6.569 

.646055 

16 

17 

6.545 

.671315 

6.569 

.669115 

6.593 

.666813 

6.619 

.664401 

17 

18 

6.593 

.689886 

6.619 

.687584 

6.646 

.685183 

6.675 

.682581 

18 

19 

6.646 

.708419 

6.674 

.706021 

6.705 

.703421 

6.736 

.700709 

19 

20 

6.704 

0.726900 

6.736 

0.724295 

6.769 

0.721592 

6.803 

0. 718741 

20 

21 

6.768 

.745231 

6.803 

.742532 

6.839 

.739681 

6.877 

.736702 

21 

22 

6.838 

.763537 

6.876 

.760694 

6.916 

.757714 

6.957 

.754542 

22 

23 

6.916 

.781738 

6.957 

.778765 

7.001 

.775606 

7.046 

.772270 

23 

24 

7.000 

.799881 

7.046 

.796722 

7.094 

.793392 

7.145 

.789811 

24 

25 

7.094 

0.817907 

7.144 

0.814585 

7.197 

0.811003 

7.252 

0.807277 

25 

26 

7.197 

.835813 

7.253 

.832240 

7.311 

.828519 

7.371 

.824619 

26 

27 

7.310 

.853562 

7.371 

.849848 

7.434 

.845953 

7.501 

.841813 

27 

28 

7.435 

.871237 

7.501 

.867354 

7.571 

.863218 

7.644 

.858826 

28 

29 

7.571 

.888805 

7.645 

.884685 

7.721 

.880305 

7.802 

.875655 

29 

30 

7.720 

0.906271 

7.801 

0.901898 

7.886 

0.897254 

7.974 

0.892401 

30 

31 

7.885 

.923554 

7.974 

.918920 

8.066 

.914081 

8.164 

.908872 

31 

32 

8.067 

.940668 

8.164 

.935843 

8.266 

.930648 

8.372 

.925198 

32 

33 

8.266 

.957678 

8.373 

.952498 

8.485 

.947064 

8.602 

.941282 

33 

34 

8.486 

.974448 

8.603 

.969034 

8.726 

.963270 

8.854 

.957146 

34 

35 

8.727 

0.991097 

8.856 

0.985349 

8.990 

0.979248 

9.132 

0.972783 

35 

36 

8.990 

1.007578 

9.132 

1.001491 

9.280 

.995046 

9.435 

.988189 

36 

37 

9.282 

.023816 

9.437 

.017393 

9.599 

1.010559 

9.769 

1.003301 

37 

38 

9.602 

.039835 

9.772 

.033028 

9.950 

.025796 

10.137 

.018117 

38 

39 

9.953 

.055630 

10.140 

.048425 

10.335 

.040775 

10.540 

.032621 

39 

40 

10.339 

1.071190 

10.544 

1.063574 

10.7e59 

1.055448 

10.982 

1.046804 

40 

41 

10.762 

.086519 

10.988 

.078425 

11.223 

.069814 

11.468 

.060645 

41 

42 

11.229 

.101504 

11.476 

.092935 

11.734 

.083808 

12.002 

.074092 

42 

43 

11.741 

.116252 

12.011 

.107164 

12.293 

.097490 

12.587 

.087184 

43 

44 

12.303 

.130650 

12.599 

.121025 

12.908 

.110770 

13.230 

.099802 

44 

45 

12.921 

1.144737 

13.244 

1.134535 

13.583 

1.123621 

13.934 

1.111980 

45 

46 

13.597 

158485 

13.953 

.147629 

14.323 

.136048 

14.708 

.123637 

46 

47 

14.342 

.171819 

14.730 

.160304 

15.136 

.147960 

15.556 

.134772 

47 

48 

15.158 

.184764 

15.584 

.172490 

16.027 

.159378 

16.485 

.145355 

48 

49 

16.055 

.197237 

16.520 

.184203 

17.003 

.170264 

17.504 

.155314 

49 

50 

17.038 

1.209248 

17.546 

1.195400 

18.073 

1.180543 

18.620 

1.164597 

50 

51 

18.116 

.220788 

18.672 

.206028 

19.247 

.190187 

19.841 

.173207 

51 

52 

19.298 

.231771 

19.905 

.216038 

20.531 

.199176 

21.178 

.181035 

52 

53 

20.595 

.242162 

21.255 

.225422 

21.938 

.207409 

22.641 

.188040 

53 

54 

22.016 

.251953 

22.736 

.234076 

23.478 

.214850 

24.243 

.194125 

54 

55 

23.574 

1.261047 

24.358 

1.241974 

25.166 

1.221407 

25.993 

1.199187 

55 

56 

25.280 

.269440 

26.133 

.249038 

27.008 

.226989 

27.906 

.203328 

56 

57 

27.149 

.277017 

28.075 

.255146 

29.024 

.231688 

29.992 

.206313 

57 

58 

29.191 

.283700 

30.197 

.260457 

31.223 

.235299 

32.269 

.208025 

58 

59 

31.428 

.289625 

32.515 

.264700 

33.625 

.237667 

34.750 

.208422 

59 

60 

33.872 

1.294528 

35.050 

1.267751 

36.245 

1.238777 

37.455 

1.207347 

60 

61 

36.544 

.298311 

37.815 

.269622 

39.102 

.238491 

40.398 

.204706 

61 

62 

39.460 

.300979 

40.830 

.270165 

42.211 

.236713 

43.595 

.200380 

62 

63 

42.646 

.302366 

44.118 

.269269 

45.595 

.233311 

47.073 

.194101 

63 

64 

46.119 

.302418 

47.697 

.266860 

49.277 

.228062 

50.844 

.185804 

64 

65 

49.902 

.301039 

51.5j92 

.262680 

53.272 

.220883 

54.929 

.175306 

65 

In  valuing  Term  Policies  by  Table  LXIII,  (tt — P)  B/"  will  be  stibtractive. 


TABLE     LIII. 


*121 


ANNUAL  PREMIUM  (P)  OP  TEMPORARY  INSURANCE  OF  1000  FOR  m  YEARS. 

ALSO  A(7r— P).* 

4  PER  CENT. 


AQE. 
X. 

m- 

=  13. 

14. 

15. 

AGE, 
z. 

15 

P. 

A(7r— P). 

P. 

A(7r^P). 

P. 

A(7r-P). 

15 

6.546 

0.625336 

6.569 

0.622924 

6.594 

0.620319 

16 

6.593 

.643643 

6.620 

.641039 

6.647 

.638319 

16 

17 

6.647 

.661795 

6.675 

.659077 

6.705 

.656216 

17 

18 

6.705 

.679867 

6.736 

.677006 

6.769 

.674007 

18 

19 

6.769 

.697854 

6.803 

.694858 

6.839 

.691677 

19 

20 

6.839 

0.715751 

6.877 

0.712573 

6.917 

0.709226 

20 

21 

6.916 

.733532 

6.958 

.730182 

7.002 

.726594 

21 

22 

7.001 

.751204 

7.047 

.747616 

7.095 

.743870 

22 

23 

7.095 

.768685 

7.145 

.764946 

7.198 

.761015 

23 

24 

7.198 

.786078 

7.252 

.782156 

7.310 

.777990 

24 

25 

7.310 

0.803363 

7.371 

0.799202 

7.434 

0.794785 

25 

26 

7.435 

.820466 

7.501 

.816058 

7.572 

.811378 

26 

27 

7.571 

.837412  1 

7.644 

.832740 

7.721 

.827846 

27 

28 

7.721 

.854168  : 

7.801 

.849285 

7.886 

.844048 

28 

29 

7.886 

.870786 

7.975 

.865563 

8.067 

.860072 

29 

30 

8.067 

0.887182 

8.164 

0.881705 

8.265 

0.875876 

30 

31 

8.265 

.903407 

8.372 

.897595 

8.483 

.891421 

31 

32 

8.484 

.919399 

8.601 

.913241 

8.723 

.906715 

32 

33 

8.725 

.935143 

8.853 

.928636 

8.987 

.921720 

33 

34 

8.989 

.950662 

9.130 

.943764 

9.276 

.936437 

34 

35 

9.279 

0.965909 

9.433 

0.958602 

9.594 

0.950845 

35 

36 

9.596 

.980904 

9.765 

.973169 

9.942 

.964925 

36 

37 

9.946 

.995592 

10.132 

.987375 

10.325 

.978631 

37 

38 

10.331 

1.009931 

10.534 

1.001221 

10.746 

.991945 

38 

39 

10.753 

.023943 

10.975 

.014702 

11.207 

1.004864 

39 

40 

11.216 

1.037598 

11.460 

1.027799 

11.713 

1.017357 

40 

41 

11.724 

.050885 

11.989 

.040486 

12.267 

.029368 

41 

42 

12.282 

.063739 

12.573 

.052671 

12.876 

.040863 

42 

43 

12.893 

.076163 

13.211 

.064406 

13.543 

.051815 

43 

44 

13.564 

.088101 

13.913 

.075567 

14.274 

.062175 

44 

45 

14.301 

1.099505 

14.681 

1.086178 

15.074 

1.071927 

45 

46 

15.108 

.110376 

15.522 

.096198 

15.951 

.080996 

46 

47 

15.992 

.120667  ' 

16.444 

.105546 

16.911 

.089324 

47 

48 

16.961 

.130316  1 

17.453 

.114180 

17.961 

.096891 

48 

49 

18.022 

.139272 

18.557 

.122080 

19.109 

.103598 

49 

50 

19.184 

1.147512  : 

19.765 

1.129137 

20.364 

1.109387 

50 

51 

20.455 

.154948 

21.086 

.135317 

21.735 

.114174 

51 

52 

21.845 

.161532 

22.530 

.  .140519 

23.231 

.117843 

52 

53 

23.365 

.167167 

24.106 

.144633 

24.864 

.120438 

53 

54 

25.026 

.171744 

25.827 

.147716 

26.643 

.121755 

54 

55 

26.842 

1.175338 

27.704 

1.149560 

28.583 

1.121651 

55 

56 

28.820 

.177745 

29.750 

.150034 

30.692 

.120077 

56 

57 

30.979 

.178815 

31.977 

.149081 

32.985 

.116863 

57  1 

58 

33.329 

.178529 

34.399 

.146556 

35.475 

.111893 

58 

59 

35.888 

.176713 

37.031 

.142323 

38.174 

.105012 

59  ] 

60 

38.672 

1.173251 

39.890 

1.136245 

41.102 

1.095957 

60 

61 

41.696 

.168027 

42.989 

.128075 

44.269 

.084614 

61 

62 

44.978 

.160787 

46.346 

.117699 

47.688 

.070781 

62 

63 

48.537 

.151417 

49.975 

.104913 

51.381 

.054124 

63 

64 

52.387 

.139747 

53.896 

.089416 

55.358 

.034441 

64 

65 

56.552 

■  .125466 

58.126 

.070998 

59.636 

.011425 

65 

*122 


TABLE     LIY. 


SINGLE    PREMIUM    OR  RESERVE   (A),    FOR  ENDOWMENT  INSURANCE  OF  1,000  CON- 
TINUING m  YEARS  FROM   THE  PRESENT  AGE. 


4 

PER  ( 

:;ent. 

PEESENT 
A&E. 

m=l.     li-. 

l^m.  d. 

2. 

2i. 

Jm.d. 

3. 

3i. 

^m.d. 

PRESENT 
AGE. 

15 

961.538  943.169 

1.531 

924.800 

907.254 

1.462 

889.708 

872.949 

1.397 

15 

16 

961.538 

943.169 

1.531 

924.801 

907.256 

1.462 

889.711 

872.953 

1.397 

16 

17 

961.538 

943.170 

1.531 

924.802 

907.258 

1.462 

889.715 

872.959 

1.396 

17 

18 

961.538 

943.171 

1.531 

924.803 

907.261 

1.462 

889.718 

872.964 

1.396 

18 

19 

961.538  943.171 

1.531 

924.805 

907.264 

1.462 

889.723 

872.971 

1.396 

19 

20 

961.538  943.172 

1.531 

924.806 

907.267 

1.462 

889.727 

872.978 

1.396 

20 

21 

961.538 

943.173 

1.530 

924.808 

907.270 

1.462 

889.733 

872.986 

1.396 

21 

22 

961.538 

943.174 

1.530 

924.810 

907.274 

1.461 

889.738  872.994 

1.395 

22 

23 

961.538 

943.175 

1.530 

924.812 

907.278 

1.461 

889.7441873.003 

1.395 

23 

24 

961.538 

945.176 

1.530 

924.814 

907.282 

1.461 

889.751873.013 

1.395 

24 

25 

961.538 

943.177 

1.530 

924.816 

907.287 

1.461 

889.758  873.024 

1.395 

25 

26 

961.538 

943.178 

1.530 

924.819 

907.292 

1.461 

889.766i873.037 

1.394 

26 

27 

961.538 

943.180 

1.530 

924.822 

907.299 

1.460 

889.775|873.049 

1.394 

27 

28 

961.538 

943.181 

1.530 

924.825 

907.305 

1.460 

889.785i873.064 

1.393 

28 

29 

961.538|943.184 

1.530 

924.829  907.312 

1.460 

889.796 

873.082 

1.393 

29 

30 

961.538 

943.185 

1.530 

924.833  907.320 

1.459 

889.808 

873.099 

1.392 

30 

31 

961.538 

943.188 

1.529 

924.838 

907.329 

1.459 

889.821 

873.118 

1.392 

31 

32 

961.538 

943.190 

1.529 

924.842 

907.339 

1.459 

889.835 

873.139 

1.391 

32 

33 

961.538 

943.192 

1.529 

924.847 

907.349 

1.458 

889.851 

873.163 

1.391 

33 

34 

961.538 

943.196 

1.529 

924.853 

907.361 

1.458 

889.868 

873.190 

1.390 

34 

35 

961.538 

943.199 

1.528 

924.860 

907.374 

1.457 

889.888 

873.219 

1.389 

35 

36 

961.538 

943.202 

1.528 

924.867 

907.388 

1.457 

889.908 

873.249 

1.388 

36 

37 

961.538 

943.206 

1.528 

924.874 

907.402 

1.456 

889.931 

873.283 

1.387 

37 

38 

961.538 

943.210 

1.527 

924.883 

907.420 

1.455 

889.957 

873.322 

1.386 

38 

39 

961.538 

943.215 

1.527 

924.892 

907.438 

1.455 

889.985 

873.364 

1.385 

39 

40 

961.538 

943.220 

1.527 

924.902 

907.458 

1.454 

890.015 

873.410 

1.384 

40 

41 

961.538 

943.225 

1.526 

924.913|907.480 

1.453 

890.048 

873.460 

1.382 

41 

42 

961.538 

943.232 

1.526 

924.926 

907.506 

1.452 

890.086 

873.516 

1.381 

42 

43 

961.538 

943.239 

1.525 

924.939 

907.532 

1.451 

890.126 

873.576 

1.379 

43 

44 

961.538 

943.246 

1.524 

924.954 

907.562 

1.449 

890.171 

873.644 

1.377 

44 

45 

961.538 

943.254 

1.524 

924.971 

907.595 

1.448 

890.220 

873.717 

1.375 

45 

46 

961.538 

943.263 

1.523 

924.989 

907.631[1.447 

890.274 

873.798 

1.373 

46 

47 

961.538 

943.273 

1.522 

925.008 

907.670il.445 

890.333 

873.887 

1.371 

47 

48 

961.538 

943.284 

1.521 

925.030 

907.7141.443 

890.399|873.985 

1.368 

48 

49 

961.538 

943.296 

1.520 

925.054 

907.7621.441 

890.470  874.091 

1.365 

49 

50 

961.538 

943.309 

1.519 

925.080 

907.8141.439 

890.549  874.210 

1.362 

50 

51 

961.538 

943.323 

1.518 

925.109 

907.872:1.436 

890.635  874.338 

1.358 

51 

52 

961.538 

943.339 

1.517 

925.141 

907.935 

1.434 

890.730  874.480 

1.354 

52 

53 

961.538 

943.357 

1.515 

925.176 

908.004 

1.431 

890.833;874.635 

1.350 

53 

54 

961.538 

943.376 

1.514 

925.214 

908.080 

1.428 

890. 9471874. 805 

1.345 

54 

55 

961.538 

943.397 

1.512 

925.256 

908.164 

1.424 

891.073'874.994 

1.340 

55 

56 

961.538 

943.420 

1.511 

925.302 

908.256 

1.421 

891.211875.199 

1.334 

56 

57 

961.538 

943.446 

1.508 

925.354 

908.359 

1.416 

891.363|875.425 

1.328 

57 

58 

961.538 

943.473 

1.505 

925.409 

908.469 

1.412 

891.528'875.670 

1.322 

58 

59 

961.538 

943.504 

1.503 

925.470 

908.589 

1.407 

891.709 

875.940 

1.314 

59 

60 

961.538J943.537 

1.500 

925.537 

908.722 

1.401 

891.908'876.237 

1.306 

60 

61 

961.5381943.575 

1.497 

925.611 

908.868 

1.395 

892.126  876.560 

1.297 

61 

62 

961.538  943.615 

1.494 

925.692i909.028 

1.389 

892.365  876.915 

1.288 

62 

63 

961.538  943.659 

1.490 

925.781i909.204 

1.381 

892.627  877.303 

1.277 

63 

64 

961.538  943.708 

1.486 

925.878i909.396 

1.374 

892.914  877.728 

1.266 

64 

65 

961.538  943.761 

1.481 

925.985,909.606 

1.365 

893.228,878.192 

1.253 

65 

Formula,  Ag^>  =  1000  \ 


|  =  1000|l-(l-i;)(l+ar0} 


TABLE      LIY 


♦123 


SINGLE    PREMIUM  OR    RESERVE  (A).  FOR  ENDOWMENT    INSURANCE    OF    1,000    CON. 
TINUING   m  YEARS  FROM  THE  PRESENT   AGE. 

4  PER  CENT. 


PRESENT 
AGE. 

4. 

4i. 

^m.d. 

5. 

5i 

|m.d. 

6. 

6i. 

im.d. 

PEESENT 
AQE. 

15 

856.191 

840.184 

1.334 

824.177 

808.889 

1.274 

'  793.602 

779.002 

1.217 

15 

16 

856.196 

840.191 

1.334 

824.187 

808.902 

1.274 

793.617 

779.020 

1.216 

16 

17 

856.203 

840.201 

1.334 

824.199 

808.917 

1.274 

793.635 

779.041 

1.216 

17 

18 

856.211 

840.211 

1.333 

824.212 

808.933 

1.273 

793.654 

779.064 

1.216 

18 

19 

856.220 

840.223 

1.333 

824.226 

808.950 

1.273 

793.675 

779.090 

1.215 

19 

20 

856.229 

840.235 

1.333 

824.241 

808.970 

1.273 

793.699 

779.118 

1.215 

20 

21 

856.239 

840.248 

1.333 

824.258 

808.991 

1.272 

793.724 

779.149 

1.215 

21 

22 

856.250 

840.263 

1.332 

824.277 

809.014 

1.272 

793.752 

779.182 

1.214 

22 

23 

856.262 

840.279 

1.332 

824.297 

809.039 

1.272 

793.782 

779.218 

1.214 

23 

24 

856.276 

■840.297 

1.332 

824.319 

809.068 

1.271 

793.816 

779.259 

1.213 

24 

25 

856.290 

840.317 

1.331 

824.344 

809.099 

1.270 

793.853 

779.303 

1.213 

25 

26 

856.307 

840.339 

1.331 

824.372 

809.133 

1.270 

793.894 

779.353 

1.212 

26 

27 

856.324 

840.363)1.330 

824.401 

809.170 

1.269 

793.939 

779.407 

1.211 

27 

28 

856.344 

840.3891.330 

824.434 

809.211 

1.269 

793.989 

779.467 

1.210 

28 

29 

856.367 

840.419,1.329 

824.471 

809.258 

1.268 

794.044 

779.533 

1.209 

29 

30 

856.390 

840.45oll.328 

824.510 

809.306 

1.267 

794.102 

779.603 

1.208 

30 

31 

856.416 

840.485 

1.328 

824.553 

809.360 

1.266 

794.168 

779.682 

1.207 

31 

32 

856.444 

840.522 

1.327 

824.601 

809.420 

1.265 

794.240 

779.769 

1.206 

32 

33 

856.476 

840.566 

1.326 

824.655 

809.488 

1.264 

794.320 

779.864 

1.205 

33 

34 

856.512 

840.612 

1.325 

824.713 

809.560 

1.263 

794.408 

779.970 

1.203 

34 

35 

856.550 

840.663 

1.324 

824.777 

809.640 

1.261' 

794.504 

780.085 

1.202 

35 

36 

856.591 

840.718 

1.323 

824.846 

809.726 

1.260 

794.607 

780.209 

1.200 

36 

37 

856.636 

840. 779 

1.321 

824.922 

809.822 

1.258 

794.722 

780.348 

1.198 

37 

38 

856.688 

840.848 

1.320 

825.008 

809.929 

1.257 

794.850 

780.501 

1.196 

38 

39 

856.744 

840.922 

1.319 

825.101 

810.045 

1.255 

794.990 

780.669 

1.193 

39 

40 

856.805 

841.004 

1.317 

825.203 

810.173 

1.253 

795.143 

780.853 

1.191 

40 

41 

856.872 

841.093 

1.315 

825.314 

810.312 

1.250 

795.310 

781.054 

1.188 

41 

42 

856.947 

841.193 

1.313 

825.439 

810.468 

1.248 

795.497 

781.278 

1.185 

42 

43 

857.027 

841.300 

1.311 

825.573 

810.635 

1.245 

795.698 

781.519 

1.182 

43 

44 

857.117 

841.419 

1.308 

825.722 

810.822 

1.242 

795.922 

781.788 

1.178 

44 

45 

857.215 

841.550 

1.305 

825.886 

811.026 

1.238 

796.167 

782.081 

1.174 

45 

46 

857.322 

841.693 

1.302 

826.065 

811.250 

1.235 

796.435 

782.403 

1.169 

46 

47 

857.441 

841.851 

1.299 

826.262 

811.496 

1.231 

796.730 

782.757 

1.164 

47 

48 

857.571 

842.025 

1.296 

826.478 

811.766 

1.226 

797.054 

783.144 

1.159 

48 

49 

857.713 

842.2141.292 

826.715 

812.061 

1.221 

797.408 

783.568 

1.153 

49 

50 

857.871 

842.4231.287 

826.976 

812.386 

1.216 

797.797 

784.034 

1.147 

50 

51 

858.042 

842.651  1.283 

827.260 

812.741 

1.210 

798.223 

784.544 

1.140 

51 

52 

858.230 

842.901 

1.277 

827.572 

813.130 

1.204 

798.688 

785.101 

1.132 

52 

53 

858.437 

843.176 

1.272 

827.915 

813.557 

1.197 

799.199 

785.712 

1.124 

53 

54 

858.664 

843.477 

1.266 

828.291 

814.025 

1.189 

799.759 

786.381 

1.115 

54 

55 

858.914 

843.809 

1.259 

828.704 

814.539 

1.180 

800.374 

787.115 

1.105 

55 

56 

859.187 

844.171 

1.251 

829.155 

815.099 

1.171 

801.044 

787.915 

1.094 

56 

67 

859.487 

844.568 

1.243 

829.650 

815.714 

1.161 

801.779 

788.791 

1.082 

57 

58 

859.813 

845.001 

1.234 

830.189 

816.383 

1.151 

802.578 

789.743 

1.070 

58 

59 

860.172 

845.475 

1.225 

830.779 

817.116 

1.139 

803.453 

790.784 

1.056 

59 

60 

860.566 

845.996 

1.214 

831.426 

817.917 

1.126 

804.409 

791.921 

1.041 

60 

61 

860.995 

846.563 

1.203 

832.132 

818.791 

1.112 

805.450 

793.158 

1.024 

61 

62 

861.465 

847.183 

1.190 

832.901 

819.742 

1.097 

806.584 

794.504 

1.007 

62 

63 

861.980 

847.862 

1.177 

833.744 

820.783 

1.080 

807.823 

795.972 

.988 

63 

64 

862.542 

848.601 

1.162 

834.661 

821.914 

1.062 

809.167 

797.563 

.967 

64 

65 

863.157 

849.409 

1.146 

835.661  823.145 

1.043 

810.629 

799.290]  .945  1 

65 

Note  that  i^  m.  d.  is  ^  of  the  difference  of  the  integer  or  m  columns,  4  —  5,  etc. 


*124 


TABLE     LIT 


SINGLE    PREMIUM    OR  RESERVE    (A),    FOR  ENDOWMENT  INSURANCE  OF  1,000  CON. 
TINUING  m  YEARS  FROM  THE  PRESENT   AGE. 

4  PER   CENT. 


PRESENT 
AGE. 

m  =  7. 

7i. 

imA. 

8. 

8i. 

^m.d. 

9. 

9i. 

|m.d. 

PEESENT 
AGE, 

15 

764.402 

750.459 

1.162 

736.516 

723.201 

1.110 

709.886 

697.171 

1.060 

15 

16 

764.^23 

750.483 

1.162 

736.544 

723.233 

1.109 

709.923 

697.213 

1.059 

16 

17 

764.448 

750.512 

1.161 

736.577 

723.272 

1.109 

709.966 

697.262 

1.059 

17 

18 

764.475 

750.544 

1.161 

736.614 

723.313 

1.108 

710.013 

697.314 

1.058 

18 

19 

764.505 

750.579 

1.161 

736.653 

723.358 

1.108 

710.063 

697.371 

1.058 

19 

20 

764.537 

750.617 

1.160 

736.697 

723.408 

1.107 

710.120 

697.435 

1.057 

20 

21 

764.573 

750.659 

1.160 

736.,  745 

723.463 

1.107 

i  710.181 

697.504 

1.056 

21 

22 

764.612 

750.704 

1.159 

736.797 

723.523 

1.106 

710.249697.581 

1.056 

22 

23 

764.654 

750.754 

1.158 

736.854 

723.588 

1.106 

710.323697.664 

1.055 

23 

24 

764.702 

750.810 

1.158 

736.918 

723.661 

1.105 

710.405  697.757 

1.054 

24 

25 

764.754 

750.870 

1.157 

736.987 

723. 741 

1.104 

710.495  697.858 

1.053 

25 

26 

764.812  750.938 

1.156 

737.065 

723.830 

1.103 

710.595'697.971 

1.052 

26 

27 

764.875  751.012 

1.155 

737.149 

723.926 

1.102 

710. 7031698.093 

1.051 

27 

28 

764.945  751.093 

1.154 

737. 2421724. 032 

1.101 

710.823l698.228 

1.050 

28 

29 

765.022,751.183 

1.153 

737.345  724.150 

1.100 

710.956  698.378 

1.048 

29 

30 

765.104 

751.280 

1.152 

737.456  724.277 

1.098 

711,0991698.539 

1.047 

30 

31 

765.197 

751.388 

1.151 

737.579 

724.418 

1.097 

711.257 

698.718 

1.045 

31 

32 

765.297 

751.505 

1.149 

737.713 

724.572 

1.095 

711.431 

698.913 

1.043 

32 

33 

765.409 

751.636 

1.148 

737.863 

724.743 

1.093 

711.624 

699.131 

1.041 

33 

34 

765.532 

751.779 

1.146 

738.027 

724.931 

1.091 

711.835 

699.368 

1.039 

34 

35 

765.667 

751.937 

1.144 

738.207 

725.137 

1.089 

712.067 

699.629 

1.037 

35 

36 

765.812 

752.107 

1.142 

738.402 

725.360 

1.087 

712.318 

699.913 

1.034 

36 

37 

765.974 

752.295 

1.140 

738.617  725.606 

1.084 

712.596 

700.226 

1.031 

37 

38 

766.153 

752.505 

1.137 

738.857  725.880 

1.081 

712.904 

700.572 

1.028 

38 

39 

766.349 

752.733 

1.135 

739.118 

726.179 

1.078 

713.241 

700.951 

1.024 

39 

40 

766.564  752.984 

1.132 

739.404 

726.506 

1.075 

713.609  701.366 

1.020 

40 

41 

766.798  753.257 

1.128 

739.717|726.864 

1.071 

714.012  701.820 

1.016 

41 

42 

767.059  753.562 

1.125 

740.065j727.261 

1.067 

714.458  702.322 

1.011 

42 

43 

767.341753.891 

1.121 

740.4411727. 692 

1.062 

714.943  702.868 

1.006 

43 

44 

767.654  754.256 

1.117 

740.858  728.168 

1.058 

715.478  703.469 

1.001 

44 

45 

767.996  754.655 

1.112 

741.3141728.689 

1.052 

716.064!704.127 

.995 

45 

46 

768.371  755.092 

1.107 

741.813  729.2591.046 

716.705!704.848 

.988 

46 

47 

768.783,755.572 

1.101 

742.362  729.885  1.040 

717.408  705.638 

.981 

47 

48 

769.235  756.098 

1.095 

742.962  730.5691.033 

718.177:706.502 

.973 

48 

49 

769.729  756.674 

1.088 

743.619  731.319|1.025 

719.019  707.447 

1 

.964 

49 

50 

770.272  757.305 

1.081 

744.339 

732.1401.017 

719.941708.482 

.955 

50 

51 

770.865  757.995 

1.073 

745.126 

733.0371.007 

720.948  709.611 

.945 

51 

52 

771.514  758.751 

1.064 

745.987 

734.018    .997 

722.049  710.845 

.934 

52 

53 

772.225  759.577 

1.054 

746.929 

735.090    .987 

723.251:712.192 

.922 

53 

54 

773.003  760.481 

1.044 

747.959 

736.2621  .975 

724.565.713.663 

.908 

54 

55 

773.856  761.471 

1.032 

749.086 

737.542    .962 

725.999  715.267 

.894 

55 

56 

774.786,762.549 

1.020 

750.313 

738.936    .948 

727.560  717.012 

.879 

56 

57 

775.803  763.728 

1.006 

751.653 

740.457!  .933 

729.261:718.912 

.862 

57 

58 

776.909 

765.008 

.992 

1  753.108 

742.108'  .917 

731.108  720.973 

.845 

58 

59 

778.116 

766.406 

.976 

;  754.696 

743.906    .899 

733.117  723.212 

.825 

59 

60 

779.434 

767.929 

.959 

i  756.424 

745.8621  .880 

735.300  725.642 

.805 

60 

61 

780.867 

769.583 

.940 

758.300 

747.982!  .860 

737.665  728.272 

.783 

61 

62 

782.425 

771.380 

.920 

760.335 

750.280 

.838 

740.225  731.115 

.759 

62 

63 

784.121 

773.332 

.899 

762.544 

752.770 

.815 

742.996  734.188 

.734 

63 

64 

785.959 

775.446 

.876 

764.933 

755.458 

.790 

745.984^37.495 

.707 

64 

65 

787.952 

777.733 

.852 

767.515 

758.360 

.763- 

749.205  741.054 

.679 

65 

TABLE     LIT. 


*J35 


SINGLE    PREMIUM  OR    RESERVE    (A),   FOR  ENDOWMENT  INSURANCE    OF    1,000  CON- 
TINUING  ni  YEARS  FROM  THE  PRESENT   AGE. 
^  4  PER   CENT. 


PRESENI 
AGE. 

10. 

lOj. 

^m.d. 
1.012 

11. 

Hi    iin.d. 

12. 

12i. 

im.d. 

PRESENT 
AGB. 

15 

684.45? 

672.317 

660.177 

648.586   .966 

636.995 

625.929 

.922 

15 

16 

684.504!  672.369 

1.011 

660.235 

648.650 

.965 

637.f^65 

626.006 

.922 

16 

17 

684.558,'  672.429 

1.011 

660.301 

648.722 

.965 

637.144 

626.092 

.921 

17 

18 

684.616 

672.494 

1.010 

660.372 

648.801 

.964 

637.231 

626.187 

.920 

18 

19 

;  684.680 

672.566 

1.009 

660.451 

648.888 

.964 

637.326 

626.291 

.920 

19 

20 

684.751 

672.645 

1.009 

:  660.538 

648.984 

.963 

637.430 

626.405 

.919 

20 

21 

684.828 

672.730 

1.008 

660.633 

649.089 

.962 

637.545 

626.530 

.918 

21 

22 

684.913 

672.825 

1.007 

660.737 

649.203 

.961 

637.670 

626.667 

.917 

22 

23 

685.006 

672.928 

1.007 

660.851 

649.329 

.960 

637.808 

626.818 

.916 

23 

24 

685.109 

673.043 

1.006 

660.977 

649.469 

.959 

637.960 

626.985 

.915 

24 

25 

685.222 

673.169 

1.004 

661.116 

649.621 

.958 

638.127 

627.167 

.913 

25 

26 

685.347  673.308 

1.003 

661.270 

649.791 

.957 

638.312 

627.370 

.912 

26 

27 

685.483j  673.460 

1.002 

661.437 

649.975 

.955 

638.514 

627.590 

.910 

27 

28 

685.634 

673  627 

1.001 

661.621 

650.178 

.954 

638.736 

627.834 

.909 

28 

29 

685.800 

673.812 

.999 

661.825 

650.403 

.952 

638.981 

628.101 

.907 

29 

30 

685.979 

674.012 

.997 

662.045 

650.646 

.950 

639.247 

628.392 

.905 

30 

31 

686.178  674.233 

.995  1 

662.289 

650.915 

.948 

639.541 

628.713 

.902 

31 

32 

686.396  674.476 

.993 

662.557 

651.210 

.946 

639.863 

629.065 

.900 

32 

33 

686.638i  674.745 

.991 

662.852 

651.535 

.943 

640.219 

629.454 

.897 

33 

34 

686.902,  675.039 

.989! 

663.177 

651.893 

.940 

640.609 

629.880 

.894 

34 

35 

687.192 

675.362 

.986 

663.532 

652.284 

.937 

641.037 

630.348 

.891 

35 

36 

687.508 

675.713 

.983 

663.919 

652.710 

.934 

641.502 

630.857 

.887 

36 

37 

687.856 

676.101 

.980 

664.346 

653.181 

.930 

642.016 

631.418 

.883 

37 

38 

688.241 

676.529 

.976 

664.817 

653.699 

.927 

642.582 

632.036 

.879 

38 

39 

688.662 

676.997 

.972 

665.332 

654.267 

.922 

643.202 

632.713 

.874 

39 

40 

689.123 

677.510 

.968 

665.897 

654.888 

.917 

643.880 

633.453 

.869 

40 

41 

689.628 

678.071 

.963 

666.514 

655.568 

.912 

644.621 

634.262 

.863 

41 

42  • 

690.186 

678.691 

.958 

667.196 

656.318 

.907 

645.440 

635.155 

.857 

42 

43 

690.792 

679.364 

.952 

667.937 

657.133 

.900 

646.329 

636.125 

.850 

43 

44 

691.461 

680.107 

.946 

668.753 

658.030 

.894 

647.308 

637.192 

.843 

44 

45 

692.191 

680.918 

.939 

669.645 

659.011 

.886 

648.377 

638.358 

.835 

45 

46 

692.991 

681.806 

.932 

670.621 

660.083 

.878 

649.546 

639.631 

.826 

46 

47 

693.868 

682.779 

.924 

671.690 

661.258 

.869 

650.825 

641.025 

.817 

47 

48 

694.827 

683.843 

.915 

673.859' 

662.540 

.860 

652.222 

642.546 

.806 

48 

49 

695.875 

685.005 

.906 

674.135 

663.941 

.850 

653.747 

644.205 

.795 

49 

50 

697.023 

686.276 

.896 

675.530 

665.471 

.838 

655.413 

646.017 

.783 

50 

51 

698.275 

687.663 

.884 

677.052 

667.139 

.826  1 

657.227 

647.988 

.770 

51 

52 

699.641 

689.176 

.872 

678.711 

668.957 

.813 

659.203 

650.134 

.756 

52 

53 

701.133 

690.826 

.859 

680.519 

670.936 

.799 

661.354 

652.469 

.740 

53 

54 

702.761 

692.625 

.845 

682.489 

673.092 

.783 

663.695 

655.008 

.724 

54 

55 

704.535 

694.585 

.829 

684.635 

675.437 

.767 

666.239 

657.764 

.706 

55 

56 

706.464 

696.713 

.813 

686.963 

677.979 

.749 

668.996 

660.749 

.687 

56 

57 

708.563 

699.028 

.795 

689.493 

680.739 

.730 

671.986 

663.982 

.667 

57 

58 

710.838 

701.533 

.775 

692.229 

683.721 

.709 

675.214 

667.469 

.645 

58 

59 

713.308 

704.251 

.755 

695.194 

686.949 

.687 

678.705 

671.235 

.623 

59 

60 

715.985 

707.193 

.733 

698.402 

690.437 

.664 

682.472 

675.294 

.598 

60 

61 

718.880 

710.371 

.709 

701.862 

694.193 

.639  1 

686.525 

679.654 

.573 

61 

62 

722.006 

713.797 

.684 

705.587 

698.231 

.613 

690.876 

684.328 

.546 

62 

63 

725.379 

717.488 

.658 

709.596 

702.570 

.586 

695.545 

689.335 

.518 

63 

64 

729.007 

721.450 

.630 

713.894 

707.214 

.557 

700.535 

694.676 

.488 

64 

65 

732.904 

725.699 

.600 

718.495 

712.176 

.527 

705.857 

700.361 

.458 

65 

♦126 


TABLE    LIY. 


SINGLE   PREMIUM   OR   RESERVE  (A),    FOR  ENDOWMENT   INSURANCE  OF   1,000  CON- 
TINUING m  YEARS  FROM  THE  PRESENT  AGE. 

4  PER  CENT. 


1  PRESENT 
AGE, 

m=13.  13i. 

^mA. 

14. 

14i. 

^m.d. 

15. 

15i. 

\mA. 

PEESENT 
AGE. 

15 

614.863  604.299 

.880 

593.736 

583.652 

.840 

573.569 

563.944 

.802 

15 

16 

614.947  604.390 

.880 

593.834 

583.758 

.840 

573.683 

564.067 

.801 

16 

17 

615.040  604.492 

.879 

593.944 

583.877 

■.839 

573.810 

564.204 

.801 

17 

18 

615.143  604.603 

.878 

594.064 

584.007 

.838 

573.950 

564.354 

.800 

18 

19 

615.256;  604.726 

.878 

594.197 

584.150 

.837 

574.104 

564.520 

.799 

19 

20 

615.380 

604.861 

.877 

594.342 

584.307 

.836 

574.273 

564.701 

.798 

20 

21 

615.516 

605.009 

.876 

594.502 

584.480 

.835 

574.458 

564.900 

.797 

21 

22 

615.665 

605.170 

.875 

594.676 

584.668 

.834 

574.661 

565.119 

.795 

22 

23 

615.829 

605.349 

.873 

594.869 

584.876 

.833 

574.884 

565.358 

.794 

23 

24 

616.010 

605.546 

.872 

595.081 

585.105 

.831 

575.130 

565.623 

.792 

24 

25 

616.208 

605.761 

.871 

595.314 

585.357 

.830 

575.400 

565.913 

.791 

25 

26 

616.428 

605.999 

.869 

595.571 

585.634 

.828 

575.698 

566.233 

.789 

26 

27 

616.667 

606.259 

.867 

595.851 

585.937 

.826 

576.023 

566.582 

.787 

27 

28 

616.931 

606.545 

.866 

596.160 

586.271 

.824 

576.382 

566.968 

.785 

28 

29 

617.222 

606.861 

.863 

596.501 

586.638 

.822 

576.776 

567.392 

.782 

29 

30 

617.537 

607.204 

.861 

596.871 

587.038 

.819 

577.205 

567.852 

.779 

30 

31 

617.886 

607.582 

.859 

597.279 

587.479 

.817 

577.679 

568.361 

.777 

31 

32 

618.268 

607.997 

.856 

597.727 

587.962 

.814 

578.198 

568.918 

.773 

32 

33 

618.690 

608.455 

.853 

598.221 

588.495 

.811 

578.769 

569.532 

.770 

33 

34 

619.152 

608.957 

.850 

598.762 

589.079 

.807 

579.396 

570.204 

.766 

34 

35 

619.659 

609.507 

.846 

599.355 

589.719 

.803 

580.083 

570.941 

.762 

35 

36 

620.211 

610.106 

.842 

600.002 

590.416 

.799 

580.831 

571.745 

.757 

36 

37 

620. 82€ 

610.767 

.838 

600.714 

591.184 

.794 

581.655 

572.629 

.752 

37 

38 

621.491 

611.494 

.833- 

601.498 

592.029 

.789 

582.561 

573.601 

.747 

38 

39 

622.224 

612.289 

.828 

602.354 

592.952 

.784 

583.551 

574.662 

.741 

39 

40 

623.026 

613.159 

.822 

603.292 

593.963 

.777 

584.634 

575.823 

.734 

40 

41 

623.904 

614.110 

.816 

604.317 

595.067 

.771 

585.818 

577.092 

.727 

41 

42 

624.871 

615.157 

.810 

605.444 

596.281 

.764 

587.119 

578.486 

.719 

42 

43 

625.922 

616.296 

.802 

606.671 

597.602 

.756 

588.534 

580.002 

.711 

43 

44 

627.077 

617.547 

.794 

608.017 

599.051 

.747 

590.086 

581.663 

.702 

44 

45 

628.339 

618.913 

.786 

609.487 

600.632 

.738 

591.778 

583.474 

.692 

45 

46 

629.717 

620.404 

.776 

611.092 

602.358 

.728 

593.625 

585.450 

.681 

46 

47 

631.225 

622.035 

.766 

612.845 

604.242 

.717 

595.640 

587.604 

.670 

47 

48 

632.870 

623.813 

.755 

614.756 

606.295 

.705 

597.835 

589.949 

.657 

48 

49 

634.664 

625.751 

.743 

616.838 

608.531 

.692 

600.224 

592.501 

.644 

49 

50 

636.621 

627.863 

.730 

619.106 

610.964 

.679 

602.823 

595.274 

.629 

50 

51 

638.750 

630.161 

.716 

621.572 

613.608 

.664 

605.645 

598.283 

.613 

51 

52 

641.066 

632.658 

.701 

624.251 

616.479 

.648 

608.707 

601.546 

.597 

52 

53 

643.585 

635.372 

.684 

627.159 

619.592 

.631 

612.025 

605.078 

.579 

53 

54 

646.321 

638.317 

.667 

630.313 

622.966 

.612 

615.619 

608.900 

.560 

54 

55 

649.290 

641.510 

.648 

633.731 

626.617 

.593 

619.504 

613.028 

.540 

55 

56 

652.502 

644.961 

.628 

637.421 

630.556 

.572 

623.691 

617.472 

.518 

56 

57 

655.978 

648.692 

.607 

641.406 

634.804 

.550 

628.203 

622.254 

.496 

67 

58 

659.725 

652.709 

.585 

645.692 

639.368 

.527 

633.045 

627.375 

.473 

58 

59 

663.766 

657.034 

.561 

650.303 

644.272 

.503 

638.242 

632.873 

.447 

59 

60 

668.116 

661.685 

.536 

655.254 

649.529 

.477 

643.804 

638.743 

.422 

60 

61 

672.783 

666.667 

.510 

660.551 

655.144 

.451 

649.737 

644.995 

.395 

61 

62 

677.780 

671.992 

.482 

666.205 

661.128 

.423 

656.051 

651.636 

.368 

32 

63 

683.125 

677.678 

.454 

672.231 

667.493 

.395 

662.756 

658.675 

.340 

63 

64 

688.817 

683.721 

.425 

678.626 

674.236 

.366 

669.846 

666.102 

.312 

64 

65 

694.866 

690.131 

.395 

685.396 

681.358 

.337 

677.321 

673.917 

.284 

65 

TABLE    LIT. 


*i2r 


SINGLE   PREMIUM  OR  RESERVE  (A),  FOR  ENDOWMENT    INSURANCE    OF   1,000    CON- 
TINUING  m  YEARS  FROM  THE  PRESENT  AGE. 

4  PER  CENT. 


PBESENT 
AQE. 

16. 

lei 

|m.d. 

17. 

17i. 

^m.d. 

18. 

18i. 

■Jm.d. 

PRESENT 
AOE. 

15 

554.320 

545.135 

.765 

535.951 

527.186 

.730 

518.422 

510.060 

.697 

15 

16 

554.452 

545.276 

.765 

536.101 

527.347 

.730 

518.593 

510.241 

.696 

16 

17 

554.598 

545.433 

.764 

536.268 

527.525 

.729 

518.782 

510.442 

.695 

17 

18 

554.759 

545.605 

.763 

536.451 

527.720 

.728 

518.989 

510.662 

.694 

18 

19 

554.936 

545.794 

.762 

536.653 

527.934 

.727 

519.216 

510.904 

.693 

19 

20 

555.130 

546.002 

.761 

536.874 

528.171 

.725 

519.469 

511.172 

.691 

20 

21 

555.343 

546.230 

.759 

537.117 

528.430 

.724 

519.744 

511.464 

.690 

21 

22 

555.576 

546.480 

.758 

537.384 

528.713 

.723 

520.043 

511.782 

.688 

22 

23 

555.833 

546.754 

.757 

537.676 

529.027 

.721 

520.378 

512.138 

.687 

23 

24 

556.116 

547.057 

.755 

537.999 

529.369 

.719 

520.740 

512.523 

.685 

24 

25 

556.426 

547.389 

.753 

5.38.352 

529.746 

.717 

521.140 

512.948 

.683 

25 

26 

556.768 

547.755 

.751 

538.742 

530.162 

.715 

521.583 

513.419 

.680 

26 

27 

557.142 

548.155 

.749 

539.168 

530.616 

.713 

522.065 

513.930 

.678 

27 

28 

557.554 

548.595 

.747 

539.637 

531.115 

.710 

522.594 

514.492 

.675 

28 

29 

558.007 

549.080 

.744 

540.153 

531.666 

.707 

523.180 

515.114 

.672 

29 

30 

558.499 

549.606 

.741 

540.714 

532.263 

.704 

523.813 

515.787 

.669 

30 

31 

559.043 

550.188 

.738 

541.333 

532.922 

.701 

524.511 

516.528 

.665 

31 

32 

559.639 

550.826 

.734 

542.012 

533.646 

.697 

525.280 

517.345 

.661 

32 

33 

560.295 

551.526 

.731 

542.758 

534.440 

.693 

526.122 

518.238 

.657 

33 

34 

561.013 

552.294 

.727 

543.576 

535.310 

.689 

527.045 

519.217 

.652 

34 

35 

561.800 

553.135 

.722 

544.471 

536.264 

.684 

528.057 

520.290 

.647 

35 

36 

562.659 

554.053 

.717 

545.447 

537.302 

.679 

529.157 

521.457 

.642 

36 

37 

563.603 

555.061 

.712 

546.520 

538.445 

.673 

530.370 

522.743 

.636 

37 

38 

564.641 

556.169 

.706 

547.698 

539.697 

.667 

531.697 

524.149 

.629 

38 

39 

565.774 

557.379 

.700 

548.985  541.066 

.660 

533.147 

525.686 

.622 

39 

40 

567.013 

558.702 

.693 

550.391 

542.560 

.653 

534.730 

527.363 

.614 

40 

41 

568.367 

560.146 

.685 

551.926 

544.192 

.645 

536.459 

529.194 

.605 

41 

42 

569.854 

561.732 

.677 

553.610 

545.980 

.636 

538.351 

531.196 

.596 

42 

43 

571.470 

563.455 

.668 

555.441 

547.925 

.626 

540.410 

533.2r75 

.586 

43 

44 

573.241 

565.343 

.658 

557.445 

550.052 

.616 

1542.658 

535.752 

.576 

44 

45 

575.171 

567.398 

.648 

559.626 

552.366 

.605 

545.106 

538.339 

.564 

45 

46 

577.275 

569.639 

.636 

562.003 

554.886 

.593 

547.770 

541.153 

.551 

46 

47 

579.569 

572.080 

.624 

564.591 

557.628 

.580 

550.666 

544.210 

.538 

47 

48 

582.064 

574.733 

.611 

567.403 

560.606 

.566 

553.808 

547.525 

.524 

48 

49 

584.777 

577.616 

.597 

570.456 

563.837 

.552 

557.218 

551.119 

.508 

49 

50 

587.726 

580.748 

.582 

573.770 

567.340 

.536 

560.911 

555.009 

.492 

50 

51 

590.922 

584.139 

.565 

577.357 

571.131 

.519 

564.905 

559.212 

.474 

51 

52 

594.385 

587.811 

.548 

581.238 

575.227 

.501 

569.217 

563.745 

.456 

52 

53 

598.132 

591.780 

.529 

585.429 

579.647 

.482 

573.866 

568.627 

.437 

53 

54 

602.182 

596.066 

.510 

589.950 

584.409 

.462 

578.868 

573.874 

.416 

54 

55 

606.552 

600.685j  .489! 

594.818 

589.532 

.441 

584.246 

579.509 

.395 

55 

56 

611.2531  605.648 

.467 

600.043 

595.022 

.418 

1 590.001 

585.530 

.373 

56 

57 

616.305  610.975 

.444 

605.646 

600.900 

.396 

596.155 

591.961 

.350 

57 

58 

621.705:616.661 

.420 

611.618 

607.161 

.371 

602. 704 

598.793 

.326 

58 

59 

627.504  622.758 

.396 

618.012 

613.849 

.347 

609.686 

606.065 

.302 

59 

60 

633.682  629.243 

.370 

624.804 

620.943 

.322 

617.083 

613.757 

.277 

60 

61 

640.253:636.128 

.344 

632.004 

628.452 

.296 

624.900 

621.870 

.252 

61 

62 

647.221 

643.417 

.317 

639.613 

636.369 

.270 

633.126 

630.391 

.228 

62 

63 

654.594 

651.113 

.290 

647.633 

644.699 

.245 

641.764 

639.320 

.204 

63 

64 

662.35S 

659.203 

.263 

656.047 

653.420 

.219 

650.794 

648.635 

.180 

64 

65 

670.5141  667.67ii 

.236 

664.845 

662.518 

.194 

660.191 

658.308 

.157 

65 

*128 


TABLE      LIV 


SINGLE    PREMIUM  OR    RESERVE  (A),  FOR  ENDOWMENT    INSURANCE    OF    l.OUU    COJS- 
TINUING   m  YEARS  FROM  THE  PRESENT   AGE. 

4  PER  CENT. 


PRESENT 
AGE. 

w=19. 

19i. 

^m.d. 

20. 

20i. 

|m.d. 

21. 

21i. 

^m.d. 

PEESEHtI 
AGE. 

15 

501.698 

493.720 

.665 

485.743^478.134 

.634 

470.525 

463.269 

.605 

15 

16 

501.890 

493.924 

.664 

485.959  478.362 

.633 

470.766 

463.523 

.604 

16 

17 

502.103 

494.150 

.663 

486.197:478.614 

.632 

471.031 

463.802 

.602 

17 

18 

502.336 

494.397 

.662 

486.458478.890 

.631 

471.3221464.109 

.601 

18 

19 

502.592 

494.668 

.660 

486.745|479.193 

.629 

471.641 

464.446 

.600 

19 

20 

502.876 

494.969 

.659 

487.062i  479.528 

.628 

471.995 

464.818 

.598 

20 

21 

503.185 

495.296 

.657 

487.4081479.894 

.626 

472.380 

465.225 

.596 

21 

22 

503.522 

495. 654 

.656 

487.786  480.293 

.624 

472.801 

465.668 

.594 

22 

23 

503.899 

496.053 

.654 

488.207 

480.738 

.622 

473.269 

466.162 

.592 

23 

24 

504.307 

496.485 

.652 

488.664 

481.221 

.620 

473.778 

466.698 

.590 

24 

25 

504.757 

496.962 

.650 

489.167 

481.752 

.618 

474.337 

467.288 

.587 

25 

26 

505.255 

497.489 

.647 

489.723 

482.339 

.615 

474.956 

467.939 

.585 

26 

27 

505.796 

498.062 

.645 

490.328 

482.978 

.613 

475.629 

468.648 

.582 

27 

28 

506.391 

498.692 

.642 

490.994 

483.681 

.609 

476.369 

469.428 

.578 

28 

29 

507.049 

499.389 

.638 

491.729 

484.457 

.606 

477.186 

470.288 

.575 

29 

30 

507.761 

500.142 

.635 

492.524 

485.297 

.602 

478.070 

471.219 

.571 

30 

31 

508.545 

500.972 

.631 

493.399 

486.221 

.598 

479.043 

472.244 

.567 

31 

32 

509.409 

501.887 

.627 

494.3641487.239 

.594 

480.114 

473.371 

.562 

32 

33 

510.354 

502.886 

.622 

495.418 

488.351 

.589 

481.285 

474.603 

.557 

33 

34 

511.389 

503.981 

.617 

496.573 

489.569 

.584 

482.566 

475.952 

.551 

34 

35 

512.524 

505.181 

.612 

497.838 

490.903 

.578 

483.968 

477.426 

.545 

35 

36 

513.758 

506.486 

.606 

499.214 

492.354 

.572 

485.494 

479.031 

.539 

36 

37 

515.J17 

507.922 

.600 

500.728 

493.949 

,565 

487.171 

480.794 

.531 

37 

38 

516.602 

509.491 

.593 

502.381 

495.692 

.557 

489.002 

482.718 

.524 

38 

39 

518.225 

511.205 

.585 

504.186 

497.592 

.550 

490.999 

484.816 

.515 

39 

40 

519.997 

513.076 

.577 

506.156 

499.666 

.541 

498.177 

487.102 

.506 

40 

41 

521.929 

515.116 

.568 

508.303 

501.926 

.531 

495.549 

489.592 

.496 

41 

42 

524.042 

517.345 

.558 

510.648 

504.392 

.521 

498.137 

492.307 

.486 

42 

43 

526.340 

519.769 

.548 

513.197 

507.072 

.510 

500.948 

495.253 

.475 

43 

44 

528.847 

522.410 

.536 

515.974 

509.990 

.499 

504.006 

498.458 

.462 

44 

45 

531.573 

525.282 

.524 

518.991 

513.158 

.486 

507.326 

501.934 

.449 

45 

46 

534.536 

528.401 

.511 

522.266J  516.595 

.473 

510.924 

505.699 

.435 

46 

47 

537.754 

531.786 

.49? 

525.819!  520.321 

.458 

514.823 

509.775 

.421 

47 

48 

541.242 

535.453 

.482 

529.6641524.349 

.443- 

519.035 

514.176 

.405 

48 

49 

545.021 

539.422 

.467 

533.824  528.704 

.427 

523.585 

518.925 

.388 

49 

50 

549.107 

543.710 

.450 

538.3131 533.401 

.409 

'528.488 

524.037 

.371 

50 

51 

553.519 

548.336 

.432 

543.153 

538.458 

.391 

533.762 

529.530 

.353 

51 

52 

558.273 

553.315 

.413 

548.358 

543.890 

.372 

539.423 

535.420 

.334 

52 

53 

563.388 

558.667 

.393 

553.947 

549.717 

.353 

545.487 

541.721 

.314 

53 

54 

568.881 

564.407 

.373 

559.933 

555.950 

.332 

551.968 

548.447 

.293 

54 

55 

574.772 

570.554 

.352 

566.337 

562.609 

.311 

558.882 

555.612 

.273 

55 

56 

581.060 

577.108 

.329 

573.157 

569.691 

.289 

566.225 

563.210 

.251 

56 

57 

587.767 

584.088 

.307 

580.410 

577.210 

.267 

574.011 

571.254 

.230 

57 

58 

594.883 

591.482 

.283 

588.082 

685.152 

.244 

582.222 

579.723 

.208 

58 

59 

602.445 

599.326 

.260 

596.207 

593.547 

.222 

590.888 

588.645 

.187 

59 

60 

610.431 

607.595 

.236 

604.759 

602.368 

.199 

599.977 

597.986 

.166 

60 

61 

618.840 

616.285 

.213 

613.731 

611.604 

.177 

609.477 

607.730 

.146 

61 

62 

627.657 

62^.380 

.190 

623.103 

621.233 

.156 

619.363 

617.850 

.126 

62 

63 

636.877 

634.870 

.167 

632.864 

631.241 

.135 

629.618 

628.326 

.108 

63 

64 

646.477 

644.731 

.146 

642.985 

641.596 

.116 

640.207 

639.121 

.091 

64 

65 

656.425 

654.926 

.125 

653.428 

652.257 

.098 

651.087 

650.190 

.075 

65 

TABLE     LIT. 


129 


SINGLE    PREMIUM    OR  RESERVE    (A),    FOR  ENDOWMENT   INSURANCE  OF  1,000  CON- 
TINUING m  YEARS  FROM   THE   PRESENT   AGE. 

4  PER   CENT. 


PRESENT 
AGE. 

15 

22. 

22i. 

|md. 

23. 

23i 

Jm.d. 

24. 

2^. 

l^m.d. 

PRESENT 
AGE, 

456.013 

449.094 

.577 

442.176 

435.581 

.550 

428.986 

422.700 

.524 

15 

16 

456.280 

449.375 

.575 

442.471 

435.890 

.548 

:  429.310 

423.040 

.523 

16 

17 

456.574 

449.685 

.574 

442.796 

436.232 

.547 

429.667 

423.415 

.521 

17 

18 

456.897 

450.024 

.573 

443.152 

436.605 

.546 

430.059 

423.825 

.520 

18 

19 

457.251 

450.397 

.571 

443.543 

437.016 

.544 

430.490 

424.277 

.518 

19 

20 

457.642 

450.808 

.570 

443.975 

437.470 

.542 

430.965 

424.775 

.516 

20 

21 

458.070 

451.259 

.568 

444.447 

437.965 

.540 

431.484 

425.319 

.514 

21 

22 

458.536 

451.749 

.566 

444.962 

438.506 

.538 

432.050 

425.912 

.512 

22 

23 

459.055 

452.294 

.563 

445.534 

439.107 

.536 

432.679 

426.571 

.509 

23 

24 

459.618 

452.887 

.562 

446.156 

439.759 

.533 

433.363 

427.288 

.506 

24 

25 

460.238 

453.539 

.558 

446.840 

440.477 

.530 

434.114  428.074 

.503 

25 

26 

460.923 

454.259 

.555 

447.595 

441.269 

.527 

434.943^28.943 

.500 

26 

27 

461.668 

455.042 

.552 

448.417 

442.131 

.524 

435.846 

429.888 

.497 

27 

28 

462.487 

455. 903 

.549 

449.319 

443.078 

.520 

436.837 

430.926 

.493 

28 

29 

463.391 

456.852 

.545 

450.314 

444.121 

.516 

437.928 

432.068 

.488 

.  29 

30 

464.369 

457.880 

.541 

451.392 

445.252 

.512 

439.112 

433.307 

.484 

30 

31 

465.445 

459.011 

.536 

452.577 

446.494 

.507 

440.412 

434.667 

.479 

31 

32 

466.628 

460.253 

.531 

453.879 

447.859 

.502 

441.838 

436.158 

.473 

32 

33 

467.922 

461.612 

.526 

455.302 

449.349 

.496 

443.397 

437.789 

.467 

33 

34 

469.337 

463.097 

.520 

456.857 

450.979 

.490 

445.100 

439.569 

.461 

34 

35 

470.885 

464.721 

.514 

458.558 

452.759 

.483 

446.961 

441.514 

.454 

35 

S6 

472.569 

466.488 

.507 

460.408 

454.696 

.476 

448.984 

443.628 

.446 

36 

37 

474.417 

468.426 

.499 

462.436 

456.818 

.468 

451.200 

445.941 

.438 

37 

38 

476.434 

470.540 

.490 

464.647 

459.131 

.460 

453.615 

448.462 

.429 

38 

39 

478.633 

472.845 

.482 

467.057 

461.651 

.451 

456.244 

451.205 

.420 

39 

40 

481.028 

475.354 

.473 

469.680 

464.391 

.441 

459.103 

454.186 

.410 

40 

41 

483.635 

478.083 

.463 

472.531 

467.369 

.430 

462.208 

457.422 

.399 

41 

42 

486.477 

481.056 

.452 

475.636 

470.610 

.419 

465.584 

460.9381  .387 

42 

43 

489.559 

484.279 

.440 

479.000 

474.120 

.407 

469.240 

464.744  .375 

43 

44 

492.910 

487.781 

.427 

482.653 

477.928 

.394 

473.202 

468.864  .362 

44 

45 

496.542 

491.574 

.414 

486.607 

482.046 

.380 

477.486 

473.316 

.348 

45 

46 

500.474 

495.677 

.400 

490.881 

486.496 

.365 

482.110 

478.117 

.333 

46 

47 

504.728 

500.113 

.385 

495.498 

491.296 

.350 

487.095 

483.289 

.317 

47 

48 

509.317 

504.893 

.369 

500.470 

496.462 

.334 

492.454 

488.842 

.301' 

48 

49 

514.265 

510.043 

.352 

505.821 

502.016 

.317 

498.211 

494.802 

.284 

49 

50 

519.586 

515.575 

.334 

511.564 

507.971 

.299 

504.377 

501.178 

.267 

50 

51 

525.299 

521.508 

.316 

517.717 

514.342 

.281 

510.967 

507.983 

.249 

51 

52 

531.418 

527.854 

.297 

524.291 

521.141 

.263 

517.992 

515.229 

.230 

52 

53 

537.956 

534.627 

.277 

531.299 

528.380 

.243 

525.461 

522.922 

.212 

53 

54 

544.921' 

541.839 

.257 

538.751 

536.066 

.224 

533.380 

531.066 

.193 

54 

55 

552.343 

549.499 

.237 

546.656 

544.206 

.204 

541.756 

539.667 

.174 

55 

56 

1560.196 

557.599 

.216 

,555.002 

552.787 

.185 

550.573 

548.706 

.156 

56 

57 

568.498 

566.147 

.196  1  563.797 

561.815 

.165 

559.833 

558.183 

.138 

57 

58 

1  577.225 

575.118 

.176  1  573.012 

571.259 

.146 

569.505 

568.065 

.120 

58 

59 

586.403 

584.536 

.156  1582.669 

581.135 

.128 

579.602 

578.361 

.103 

59 

60 

595.995 

594.360 

.136 

592.725 

591.402 

.110 

590.079 

589.027 

.088 

60 

61 

605.983 

604.570 

.118 

603.157 

602.033 

.094 

600.908 

600.029 

.073 

61 

62 

616.337 

615.133 

.100 

613.930 

612.989 

.078 

612.049 

611.329 

.060 

62 

63 

627.035 

626.026 

.084 

625.017 

624.245 

.064 

623.472;  622.893 

.048 

63 

64 

638.036 

637.205 

.069 

636.374 

635.752 

.052 

635.129  634.674 

.038 

64 

65 

j  649.294 

648.622 

.056 

647.951 

647.461 

.041 

646.970  646.621 

.029 

65 

1 

*130 


TABLE    LIY. 


SINGLE  PREMIUM   OR  RESERVE    (A),    FOR    ENDOWMENT   INSURANCE  OF   1,000  CON- 
TINUING m  YEARS  FROM  THE   PRESENT   AGE. 

4  PER  CENT. 


PBESENT 
AGE. 

m=25. 

25}. 

1 
Jm.d. 

26. 

26i 

^m.d. 

27 

27i 

^m.d. 

PEESENT 
AOE. 

15 

416.415 

410.426 

.499 

404.437 

398.732 

.475 

393.027 

387.595 

.453 

15 

16 

416.770 

410.798 

.498 

404.826 

399.139 

.474 

393.451 

388.037 

.451 

16 

17 

417.162 

411.208 

.496 

405.254 

399.586 

.472 

393.918 

388.525 

.449 

17 

18 

417.592 

411.658 

.495 

405.724 

400.077 

.471 

394.431 

389.059 

.448 

18 

19 

418.064 

412.152 

.493 

406.240 

400.617 

.469 

394.993 

389.646 

.446 

19 

20 

418.585 

412.697 

.491 

406.808 

401.210 

.467 

395.612 

390.292 

.443 

20 

21 

419.153 

413.291 

.489 

407.430 

401.859 

.464 

396.289 

390.999 

.441 

21 

22 

419.775 

413.942 

.486 

408.109 

402.569 

.462 

397.029 

391.770 

.438 

22 

23 

420.463 

414.662 

.483 

408.860 

403.353 

.459 

397.846 

392.622 

.435 

23 

24 

421.212 

415.445 

.481 

409.678 

404.208 

.456 

398.738 

393.553 

.432 

24 

25 

422.035 

416.305 

.478 

410.576 

405.146 

.453 

399.715 

394.571 

.429 

25 

26 

422.942 

417.254 

.474 

411.566 

406.178 

.449 

400.791 

395.693 

.425 

26 

27 

423.930 

418.287 

.470 

412.644 

407.304 

.445 

401.963 

396.914 

.421 

27 

28 

425.015 

419.421 

.466 

413.826 

408.537 

.441 

403.249 

398.254 

.416 

28 

29 

426.208 

420.667 

.462 

415.126 

409.894 

.436 

404.661 

399.725 

.411 

29 

30 

427.502 

422.019 

.457 

416.536 

411.364 

.431 

406.192 

40;.319 

.406 

30 

31 

428.922 

423.502 

.452 

418.083 

412.977 

.426 

407.871 

403.068 

.400 

31 

32 

430.479 

425.129  .446 

419.778 

414.744 

.420 

409.710 

404.981 

.394 

32 

33 

432.180 

426.904  .440 

421.628 

416.672 

.413 

411.716 

407.068 

.387 

33 

34 

434.038 

428.8421  .433 

423.647 

418.775 

.406 

413.903 

409.342 

.380 

34 

35 

436.067 

430.959!  .426 

425.851 

421.069 

.398 

416.288 

411.822 

.372 

35 

36 

438.272 

433.258  .418 

1428.244 

423.561 

.390 

418.878 

414.513 

.364 

36 

37 

440.683 

435.772 

.409 

430.860 

426.282 

.382 

421.704 

417.448 

.355 

37 

38 

443.310 

438.507 

.400 

433.705 

429.241 

.372 

424.776 

420.636 

.345 

38 

39 

446.166 

441.482 

.390 

436.797 

432.453 

.362 

428.110 

424.095 

.335 

39 

40 

449.269 

444.710 

.380 

440.152 

435.938 

.351 

431.724 

427.842 

.324 

40 

41 

452.636 

448.213 

.369 

443.788 

439.712 

.340 

435.636 

431.894 

.312 

41 

42 

456.293 

452.013  .357 

447.732 

443.803 

.327 

439.874 

436.281 

.299 

42 

43 

460.247 

456.119  .344 

451.991 

448.217 

.315 

444.443 

441.007 

.286 

43 

44 

464.527 

460.560 

.331 

456.594 

452.983 

.301 

449.372 

446.101 

.273 

44 

45 

469.146 

465.350 

.316 

461.554 

458.115 

.287 

454.676  451.577 

.258 

45 

46 

474.124 

470.507 

.301 

466.890 

463.630 

.272 

460.370 

457.449 

.243 

46 

47 

479.482 

476.052 

.286 

472.621 

469.548  .256  1 

466.474 

463.738 

.228 

47 

48 

485.231 

481.995 

.270 

478.759 

475.878 

.240 

472.998 

470.452 

.212 

48 

49 

491.393 

488.358 

.253 

485.323 

482.641 

.224 

479.958 

477.605 

.196 

49 

50 

497.978 

495.150 

.236 

492.322 

489.841 

.207 

487.361 

485.204 

.180 

60 

51 

505.000 

502.383 

.218 

499.766 

497.491 

.190 

495.215 

493.254 

.163 

51 

52 

512.466 

510.063 

.200 

507.661 

505.590 

.173 

503.520 

501.755 

.147 

52 

53 

520.383 

518.196 

.182 

516.008 

514.143 

.155 

512.277 

510.704 

.131 

53 

54 

528.752 

526.779 

.164 

524.806 

523.143 

.139 

521.480 

520.095 

.115 

54 

55 

537.578 

535.817 

.147 

534.056 

532.589 

.122 

531.123 

529.919 

.100 

55 

56 

546.839 

545.284 

.130 

543.730 

542.454 

.106 

541.177 

540.144 

.086 

56 

57 

556.533 

555.178 

.113 

553.823 

552.726 

.091 

551.630 

550.758 

.073 

57 

58 

566.624 

565.459 

.097 

564.293 

563.366 

.077 

562.439 

561.714 

.060 

58 

59 

577.121 

576.134 

.082 

575.147 

574.376 

.064 

673.605 

573.015 

.049 

59 

60 

587.974 

587.152 

.069 

586.330 

585.701 

.052 

585.071 

584.599 

.039 

60 

61 

599.151 

598.478 

.056 

597.806 

597.302 

.042 

596.798 

596.429 

.031 

61 

62 

610.609 

610.069 

.045 

609.530 

609.135 

.033 

608.741 

608.460 

.023 

62 

63 

622.314 

621.891 

.035 

621.468 

621.167 

.025 

620.865 

620.661 

.017 

63 

64 

634.219 

633.895 

.027 

633.57l|633.350 

.018 

633.130 

632.987 

.012 

64 

65 

646.271 

646.033 

.020 

645.795;  645. 642 

.013 

645.488 

645.394 

.008 

65 

TABLE    LIT. 


131 


SINGLE  PREMIUM    OR    RESERVE    (A),    FOR    ENDOWMENT  INSURANCE  OF   1.000  CON- 
TINUING m  YEARS  FROM  THE  PRESENT  AGE. 

4  PER  CENT. 


PEE8ENT 
AGE. 

28 

28i 

-J^m.d. 

29. 

29i 

^m.d. 

30 

30i 

|m.d 

PEESENT 
A&E. 

15 

15 

383.162 

376.991 

.431 

371.820 

366.899 

.410 

361.978 

357.397 

.390 

16 

382.624 

377.473 

.439 

372.320 

367.430 

.408 

362.520 

357.861 

.388 

16 

17 

383.131 

378.001 

.438 

372.871 

367.993 

.407 

363.116 

358.480 

.386 

17 

18 

383.688 

378.583 

.436 

373.475 

368.633 

.404 

363.769 

359.160 

.384 

18 

19 

384.399 

379.318 

.433 

374.137 

369.313 

.402 

364.486 

359.905 

.383 

19 

20 

384.972 

379.919 

.431 

374.867 

370.071'  .400 

365.275 

360.735 

.379 

20 

21 

385.708 

380.686 

.419 

375.664 

370.900!  .397 

366.136 

361.631 

.376 

21 

22 

386.511 

381.533 

.416 

376.535 

371.806 

.394 

367.078 

363.599 

,373 

22 

23 

387.399 

383.448 

.413 

377.496 

373.806 

.391 

368.116 

363.678 

.370 

23 

24 

388.367 

383.455 

.409 

378.544373.896 

.387 

369.248 

364.854 

.366 

24 

25 

389.427 

384.559 

.406 

379.692  375.090 

.384 

370.488 

366.141 

.363 

25 

26 

390.595 

385.775 

.403 

380.955  376.403i  .379 

371.850 

367.556 

.358 

26 

27 

391.866 

387.097 

.397 

383.3391377.831 

.375 

373.333 

369.095 

.353 

27 

28 

393.259 

388.547 

.393 

383.835  379.396 

.370 

374.957 

370.780 

.348 

28 

29 

394.788,390.137 

.388 

385.486:381.111 

.365 

376.736 

373.635 

.343 

29 

30 

396.447'391.863 

.383 

387.3781383.973 

.359 

378.666 

374.638 

.337 

30 

31 

398.264^393.751 

.376 

389.339385.007'  .353 

380.776 

376.815 

.330 

31 

32 

400.252|395.818 

.370 

391.383!387.332j  .346 

383.081 

379.303 

.323 

32 

33 

402.430  398.069 

.363 

393.719i389.655:  .339 

385.591 

381.804 

.316 

33 

34 

404.782 

400.533 

.355 

396.263  393.292 

.331 

388.321 

384.630 

.308 

34 

35 

407.356 

403.194 

.347 

399.031395.161 

.323 

391.291 

387.702 

.299 

35 

36 

410.148  406.089 

.338 

402.031;398.268i  -^^^ 

394.506 

391.028 

.390 

36 

37 

413.191 

409.345 

.339 

405.2991401. 651 

.304 

398.003 

394.642 

.280 

37 

38 

416.497 

413.670 

.319 

408.843'405.318 

.394 

401.792 

398.556 

.270 

38 

39 

420.080 

416.381 

.308 

413.681409.385 

.383 

405.889 

403. 784 

.259 

39 

40 

423.959 

430.395 

.397 

416.831  413.573 

.273 

410.313  407.346 

.247 

40 

41 

438.153 

434.731 

.385 

431.310  418.195 

.260 

415.081413.259 

.235 

41 

42 

433.688 

439.417 

.373 

436.146  433.183 

.347 

430.330  417.649 

.333 

42 

43 

437.571 

434.458 

.359 

431.345  438.539 

.334 

435.734  433.331 

.309 

43 

44 

443.830 

439.883 

.346 

436.934,434.393 

.330 

431.651:439. 300 

.196 

44 

45 

448.477 

445.700 

.331 

443. 933 '440. 451 

.206 

437.979'435.794 

.183 

45 

46 

454.539 

451.939 

.317 

449.339  447.031 

.193 

444.733  443.716 

.168 

46 

47 

461.003 

458.584 

.303  ! 

456.166^454.045 

.177 

451. 9331450. 078 

.154 

47 

48 

467.905 

465.673 

.186 

463.438'461.496 

.162 

459.5531457. 879 

.140 

48 

49 

475.353  473.206 

.171 

471.160 

469.397 

.147 

467.634  466.130 

.135 

49 

50 

483.047  481.188 

.155 

479.330 

477.745 

.132 

476.160  474.834 

.111 

50 

51 

491.293  489.622 

.139 

487.950  486:540 

.118 

485.131483.957 

.098 

51 

52 

499.990 

498.503 

.134 

497.014j495.775 

.103 

494.535  493.518 

.085 

52 

53 

509.132 

507.833 

.109 

506.513i505.437 

.090 

504.363  503.492 

.073 

53 

54 

518.710 

517.573 

.095 

516.435  515.515 

.077 

514.594  513.862 

.061 

54 

55 

538.714 

537.740 

.081 

536.766  535.990 

.065 

525.315 

534.609 

.051 

55 

56 

539.111 

538.389 

.069 

537.468l536.836 

.054 

536.184 

535.693 

.041 

56 

57 

549.886  549.3051 

.057 

548.533  548.001 

.044 

547.479 

547.088    .033 

57 

58 

560.990 

560.435 

.046 

559.881 

559.466 

.035 

559.050 

558.747    .035 

58 

59 

573.424 

571.983 

.037 

571.540 

571.316 

.027 

570.893 

570.663    .019 

59 

60 

584.137 

583.783 

.029 

583.438 

583.193 

.020 

583.947 

583.780 

.014 

60 

61 

596.061 

595.799 

.022 

595.537 

595.358!  .015 

595.180 

595.065 

.010 

61 

62 

608.179 

607.988 

.016 

607.798 

607.675    .010 

607.551 

307.475 

.006 

62 

63 

630.456 

630.334 

.011 

630.191 

630.109    .007 

630.038  619.980 

.004 

63 

64 

633.845 

633.757 

.007 

633.670 

633.619    .004 

633.567  633.538 

.003 

64 

65 

645.399  645.344 

.005 

645.188 

645.157    .003 

645.1361645.110 

.001 

65 

'132 


TABLE     LIY. 


SINGLE    PREMIUM  OR    RESERVE    (A),   FOR  ENDOWMENT  INSURANCE   OF    1,000  CON- 
TINUING m  YEARS  FROM  THE  PRESENT    AGE. 

4  PER   CENT. 


PEE8ENT 
AaE. 

m=31. 

3  If 

|^m.d. 

32. 

32i. 

^m.d. 

33. 

33i. 

^m.d. 

PKESENT 
AQE. 

15 

353.616 

348.166 

.371 

343.716 

339.487 

.352 

335.258  331.241 

.335 

15 

16 

353.202 

348.774 

.369 

344.347 

340.142 

.350 

335.937i331.945 

.333 

16 

17 

353.845 

349.443 

.367 

345.041 

340.862 

.348 

336.683332.719 

.330 

17 

18 

354.551 

350.176 

.365 

345.801 

341.651 

.346 

337.501333.567 

.328 

18 

19 

355.324  350.979 

.362 

346.634 

342.515 

.343 

338.396  334.495 

1 

.325 

19 

20 

356.175  351.863 

.359 

347.550 

343.465 

.340 

339.381335.516 

.322 

20 

21 

357.105  352.828 

.356 

348.551 

344.504 

.337 

340.456  336.629 

.319 

21 

212 
23 

358.121|353.882 

.353 

349.644 

345.637 

.334 

341.630  337.846 

.315 

22 

359.2401355.044 

.350 

350.848 

346.885 

.330 

342.922  339.183 

.312 

23 

24 

360.459  356.309 

.346 

352.159 

348.244 

.326 

344.329  340.641 

.307 

24 

25 

361.795  357.695 

.342 

353.594 

349.730 

.322 

345.866342.233 

.303 

25 

26 

363.261359.215 

.337 

355.169 

351.363 

.317 

347.557  343.881 

.298 

26 

27 

364.857;360.870 

.332 

356.883 

353.138 

.312 

349.393  345.880 

.293 

27 

28 

366.603  362.680 

.327 

358.757 

355.077 

.307 

351.398  347.955 

.287 

28 

29 

368.515  364.660 

.321 

360.806 

357.199 

.301 

353.591350.221 

.281 

29 

30 

370.589 

366.809 

.315 

363.029 

359.498 

.294 

355.967 

352.676 

.274 

30 

31 

372.854 

369.154 

.308 

365.454 

362.006 

.287 

358.558 

[355.352 

.267 

31 

32 

375.328 

371.713 

.301 

368.099 

364.739 

.280 

361.379 

358.264 

.200 

32 

33 

378.016 

374.494 

.294 

370.973 

367.708 

.272 

364.443 

361.425 

.252 

33 

34 

380.939 

377.517 

.285 

374.094 

370.930 

.264 

367.766 

364.851 

.243 

34 

35 

384.114 

380.797 

.276 

377.481 

374. 425 

.255 

371.369 

368.564 

.234 

35 

36 

387.550 

384.345 

.267 

381.141 

378.199 

.245 

375.257 

372,567 

.224 

36 

37 

391.281 

388.193 

.257 

385.111 

382.290 

.235 

379.469 

376.801 

214 

37 

38 

395.319 

392.359 

.247 

389.400 

386. 706 

.225 

384.012i381.571 

.203 

38 

39 

399.679 

396.852 

.236 

394.025 

391.464 

.213 

388.903  386.595 

.192 

39 

40 

404.379  401.691 

.224 

399.003 

396.581 

.202 

394.159 

391.988 

.181 

40 

41 

409.437  406.894 

.212 

404.351 

402.072 

.190 

399.794 

397.766 

.169 

41 

42 

414.879  412.487 

.199 

410.094 

407.964 

.178 

405.834 

403.951 

.157 

42 

43 

420.707  418.469 

.187 

416.232 

414.255 

.165 

412.277 

410.542 

.145 

43 

44 

426.949  424.871 

.173 

422.792 

420. 969 

.152 

419.146 

417.560 

.132 

44 

45 

433.609'431.692 

.160 

429.776 

428.109 

.139 

426.442 

425.006 

.120 

45 

46 

440.70l'438.948 

.146 

437.194 

435.683 

.126 

434.173 

432.885 

.107 

46 

47 

448.233  446.643 

.133 

445.054 

443. 699 

.113 

442.344 

441.201 

.095 

47 

48 

456.206 

454.779 

.119 

453.352 

452. 149 

.100 

450.946 

449. 945 

.083 

48 

49 

464.627 

463.359 

.106 

462.092 

461.037 

.088 

459.981 

459.114 

.072 

49 

50 

473.488  472.375 

.093 

471.263 

470.349 

.076 

469.435 

468.696 

.062 

60 

51 

482.783  481.819 

.080 

480.855 

480.075 

.065 

479.296 

478. 675 

.052 

51 

52 

492.500  491.677 

.069 

490.853 

490.198 

.055 

489.543|489.031 

.043 

52 

53 

502.622,501.930 

.058 

501.238 

500. 697 

.045 

500.156  499.742 

.035 

53 

54 

513.130,512.558 

.048 

511.986 

511.548 

.037 

511.110  510.782 

.027 

54 

55 

524.004'523.540 

.039 

523.076 

522.729 

.029 

522.381522.127 

.021 

55 

56 

535.200  534.832 

.031 

534.464 

534.194 

.023 

533.925 

533.  734 

.016 

56 

57 

546. 697:546.411 

.024 

546.126 

545.922 

.017 

545.719 

545.580 

.012 

57 

58 

558.443 

558.227 

.018 

558.010 

557.863 

.012 

557.716 

557.621 

.C08 

58 

59 

570.433 

570.276 

.013 

,570.119 

570.018 

.008 

569.917 

569.855 

.C05 

59 

60 

582.613 

582.505 

.009 

i  582.397 

582.330 

.006 

582.264 

582.225 

.003 

60 

61 

594.950 

594.879 

.006 

594.808 

594.766 

.004 

594.724 

594. 701 

.002 

61 

62 

607.399 

607.354 

.004 

607.309 

607.285 

.002 

607.260 

607.247 

.001 

62 

63 

619.932 

619.905  .002 

619.879 

619.865 

.001 

619.851 

619.844 

.001 

63 

64 

632.510 

632.495  .001 

632.480 

632.473 

.001 

632.466 

632.463 

.000 

64 

65 

j  645.094 

645.0871  -001 

1  645.079 

645.076 

.000 

645.073 

645.0721 

.000 

65 

TABLE     LIT. 


♦133 


SINGLE    PREMIUM  OR    RESERVE  (A),   FOR    ENDOWMENT   INSURANCE    OF  1,000    CON- 
TINUING ra  YEARS    FROM    THE    PRESENT   AGE. 

4  PER  CENT. 


PEESENl 
AGE. 

34. 

34i. 

im.d. 

35. 

35i 

l-m.d. 

36. 

36i. 

im.d. 

PBESENT 
AGE. 

15 

337.234 

333.411 

.318 

319.599 

j 315.983 

.301 

312.366 

308.937 

.286 

15 

16 

337.953 

334.167 

.316 

320.381 

316.791 

.399 

313.302 

309.803 

.283 

16 

17 

338.755 

334.997 

.313 

331.340 

317.681 

.397 

314.133 

310.754 

.381 

17 

18 

339.633 

335.906 

.311 

333.180 

318.654 

.394 

315.138 

311.794 

.278 

18 

19 

330.594 

336.903 

.308 

333.210 

319.719 

.391 

316.339 

313.932 

.275 

19 

20 

331.650 

337.995 

.305 

334.340 

330.888 

.288 

317.437 

314.181 

.271 

20 

21 

333.803 

339.189 

.301 

335.574 

■333.165 

.384 

318.756 

315.544 

.268 

21 

22 

334.061 

330.491 

.398 

336.923 

323.559 

.380 

330.195 

317.031 

.264 

22 

23 

335.445 

331.933 

.394 

338.401 

335.087 

.376 

331.774 

318.^61 

.259 

23 

24 

336.953 

333.483 

.389 

330.013 

336.753 

.272 

333.493 

320.436 

.355 

24 

25 

338.600 

335.186 

.385 

331.773 

338.570 

.267 

335.369 

333.372 

.250 

25 

28 

340.405 

337.053 

.379 

333.699 

330.561 

.262 

337.433 

334.490 

.244 

26 

27 

343.368 

339.081 

.374 

335.793 

333.733 

.256 

339.651 

336.789 

.239 

27 

28 

344.511 

341.394 

.368 

338.077 

335.078 

.250 

333.080 

339.393 

.232 

28 

29 

346.851 

343.710 

.363 

340.569 

337.649 

.343 

334.738 

333.031 

.336 

29 

30 

349.385 

346.335 

.355 

343.366 

340.439 

.236 

337.593 

334.969 

.319 

30 

31 

353.146 

349.174 

.348 

346.301 

343.453 

.339 

340.705 

338.174 

.311 

31 

32 

355.149 

353.369 

.340 

349.390 

346.737 

.221 

344.084 

341. 648 

.303 

32 

33 

358.407 

355.636 

.333 

353.845 

350.393 

.213 

347.740 

345.406 

.195 

33 

34 

361.937 

359.361 

.333 

356.585 

354.138 

.304 

351.691 

349.464 

.186 

34 

35 

365.758 

363.193 

.314 

360.627 

358.392 

.195 

355.957 

353.843 

.176 

35 

36 

369.878 

367.439 

.304 

364.980 

363.763 

.185 

360.543 

358.544 

.167 

36 

37 

374.333 

373.005 

.194 

369.678 

367.581 

.175 

365.485 

363.606 

.157 

37 

38 

379.130 

376.931 

.183 

374.731 

373.761 

.164 

370.790 

369.035 

.146 

38 

39 

384.387 

383.319 

.173 

380.153 

378.311 

.153 

376.470 

374.843 

.136 

39 

40 

389.818 

387.886 

.161 

385.954 

384.346 

.142 

383.539 

381.041 

.125 

40 

41 

395.738 

393.945 

.149 

393.153 

390.579 

.131 

389.007 

387.639 

.114 

41 

42 

403.068 

400.417 

.138 

398.765 

397.339 

.120 

395.893 

394.656 

.103 

42 

43 

408.807 

407.398 

.136 

405.790 

404.490 

.108 

403.190 

403.081 

.092 

43 

44 

415.974 

414.608 

.114 

413.343 

413.077 

.097 

410.913 

409.931 

.083 

44 

45 

433.570 

433.346 

.103 

431.131 

430.089 

.086 

419.056 

418.197 

.073 

45 

46 

431.597 

4.30.511 

.091 

439.436 

438.531 

.075 

437.617 

436.874 

.063 

46 

47 

440.058 

439.107 

.079 

438.155 

437.374 

.065 

436.593 

435.960 

.053 

47 

48 

448.943 

448.130 

.009 

447.397 

446.631 

.056 

445.966 

445.437 

.044 

48 

49 

458.348 

457.547 

.058 

456.845 

456.388 

.046 

455.730 

455.294 

.036 

49 

50 

467.957 

467.369 

.049 

466.781 

466.331 

.038 

465.863 

465.510 

.039 

50 

51 

478.055 

477.570 

.040 

477.085 

476.714 

.031 

476.343 

476.065 

.033 

51 

52 

488.530 

488.138 

.033 

487.736 

487.443 

.024 

487.149, 

486.934 

.018 

52 

53 

499.338 

499.017 

.036 

498.707 

498.480 

.019 

498.354 

498.093 

.014 

53 

54 

510.454 

510.314 

.030 

509.974 

509.803 

.014 

509.633 

509.516 

.010 

54 

55 

531.873 

531.693 

.015 

531.513 

531.389 

.010 

531.366 

531.187 

.007 

55 

56 

533.543 

533.411 

.011 

533.381 

533.197 

.007 

533.113 

533.061 

.004 

56 

57 

545.443 

545.353 

.007 

545.363 

545.308 

.005 

545.153 

545.130 

.003 

57 

58 

557.536 

557.479 

.004 

557.433 

557.399 

.003 

557.364 

557.345 

.003 

58 

59 

569.793 

569.756 

.003 

569.719 

569.699 

.002 

569.679 

569.669 

.001 

59 

60 

583.186 

583.164 

.003 

583.143 

583.133 

.001 

583.131 

583.115 

.001 

60 

61 

594.678 

594.666 

.001 

594.654 

594.648 

.001 

594.643 

594.641 

.000 

61 

62 

607.334 

607.338 

.001 

607.333 

607.319 

.000 

607.317: 

607.316 

.000 

62 

63 

619.838 

619.836 

.000 

619.833 

619.831 

.000 

619.830 

619.830 

.000 

63 

64 

633.460 

633.459 

.000 

632.458 

633.458 

.000 

64 

65 

645.070  645.069 

.000 

65 

*]34 


TABLE     LIT. 


SINGLE    PREMIUM   OR    RESERVE    (A),    FOR  ENDOWMENT  INSURANCE    OF    1,000  (X)N. 
TINUING  m  YEARS  FROM  THE.  PRESENT    AGE. 

4  PER    CENT. 


PKTiaENT 
A&E. 

m=37. 

37i. 

|rm.(l. 

38. 

38i. 

Jm.d. 

39. 

39i. 

^m.d. 

FBESENT 
AGE, 

15 

305.509 

302.261 

.271 

299.014 

295.941 

.256 

292.869 

289.963 

.242 

15 

16 

306.403 

303.186 

.268 

299.969 

296.928 

.253 

293.886 

291.014 

.239 

16 

17 

307.386 

304.202!  .265 

301.017 

298.010 

.251 

295.003|  292.166 

.236 

17 

18 

308.460 

305.311!  .262 

302.163 

299.198 

.248 

296.223  293.425 

.233 

18 

19 

309.636 

306.527 

.259 

303.417 

300.487 

.244 

297.557,294.800 

.230 

19 

20 

310.925 

307.857 

.256 

304. 790 

801.904 

.241 

299.018;  296.307 

.226 

20 

21 

312.332 

309.310 

.252 

306.288:303.449 

.237 

300.611  297.949 

.222 

21 

22 

313.866 

310.894 

.248 

307.9211305.134 

.232 

802.346  299.737 

.217 

22 

23 

315.548 

3ia.629 

.243 

309.710 

806.978 

.228 

304.246  301.694 

.213 

23 

24 

317.379 

314.517 

.239 

311.656 

808.983 

.223 

306.3111303.820 

1 

.208 

24 

25 

319.376 

316.577 

.233 

313.777 

311.168 

.217 

808.559  306.133 

.202 

25 

26 

321.558 

318.825 

.228 

316.093 

818.558 

.212 

311.012  308.657 

.196 

26 

27 

323.927  321.266 

.222 

318.605 

816.187 

.206 

313.670: 311.389 

.190 

27 

28 

326.506  323.922 

.215 

321.337 

818.948 

.199 

816.559;  314.358 

.183 

28 

29 

329.313 

326.810 

.209 

324.307j322.001 

.192 

319.695  317.578 

.176 

29 

30 

332.347 

329.931 

.201 

327.515 

825.297 

.185 

323.079  321.051 

.169 

30 

31 

335.642 

333.318 

.194 

330.994 

328.869 

.177 

326.7441324.809 

.161 

31 

32 

339.213 

336.986 

.186 

334.759 

332.782 

.169 

380.7041328.867 

.153 

32 

33 

343.072 

340.947 

.177 

338.822 

386.897 

.160 

384.972  333.237 

.145 

33 

34 

347.237 

345.219 

.168 

343.201341.882 

.152 

339.564  337.985 

.136 

34 

35 

351.726 

349.819 

.159 

347.918  346.205 

.142 

344.496  342.975 

.127 

35 

36 

356.545 

354.754 

.149 

352.962  351.867 

.138 

349. 7731  348.364 

.117 

36 

37 

361.727 

360.055 

.139 

358.383  356.905 

.123 

355.426 

354.129 

.108 

37 

38 

367.281 

365.730 

.129 

364.179  362.819 

.113 

361.459 

360.276 

.099 

38 

39 

373.215 

371.788 

.119 

370.861 

869.119 

.104 

367.878 

366.809 

.089 

39 

40 

379.543  378.240 

.109 

376.937  875.815 

.094 

374.693 

373.736 

.080 

40 

41 

386.272  385.093 

.098 

383.915  382.911 

.084 

381.906 

381.058 

.071 

41 

42 

393.418  392.363 

.088 

391.308  390.418 

.074 

389.529 

388.788 

.062 

42 

43 

400.973  400.039 

.078 

399.104  898.826 

.065 

397.548 

396.909 

.063 

43 

44 

408.949  408.131 

.068 

407.3181406.642 

.056 

405.970 

405.427 

.045 

44 

45 

417.337,416.631 

.059 

415.925  415.858 

.048 

414.782 

414.328 

.038 

45 

46 

426.132  425.531 

.050 

424.981 

424.453 

.040 

423.975 

423.601 

.031 

46 

47 

435.328  434.825 

.042 

434.822 

488.929 

.033 

433.536 

433.235 

.025 

47 

48 

444.907  444.493 

.035 

444.079 

448.763 

.026 

443.446  448.209 

.020 

48 

49 

454.858  454.524 

.028 

454.190 

453.940 

.021 

453. 690|  453.507 

.015 

49 

50 

465.158  464.895 

.022 

464.631 

464.488 

.016 

464.245!  464.108 

.011 

50 

51 

475.787  475.583 

.017 

475.380 

475.285 

.012 

475.091 

474.993 

.008 

51 

52 

486.719  486.567 

.013 

486.414 

486.310 

.009 

486.206 

486.139 

.006 

52 

53 

497.931 

497.821 

.009 

497.711 

497.640 

.006  1 

497.569 

497.525 

.004 

53 

54 

509.400 

509.325 

.006 

509.250 

509.204 

.004 

509.157 

509.130 

.002 

54 

55 

521.107 

521.058 

.004 

521.009 

520.980 

.002 

520.951 

520.936 

.001 

55 

56 

533.009 

532.978 

.003 

532.948 

532.931 

.001 

532.914 

532.905 

.001 

56 

57 

545.088 

545.071 

.001 

545.053 

545.043 

.001 

545.034 

545.029 

.000 

57 

58 

557.326 

557.316 

.001 

557.306 

557.302 

.000 

557.297 

557.295 

.000 

58 

59 

569.658 

569.653 

.000 

569.648 

569.645 

.000 

569.643 

569.643 

.000 

59 

60 

582  110 

582.107 

.000 

582.105 

582.104 

.000 

582.103 

582.103 

.000 

60 

61 

594.638 

594.637 

.000 

594.686 

594.636 

.000 

61 

62 

607.215  607.215 

.000 

62 

TABLE    LT. 


*135 


CONTINUED  ANNUAL  PREMIUM  (P),  ALSO  A  (P  —  rr),  FOR  ENDOWMENT  INSURANCE 

OF  1,000,  PAYABLE  AT  DEATH  OR  AGE  30,  86, 75. 

4  PER  CENT. 


Formula,  PS 


1000 


Ma;— Ma;m  +  D; 


x+m 


Na,-N. 


=  iooo|- 


_|_am-l 


(1- 


,)  10( 

-V)h    773.=  — 


lOOOMa 


D  or  30. 

D  or  40. 

D  or  45. 

AQE. 

X. 

P. 

A  (P  -  n). 

AGE. 
X. 

P. 

A(P-7r). 

AGE. 

X. 

P. 

A(P-7r). 

10 

36.209 

1.422188 

10 

21.626 

1.073792 

27 

42.013 

1.440353 

11 

38.628 

1.457505 

11 

22.610 

1.102321 

28 

45.085 

1.480236 

12 

41.333 

1.494033 

12 

23.674 

1.131372 

29 

48.557 

1.521718 

13 

44.374 

1.531914 

13 

24.828 

1.160996 

30 

52.508 

1.565008 

14 

47.814 

1.571314 

14 

26.080 

1.191238 

31 

57.043 

1.610358 

15 

51.732 

1.612430 

15 

27.444 

1.222149 

32 

62.294 

1.658046 

16 

56.232 

1.655497 

16 

28.933 

1.253772 

33 

68.441 

1.708448 

17 

61.449 

1.700814 

17 

30.564 

1.286187 

34 

75.728 

1.762024 

18 

67.560 

1.748737 

18 

32.357 

1.319456 

35 

84.494 

1.819347 

19 

74.811 

1.799719 

19 

34.333 

1.353668 

36 

95.233 

1.881195 

20 

83.542 

1.854341 

20 

36.521 

1.388905 

37 

108.685 

1.948607 

21 

94.247 

1.913374 

21 

38.955 

1.425278 

38 

126.012 

2.023045 

22 

107.667 

1.977848 

22 

41.674 

1.462912 

39 

149.147 

2.106622 

23 

124. 964 

2.049214 

23 

44.730 

1.501943 

40 

181.574 

2.202634 

24 

148.078 

2.129593 

24 

48.186 

1.542552 

41 

230.259 

2.316583 

25 

180.498 

2.222272 

25 

52.122 

1.584929 

42 

311.463 

2.458789 

26 
27 

229.202 
310.474 

2.332749 
2.471330 

26 
27 

56.639 
61.873 

1.629316 
1.676005 

43 

473.944 

2.652376 

28 

473.167 

2.661148 

28 

68.002 

1.725368 

D  or  50. 

29 

75.271 

1.777851 

D  or  a 

5. 

30 

84.019 

1.834038 

31 

94.742 

1.894707 

10 

15.173 

0.732305 

32 

108.178 

1.960887 

11 

15.680 

0.757859 

10 

27.291 

1.243468 

33 

125.490 

2.034036 

12 

16.219 

0.783718 

11 

28.773 

1.274618 

34 

148.615 

2.116277 

13 

16.795 

0.809903 

12 

30.397 

1.306530 

35 

181.039 

2.210894 

14 

17.410 

0.836438 

13 

32.181 

1.339279 

36 

229.732 

2.323388 

15 

18.066 

0.863341 

14 

34.150 

1.372945 

37 

310.967 

2.464075 

16 

18.769 

0.890617 

15 
16 

36.329 
38.753 

1.407614 
1.443390 

38 

473.559 

2.656095 

17 
18 

19.522 
20.330 

0.918329 
0.946482 

17 

41.464 

1.480401 

D  or  4 

•5. 

19 

21.199 

0.975105 

18 
19 

44.510 
47.956 

1.518786 
1.558715 

20 
21 

22.134 
23.142 

1.004235 
1.033906 

20 

51.882 

1.600380 

10 

17.819 

0.905510 

22 

24.232 

1.064158 

21 

56.388 

1.644025 

11 

18.510 

0.932276 

23 

25.412 

1.095030 

22 

61.611 

1.689944 

12 

19.250 

0.959437 

24 

26.692 

1.126579 

23 

67.730 

1. 738495 

13 

20.045 

0.987018 

25 

28.085 

LI  58863 

24 

74.987 

1.790134 

14 

20.901 

1.015049 

26 

29.605 

1.191915 

25 

83.725 

1.845446 

15 

21.821 

1.043559 

27 

31.268 

1.225823 

26 

94.437 

1.905194 

16 

22.814 

1.072577 

28 

33.093 

1.260654 

27 

107.863 

1.970416 

17 

23.888 

1.102152 

29 

35.105 

1.296492 

28 

125.166 

2.042566 

18 

25.052 

1.132321 

30 

37.328 

1.333431 

29 

148.285 

2.123761 

19 

26.315 

1.163126 

31 

39.799 

1.371589 

30 

180.704 

2.217287 

20 

27.690 

1.194622 

32 

42.558 

1.411076 

31 

229.405 

2.328653 

21 

29.191 

1.226870 

33 

45.655 

1.452050 

32 

310.663 

2.468160 

22 

30.834 

1.259935 

34 

49.153 

1.494684 

33 

473.316 

2.658944 

23 
24 

32.639 
34.628 

1.293878 
1.328793 

35 
36 

53.132 
57.693 

1.539172 

1.585758 

25 

36.830 

1.364772 

37 

62.972 

1.634744 

26 

39.279 

1.401919 

38 

69.148 

1.686510 

♦136 


TABLE    LY. 


CONTINUED  ANNUAL  PREMIUM  (P),  ALSO  A  (P  —  rr),  FOR  ENDOWMENT   INSURANCE 

OP  1,000,  PAYABLE  AT  DEATH  OR  AGE  30,  35, 75. 

4  PEli  CENT. 


D  or  50. 

D  or  55. 

D  or  60. 

Aa£. 

X. 

P. 

A(P-Tr). 

AQE. 
X. 

P. 

A(P-rr). 

A&E. 

X. 

P. 

A  (P  -  tt).  ' 

39 

76.463 

1.741492 

46 

97.304 

1.840747  ' 

48 

72.131 

1.619831 

40 

85.258 

1.800288 

47 

110.824 

1.911844 

49 

79.567 

1.679106 

41 

96.025 

1.863669 

48 

128.208 

1.990107 

50 

88.483 

1.742373 

42 

109.504 

1.932686 

49 

151.386 

2.077669 

51 

99.369 

1.810412 

43 

126.851 

2.008777 

50 

183.827 

2.177823 

52 

112.954 

1.884252 

44 

150.003 

2.094087 

51 

232.476 

2.296083 

53 

130.395 

1.965369 

45 

182.437 

2,191901 

52 

313.525 

2.442754 

54 

153.615 

2.055898 

46 

47 
48 

231.108 
312.252 

474.564 

2.307724 

2.451875 
2.647485 

53 

475.564 

2.640983 

55 
56 
57 

186.071 
234.677 
315.575 

2.159133 
2.280580 
2.430562 

T>  rkf  df^ 

u  or  o 

\j. 

58 

477.171 

2.632212 

D  or  6 

5. 

10 

11.984 

0.344432 

D  or  65. 

11 

12 

12.290 
12.613 

0.368547 
0.392838 

10 

13.304 

0.547799 

11 

13.690 

0.572500 

13 

12.954 

0.417355 

10 

11.069 

0.112203 

12 

14.100 

0.597443 

14 

13.316 

0.442119 

11 

11.321 

0.135832 

13 

14.534 

0.622659 

15 

13.698 

0.467164 

12 

11.586 

0.159718 

14 

14.996 

0.648155 

16 

14.103 

0.492439 

13 

11.867 

0.183754 

15 

15.486 

0.673960 

17 

14.533 

0.518014 

14 

12.163 

0.208038 

16 

16.008 

0.700054 

18 

14.988 

0.543869 

15 

12.474 

0.232590 

17 

16.563 

0.726491 

19 

15.472 

0.570029 

16 

12.804 

0.257270 

18 

17.156 

0.753284 

20 

15.985 

0.596509 

17 

13.152 

0.282237 

19 

17.788 

0.780440 

21 

16.532 

0.623363 

18 

13.520 

0.307475 

20 

18.463 

0.807995 

22 

17.113 

0.650570 

19 

13.909 

0.332963 

21 

19.185 

0.835969 

23 

17.732 

0.678154 

20 

14.320 

0.358715 

22 

19.958 

0.864398 

24 

18.392 

0.706146 

21 

14.756 

0.384801 

23 

20.787 

0.893296 

25 

19.096 

0.734600 

22 

15.217 

0.411199 

24 

21.678 

0.922710 

26 

19.849 

0.763488 

23 

15.706 

0.437893 

25 

22.636 

0.952662 

27 

20.655 

0.792868 

24 

16.225 

0.464966 

26 

23.669 

0.983189 

28 

21.518 

0.822782 

25 

16.776 

0.492453 

27 

24.783 

1.014332 

29 

22.445 

0.853236 

26 

17.362 

0.520248 

28 

25.990 

1.046160 

30 

23.440 

0.884274 

27 

17.984 

0.548488 

29 

27.299 

1.078678 

31 

24.512 

0.915959 

28 

18.646 

0.577170 

30 

28.720 

1.111975 

32 

25.668 

0.948305 

29 

19.352 

0.606274 

31 

30.271 

1.146109 

33 

26:918 

0.981366 

30 

20.103 

0.635896 

32 

31.965 

1.181126 

34 

28.271 

1.015213 

31 

20.906 

0.666059 

33 

33.824 

1.217123 

35 

29.741 

1.049865 

32 

21.764 

0.696715 

34 

35.870 

1.254188 

36 

31.340 

1.085416 

33 

22.683 

0.727972 

35 

38.130 

1.292396 

37 

33.086 

1.121911 

34 

23.668 

0.759872 

36 

40.638 

1.331870 

38 

34.999 

1.159474 

35 

24.724 

0.792378 

37 

43.436 

1.372737 

39 

37.101 

1.198149 

36 

25.859 

0.825595 

38 

46.574 

1.415162  ' 

40 

39.420 

1.238041 

37 

27.082 

0.859529 

39 

50.113 

1.459295  i 

41 

4L990 

1.279284 

38 

28.402 

0.894311 

40 

54.135 

1.505350 

42 

44.852 

1.322000 

39 

29.829 

0.929894 

41 

58.741 

1.553575 

43 

48.055 

1.366328 

40 

31.376 

0.966381 

42 

64.067 

1.604276 

44 

51.663 

1.412456 

41 

33.056 

1.003848 

43 

70.288 

1.657804 

45 

55.756 

1.460599 

42 

34.888 

1.042375 

44 

77.650 

1.714635 

46 

60.435 

1.510991 

43 

36.888 

1.082002 

\   45 

86.492 

1.775362 

47 

65.834 

1.568945 

44 

39.083 

1.122855 

TABLE    LY. 


♦137 


CONTINUED  ANNUAL  PREMIUM  (P),  ALSO  A  (P  —  tt),  FOR  ENDOWMENT  INSURANCE 

OF  1,000,  PAYABLE  AT  DEATH  OR  AGE  30,  35, 75. 

4  PER  CENT. 


D  or  65. 

D  or  70. 

D  or  75. 

AaE, 

X. 

P. 

A(P-7r). 

AGE. 

X. 

P. 

A(P-Tr). 

A&E, 

X. 

24 

P. 

A(P-Tr). 

45 

41.499 

1.165036 

37 

23.520 

0.565210 

14.001 

1.840420 

46 

44.169 

1.208648 

38 

24.528 

0.598353 

25 

14.405 

1.866996 

47 

47.135 

1.253832 

39 

25.607 

0.6.32133 

26 

14.831 

1.893595 

48 

50.447 

1.300737 

40 

26.762 

0.666658 

27 

15.281 

1.920697 

49 

54.167 

1.349551 

41 

28.001 

0.701982 

28 

15.756 

1.948119 

50 

58.375 

1.400484 

42 

29.335 

0.738154 

29 

16.258 

1.975891 

51 

63.174 

1.453807 

43 

30.769 

0.775181 

30 

16.789 

0.004106 

52 

68.694 

1.509788 

44 

32.317 

0.813167 

31 

17.350 

0.032780 

53 

75.113 

1.568822  1 

45 

33.991 

0.852175 

32 

17.943 

0.061754 

54 

82.673 

1.631384 

46 

35.804 

0.892256 

33 

18.571 

0.091210 

55 

91.711 

1.698067 

47 

37.775 

0.933497 

34 

19.237 

0.121330 

56 

102.713 

1.769645 

48 

39.922 

0.975974 

35 

19.942 

0.151737 

57 

116.408 

1.847174 

49 

42.270 

1.019810 

36 

20.689 

0.182472 

58 

133.941 

1.932106 

50 

44.845 

1.065076 

37 

21.483 

0.214208 

59 

157.224 

2.026593 

51 

47.682 

1.111954 

38 

22.326 

0.246474 

60 

189.696 

2.133927 

52 

50.821 

1.160505 

39 

23.222 

0.279233 

61 

238.231 

2.259621 

53 

54.313 

1.210926 

40 

24.175 

0.312622 

62 

318.870 

2.413989 

54 

58.220 

1.263428 

41 

25.189 

0.346764 

63 

479.753 

2.620184 

55 
56 

62.621 
67.616 

1.318189 
1.375481 

42 
43 

26.271 

27.424 

0.381638 
0.417239 

D  or  7 

'0. 

57 

73.338 

1.435614 

44 

28.655 

0.453639 

58 
59 

79.960 

87.723 

1.498957 
1.566005 

45 
46 

29.973 
31.383 

0.490983 
0.529174 

10 

10.461 

1.836830 

60 

96.960 

1.637343 

47 

32.896 

0.568331 

11 

10.678 

1.860158 

61 

108.151 

1.713757 

48 

34.520 

0.608526 

12 

10.907 

1.883718 

62 

122.019 

1.796305 

49 

36.268 

0.649812 

13 

11.148 

1.907411 

63 

139.702 

1.886456 

60 

38.152 

0.692256 

14 

11.402 

1.931356 

64 

163.086 

1.986335 

51 

40.187 

0.735998  ' 

15 

11.669 

1.955688 

65 

195.577 

2.099251 

52 

42.389 

0.780987 

16 

11.950 

1.979912 

66 

243.984 

2.230711 

53 

44.781 

0.827415 

17 

12.247 

0.004536 

67 

324.205 

2.391049 

54 

47.384 

0.875339 

18 

12.560 

0.029343 

68 

483.901 

2.603346 

55 

50.228 

0.924925 

19 

12.889 

0.054422 

56 

53.345 

0.976281 

20 

13.237 

0.079651 

D  or  7 

5. 

57 

56.777 

1.029538 

21 

13.605 

0.105272 

58 

60.571 

1.084855 

22 

13.992 

0.131137 

59 

64.792 

1.142461 

23 

14.402 

0.157275 

10 

10.088 

T.  497206 

60 

69.517 

1.202557 

24 

14.835 

0.183754 

11 

10.285 

1.520221 

61 

74.844 

1.265398 

25 

15.293 

0.210586 

12 

10.492 

1.543571 

62 

80.903 

1.331322 

26 

15.777 

0.237695 

13 

10.709 

1.567026 

63 

87.867 

1.400704 

27 

16.289 

0.265195 

14 

10.938 

1.590842 

64 

95.969 

1.474015 

28 

16.833 

0.293097 

15 

11.178 

1.614897 

65 

105.537 

1.551885 

29 

17.409 

0.321391 

16 

11.431 

1.638988 

66 

117.041 

1.635077 

30 

18.018 

0.350112 

17 

11.697 

1.663324 

67 

131.194 

1.724712 

31 

18.666 

0.379324 

18 

11.977 

1.687975 

68 

149.103 

1.822091 

32 

19.354 

0.408935 

19 

12.272 

1.712734 

69 

172.639 

1.929527 

33 

20.086 

0.439064 

20 

12.583 

1.737670 

70 

205.135 

2.050237 

34 

20.865 

0.469793 

21 

12.910 

1.762978 

71 

253.307 

2.189751 

35 

21.694 

0.500991 

22 

13.254 

1.788593 

72 

332.796 

2.358365 

36 

22.577 

0.532818 

23 

13.618 

1.814248 

■ 

i 

*i3d 


TABLE    LYI. 


FIVE  ANNUAL  PREMIUM  (P),  ALSO  A(P  —  tt),  FOR  ENDOWMENT  INSURANCE  OP  1,000, 

PAYABLE  AT  DEATH  OR  AGE  30,  35, 75. 

4  PER  CENT 


D  or  30. 

D  or  40. 

D  or  45. 

AaE. 

X. 

P. 

A  (P  -  tt). 

AGE. 

X. 

P. 

A(P-7r). 

AGE. 
X. 

P. 

A(P-rr). 

10 

106.053 

1.983531 

10 

78.712 

1.838461 

31 

130.936 

2.059429 

11 

109.592 

1.998426 

11 

80.971 

1.851367 

32 

135.574 

2.074759 

12 

113.295 

2.013483 

12 

83.332 

1.864452 

33 

140.430 

2.090231 

13 

117.171 

2.028696 

13 

85.805 

1.877745 

34 

145.515 

2.105851 

14 

121.226 

2.044062 

14 

88.386 

1.891195 

35 

150.839 

2.121609 

15 

125.469 

2.059574 

15 

91.092 

1.904855 

36 

156.415 

2.137509 

16 

129.909 

2.075234 

16 

93.919 

1.918679 

37 

162.261 

2.153558 

17 

134.558 

2.091037 

17 

96.874 

1.932666 

38 

168.393 

2.169764 

18 

139.423 

2.106984 

18 

99.967 

1.946830 

39 

174.824 

2.186120 

19 
20 

144.514 
149.845 

2.123062 
2.139278 

19 
20 

103.201 
106.584 

1.961159 
1.975654 

40 

181.574 

2.202634 

21 

155.425 

2.155624 

21 

110.123 

1.990308 

D  or  50. 

22 
23 

161.267 
167.383 

2.172098 
2.188697 

22 
23 

113.825 
117.697 

2.005115 
2.020079 

24 

173.788 

2.205423 

24 

121.750 

2.035195 

10 

61.869 

1.716798 

25 

180.498 

2.222272 

25 
26 

125.989 
130.427 

2.050457 

2.065872 

11 
12 

63.338 
64.876 

1.727415 
1.738256 

D  or  a 

5. 

27 

135.068 

2.081421 

13 

66.482 

1.749286 

28 
29 

139.927 
145.018 

2.097112 
2.112958 

14 
15 

68.161 
69.913 

1.760517 
1.771933 

10 

90.774 

1.908484 

30 

150.343 

2.128929 

16 

71.744 

1.783539 

11 

93.597 

1.922434 

31 

155.922 

2.145044  , 

17 

73.659 

1.795342 

12 

96.551 

1.936559 

32 

161.763 

2.161289  , 

18 

75.659 

1.807330 

13 

99.642 

1.950861 

33 

167.890 

2.177688  ' 

19 

77.749 

1.819498 

14 

102.876 

1.965331 

34 

3  74.310 

2.194224 

20 

79.934 

1.831855 

15 

106.257 

1.979964 

35 

181.039 

2.210894 

21 

82.215 

1.844383 

16 

109.796 

1.994759 

22 

84.598 

1.857078 

17 

113.499 

2.009715 

D  or  4 

5. 

23 

87.089 

1.869954 

18 

117.373 

2.024826 

24 

89.690 

1.882991 

19 

121.427 

2.040090 

25 

92.409 

1.896195 

20 

125.669 

2.055504 

10 

69.242 

1.774283 

26 

95.250 

1.909563 

21 

130.108 

2.071064 

11 

71.058 

1.786070 

27 

98.217 

1.923083 

22 

134.754 

2.086765 

12 

72.955 

1.798052 

28 

101.318 

1.936761 

23 

139.616 

2.102608 

13 

74.940 

1.810234 

29 

104.560 

1.950596 

24 

144.707 

2.118590 

14 

77.015 

1.822608 

30 

107.945 

1.964569 

25 

150.036 

2.134709 

15 

79.184 

1.835168 

31 

111.483 

1.978692 

26 

155.616 

2.150963 

16 

81.451 

1.847914 

32 

115.184 

1.992966 

27 

161.458 

2.167347 

17 

83.821 

1.860843 

33 

119.051 

2.007377 

28 

167.578 

2.183865 

18 

86.298 

1.873951 

34 

123.098 

2.021947 

29 

173.989 

2.200512 

19 

88.890 

1.887247 

35 

127.329 

2.036649 

30 

180.704 

2.217287 

20 

91.600 

1.900715 

36 

131.752 

2.051484 

21 

94.431 

1.914349 

37 

136.383 

2.066468 

22 

97.391 

1.928147  i 

38 

141.234 

2.081604 

23 

100.488 

1.942117  1 

39 

146.311 

2.096879 

24 

■  103.723 

1.956242  i 

40 

151.632 

2.112306 

25 

107.108 

1.970529 

41 

157.208 

2.127887 

26 

110.648 

1.984974 

42 

163.061 

2.143633 

27 

114.348 

1.999566  ' 

43 

169.200 

2.159538 

28 

118.219 

2.014313  i 

44 

175.653 

2.175626 

29 

122.269 

2.029209  i 

45 

182.437 

2.191901 

30 

126.504 

2.044246  i 

FOEMULA,      Pa;  =  1000 


Ma;  —  Marfm  +  Da 
Nar  —  Na;+6 


TABLE    LYI. 


♦139 


FIVE  ANNUAL  PREMIUM  (P),  ALSO  a(P  —  tt),  FOR  ENDOWMENT  INSURANCE  OF  1,000, 

PAYABLE  AT  DEATH  OR  AGE  30,  35, 75. 

4  PER  CENT. 


D  or  55. 

D  or  60. 

D  or  65. 

AGE, 
X. 

p. 

XiV-rr). 

Aa£. 

X. 

P. 

A  (P  -  tt). 

AGE. 

X. 

P. 

A  (P  -  tt). 

10 

56.208 

1.666834 

16 

58.694 

1.678507 

17 

55.747 

1.648466 

11 

57.413 

1.676324 

17 

59.996 

1.688058 

18 

56.906 

1.657208 

12 

58.672 

1.686008 

18 

61.353 

1.697785 

19 

58.113 

1.666112 

13 

59.987 

1.695894 

19 

62.770 

1.707688 

20 

59.371 

1.675182 

14 

61.361 

1.705974 

20 

64.248 

1.717770 

21 

60.682 

1.684414 

15 

62.795 

1.716242 

21 

65.790 

1.728022 

22 

62.049 

1.693804 

16 

64.292 

1.726698 

22 

67.396 

1.738435 

23 

63.472 

1.703346 

17 

65.856 

1.737349  : 

23 

69.074 

1.749028 

24 

64.955 

1.713045 

18 

67.487 

1.748169  '\ 

24 

70.822 

1.759771 

25 

66.500 

1.722890 

19 

69.194 

1.759203 

25 

72.645 

1.770675 

26 

68.110 

1.732886 

20 

70.976 

1.770409 

26 

74.546 

1.781737 

27 

69.781 

1.742988 

21 

72.835 

1.781787 

27 

76.528 

1.792950 

28 

71.528 

1.753272 

22 

74.774 

1.793333 

28 

78.594 

1.804308 

29 

73.345 

1.763670 

23 

76.801 

1.805060 

29 

80.748 

1.815814 

30 

75.232 

1.774175 

24 

78.915 

1.816947 

30 

82.991 

1.827444 

31 

77.198 

1.784805 

25 

81.122 

1.829002 

31 

85.328 

1.839207 

32 

79.243 

1.795555 

26 

83.427 

1.841224 

32 

87.768 

1.851120 

33 

81.372 

1.806412 

27 

85.831 

1.853593 

33 

90.309 

1.863151 

34 

83.586 

1.817376 

28 

88.341 

1.866119 

34 

92.957 

1.875306 

35 

85.889 

1.828432 

29 

90.962 

1.878804 

35 

95.717 

1.887577 

36 

88.281 

1.839568 

30 

93.694 

1.891620 

36 

98.591 

1.899954 

37 

90.771 

1.850807 

31 

96.547 

1.904586 

37 

101.589 

1.912455 

38 

93.362 

1.862128 

32 

99.527 

1.917698 

38 

104.715 

1.925070 

39 

96.055 

1.873523 

33 

102.637 

1.930947 

39 

107.974 

1.937790 

40 

98.855 

1.884991 

34 

105.884 

1.944330 

40 

111.372 

1.950617 

41 

101.767 

1.896527 

35 

109.276 

1.957855 

41 

114.916 

1.963548 

42 

104.798 

1.908140 

36 

112.814 

1.971497 

42 

118.616 

1.976595 

43 

107.949 

1.919805 

37 

116.513 

1.985281 

43 

122.476 

1.989744 

44 

111.225 

1.931540 

38 

120.379 

1.999202 

44 

126.509 

2.003011 

45 

114.644 

1.943338 

39 

124.418 

2.013249 

45 

130.723 

2.016394 

46 

118.200 

1.955198 

40 

128,640 

2.027427 

46 

135.128 

2.029898 

47 

121.904 

1.967124 

41 

133.056 

2.041744 

47 

139.738 

2.043533 

48 

125.766 

1.979119 

42 

137.679 

2.056206 

48 

144.566 

2.057300 

49 

129.794 

1.991187 

43 

142.517 

2.070803 

49 

149.628 

2.071237 

50 

134.001 

2.003344 

44 

147.588 

2.085556 

50 

154.940 

2.085333 

51 

138.398 

2.015592 

45 

152.904 

2.100467 

51 

160.524 

2.099620 

52 

142.996 

2.027943 

46 

158.482 

2.115545 

52 

166.399 

2.114107 

63 

147.814 

2.040421 

47 

164.341 

2.130805 

53 

172.594 

2.128833 

54 

152.872 

2.053054 

48 

170.502 

2.146258 

54 

179.140 

2.143829 

55 

158.191 

2.065863 

49 
50 

176.988 
183.827 

2.161921 

2.177823 

55 

186.071 

2.159133 

56 

163.792 

1  /*rv  Y*^/\Ci 

2.078876 

57 
58 

169.708 

2.092141 

D  or  e 

.5. 

175.966 

2.105692 

D  or  ( 

30. 

59 

182.614 

2.119599 

60 

189.696 

2.133927 

10 

48.874 

1.592176 

10 

51.955 

1.625114 

11 

49.735 

1.599683 

11 

52.962 

1.633556 

12 

50.635 

1.607377 

12 

54.012 

1.642170 

13 

51.573 

1.615248 

13 

55.109 

1.650978 

14 

52.553' 

1.623298 

14 

56.254 

1.659974 

15 

53.573 

1.631514 

^' 

57.448 

1.669149 

1 

16 

54.637 

1.639898 

*140 


TABLE    LVI. 


FIVE  ANNUAL  PREMIUM  (P),  ALSO  A(P  —  tt),  FOR  ENDOWMENT  INSURANCE  OF  1,000, 

PAYABLE  AT  DEATH  OR  AGE  30,  35. 75, 

4  PER  CENT. 


D  or  70. 

D  or  70. 

D  or  75. 

AGE. 

X. 

P. 

MP-tt). 

AQE. 
X. 

P. 

A(P_Tr). 

AGE. 

X. 

P. 

A  (P  -  tt). 

10 

46.763 

1.568076 

51 

123.245 

1.946960 

32 

69.756 

1.723993 

11 

47.526 

1.574872 

52 

126.967 

1.957208 

33 

71.425 

1.733094 

12 

48.322 

1.581829 

53 

130.845 

1.967477 

34 

■  73.156 

1.742266 

13 

49.152 

1.588960 

54 

134.884 

1.977748 

35 

74.950 

1.751476 

14 

50.017 

1.596258 

55 

139.099 

1.988038 

36 

76.805 

1.760717 

15 

50.919 

1.603719 

56 

143.499 

1.998360 

37 

78.730 

1.770005 

16 

51.858 

1.611327 

57 

148.107 

2.008743 

38 

80.725 

1.779325 

17 

52.838 

1.619113 

58 

152.933 

2.019199 

39 

82.788 

1.788652 

18 

53.859 

1.627054 

59 

158.008  ■ 

2.029783 

40 

84.923 

1.797979 

19 

54.923 

1.635154 

60 

163.357 

2.040535 

41 

87.132 

1.807300 

20 

56.031 

1.643405 

61 

169.011 

2.051507 

42 

89.418 

1.816611 

21 

57.185 

1.651808 

62 

175,008 

2.062769 

43 

91.780 

1.825882 

22 

58.386 

1.660356 

63 

181.398 

2.074414 

44 

94.224 

1.835122 

23 

59.638 

1.669058 

64 

188.2.30 

2.086527 

45 

96.749 

1.844309 

24 

60.938 

1.677877 

65 

195.577 

2.099251 

46 

99.358 

1.853434 

25 

62.292 

1.686848 

47 

102.055 

1.862490 

26 

63.702 

1.695946 

D  or  7 

5. 

48 

104.841 

1.871459 

27 

65.165 

1.705159 

49 

107.720 

1.880339 

28 

66.690 

1.714506 

50 

110.695 

1.889115 

29 

68.275 

1.723966 

10 

45.444 

1.552301 

i  51 

113.771 

1.897785 

30 

69.919 

1.733517 

11 

46.145 

1.558602 

;  52 

116.948 

1.906322 

31 

71.629 

1.743179 

12 

46.875 

1.565061 

53 

120.235 

1.914738 

32 

73.404 

1.752924 

13 

47.638 

1.571681 

54 

123.637 

1.923025 

33 

75.252 

1.762785 

14 

48.432 

1.578460 

55 

127.161 

1.931181 

34 

77.169" 

1.772715 

15 

49.259 

1.585385 

56 

130.811 

1.939194 

35 

79.158 

1.782714 

16 

50.121 

1.592460 

57 

134.600 

1.947074 

36 

81.220 

1.792769 

17 

51.019 

1.599695 

58 

138.529 

1.954800 

37 

83.362 

1.802892 

18 

51.955 

1.607081 

59 

142.623 

1.962432 

38 

85.586 

1.813074 

19 

52.929 

1.614612 

60 

146.889 

1.969949 

39 

87.892 

1.823293 

20 

53.943 

1.622288 

61 

151.343 

1.977375 

40 

90.283 

1.833548 

21 

54.998 

1.630102 

62 

156.006 

1.984743 

41 

92.762 

1.843827 

22 

56.096 

1.638054 

63 

160.907 

1.992106 

42 

95.335 

1.854139 

23 

57.238 

1.646131 

64 

166.068 

1.999498 

43 

98.000 

1.864456 

24 

58.426 

1.654345 

65 

171.528 

2.007005 

44 

100.766 

1.874787 

25 

59.661 

1.662689 

66 

177.323 

2.014694 

45 

10.3.634 

1.885123 

26 

60.945 

1.671141 

67 

183.513 

2.022728 

46 

106.607 

1.895453 

27 

62.278 

1.679703 

68 

190.152 

2.031155 

47 

109.692 

1.905778 

28 

63.665 

1.688381 

69 

197.334 

2.040271 

48 

112.891 

1.916089 

29 

65.104 

1.697159 

70 

205.135 

2.050237 

49 

116.212 

1.926390 

30 

66.597 

1.706013 

50 

119.661 

1.936679 

31 

68.147 

1.714968 

141 


TABLE    LYII 


TEN  ANNUAL  PREMIUM  (P),  ALSO  A  (P  —  rr),  FOR  ENDOWMENT  INSURANCE  OF  1,000, 

PAYABLE  AT  DEATH  OR  AGE  30,  35, 75. 

4  PER  CENT. 


D  or  30. 

D  or  40. 

D  or  50. 

AGE. 

X. 

P. 

A(P.-7r). 

AGE. 

X. 

P. 

A(P-77). 

AGE. 
X. 

P. 

A(P-Tr). 

10 

59.073 

1.692836 

24 

67.925 

1.737328 

18 

42.171 

1.486872 

11 

61.047 

1.708370 

25 

70.306 

1.753103 

19 

43.341 

1.499481 

12 

63.114 

1.724049 

26 

72.800 

1.769018 

20 

44.565 

1.512267  ; 

13 

65.278 

1.739872 

27 

75.410 

1.785063 

21 

45.844 

1.525216 

14 

67.543 

1.755833 

28 

78.146 

1.801246 

22 

47.180 

1.538324 

15 

69.912 

1.771927 

29 

81.015 

1.817579 

23 

48.578 

1.551600 

16 
17 

72.393 
74.991 

1.788154 
1.804513 

30 

84.019 

1.834038 

24 
25 

50.039 
51.567 

1.565032 
1.578620 

18 

77.711 

1.821000 

D  or  45. 

26 

53.165 

1.592361 

19 
20 

80.559 
83.542 

1.837609 
1.854341 

27 

28 

54.835 
56.584 

1.606247 
1.620290 

10 

38.568 

1.459311 

29 

58.413 

1.634480 

D  or  a 

5. 

11 

39.582 

1.471713 

30 

60.325 

1.648805 

12 

40.642 

1.484297 

31 

62.326 

1.663279 

13 

41.750 

1.497075 

32 

64.422 

1.677900 

10 

50.562 

1.610534 

14 

42.910 

1.510035 

33 

66.616 

1.692658 

11 

52.138 

1.625153 

15 

44.122 

1.523169 

34 

68.916 

1.707581 

12 

63.786 

1.639928 

16 

45.389 

1.536479 

35 

71.325 

1.722638 

13 

55.512 

1.654872 

i  17 

46.715 

1.549963 

36 

73.848 

1.737844 

14 

57.318 

1.669970 

i  18 

48.101 

1.563619 

37 

76.496 

1.753204 

15 

59.207 

1.685216 

'  19 

49.552 

1.577441 

38 

79.275 

1.768732  , 

16 

61.185 

1.700611 

i  20 

51.069 

1.591429 

39 

82.193 

1.784423 

17 

63.255 

1.716155 

i  21 

52.655 

1.605572 

40 

85.258 

1.800288 

18 

65.421 

1.731841 

22 

54.315 

1.619876 

19 

67.689 

1.747668 

23 

56.052 

1.634337 

D  or  5 

5. 

20 

70.063 

1.763631 

24 

57.868 

1.648946 

21 

72.549 

1.779731 

25 

59.770 

1.663709 

22 

75.152 

1.795963 

26 

61.760 

1.678621 

10 

31.308 

1.333133 

23 

77.878 

1.812326 

27 

63.842 

1.693674 

11 

31.982 

1.342979 

24 

80.733 

1.828821 

28 

66.023 

1.708878 

12 

32.685 

1.353008 

25 

83.725 

1.845446 

29 

68.306 

1.724224 

13 

33.420 

1.363236 

30 

70.696 

1.739709 

14 

34.188 

1.373646 

D  or  4 

0. 

31 

73.202 

1.755344 

15 

34.990 

1.384237 

32 
33 

75.827 
78.579 

1.771120 
1.787046 

16 

17 

35.827 
36.703 

1.395008 
1.405966 

10 

43.844 

1.532368 

34 

81.466 

1.803123 

18 

37.616 

1.417076 

11 

45.105 

1.545939 

35 

84.494 

1.819347 

19 

38.572 

1.428400 

12 

46.423 

1.559682 

20 

39.571 

1.439877 

13 

47.803 

1.573607 

' 

D  or  5 

0. 

21 

40.613 

1.451521 

14 

49.246 

1.587684 

22 

41.702 

1.463319 

15 

50.757 

1.601961 

23 

42.839 

1.475290 

16 

52.337 

1.616392 

10 

34.462 

1.392484 

24 

44.027 

1.487409 

17 

53.990 

1.630969 

11 

35.283 

1.403625 

25 

45.269 

1.499686 

18 

55.719 

1.645712 

12 

36.141 

1.414955 

26 

46.566 

1.512117 

19 

57.529 

1.660609 

13 

37.038 

1.426482 

27 

47.920 

1.524686 

20 

59.423 

1.675660 

14 

37.976 

1.438201 

28 

49.336 

1.537405 

21 

61.405 

1.690861 

15 

38.956 

1.450095 

29 

50.816 

1.550270 

22 

63.480 

1.706204 

16 

39.980 

1.462172 

30 

52.361 

1.563263 

23 

65.651 

1.721694 

17 

41.051 

1.474435 

31 

53.976 

1.576399 

Formula,    P,.  =  1000 


Ma,  —  Mx+m  +  Da 

Na-  —  Na,+io 


AT 

>4' 


*142 


TABLE    LYII. 


TEN  ANNUAL  PREMIUM  (P),  ALSO  A  (P  —  rr),  FOR  ENDOWMENT  INSURANCE  OF  1.000, 

PAYABLE  AT  DEATH  OR  AGE  30,  35 75. 

4  PER  CENT. 


D  or  55. 

D  or  60. 

D  or  65. 

AGE. 

X. 

P. 

;,(P-7r). 

1.589673 

A&E. 
X. 

P. 

A  (P  -  tt). 

AGE. 
X. 

49 

P. 

1 
A(P-7r). 

32 

55.665 

43 

69.090 

1.646207 

73.955 

1.624815 

33 

57.432 

1.603081 

44 

71.458 

1.659392 

50 

76.525 

1.636458 

34 

59.279 

1.616620 

45 

73.944 

1.672733 

51 

79.233 

1.648277 

35 

61.212 

1.630306 

46 

76.557 

1.686238 

52 

82.090 

1.660296 

36 

63.233 

1.644112 

47 

79.305 

1.699929 

53 

85.110 

1.672563 

37 

65.351 

1.658064 

48 

82.200 

1.713828 

54 

88.311 

1.685133 

38 
39 

67.569 
69.894 

1.672161 
1.686402 

49 
50 

85.255 
88.483 

1.727968 
1.742373 

55 

91.711 

1.698067 

40 

72.331 

1.700792 

D  or  70. 

41 

74.887 

1.715340 

D  or  65. 

42 

77.572 

1.730049 

43 

80.395 

1.744960 

10 

26.048 

1.211486 

44 

83.364 

1.760054 

10 

27.223 

1.241780 

11 

26.474 

1.218028 

45 

86.492 

1.775362 

11 
12 

27.705 
28.207 

1.249228 
1.256850 

12 
13 

26.919 
27.383 

1.224712 
1.231551 

D  or  e 

0. 

13 

28.732 

1.264638 

14 

27.868 

1.238538 

14 

29.280 

1.272591 

15 

28.372 

1.245673 

15 

29.851 

1.280697 

16 

28.898 

1.252928 

10 

28.939 

1.282518 

16 

30.447 

1.288951 

17 

29.448 

1.260341 

11 

29.502 

1.291120 

17 

31.069 

1.297377 

18 

30.020 

1.267882 

12 

30.089 

1.299878 

18 

31.718 

1.305959 

19 

30.617 

1.275560 

13 

30.702 

1.308825 

19 

32.395 

1.314682 

20 

31.239 

1.283360 

14 

31.343 

1.317950 

20 

33.101 

1.323553 

21 

31.887 

1.291287 

15 

32.010 

1.327245 

21 

33.837 

1.332570 

22 

32.562 

1.299331 

16 

32.708 

1.336710 

22 

34.604 

1.341721 

23 

33.266 

1.307502 

17 

33.437 

1.346357 

23 

35.405 

1.351001 

24 

33.998 

1.315752 

18 

34.197 

1.356167 

24 

36.239 

1.360423 

25 

34.761 

1.324126 

19 

34.991 

1.366141 

25 

37.109 

1.369963 

26 

35.556 

1.332590 

20 

35.820 

1.376278 

26 

38.016 

1.379632 

27 

36.383 

1.341134 

21 

36.685 

1.386574 

27 

,  38.962 

1.389409 

28 

37.245 

1.349779 

22 

37.587 

1.397017 

28 

39.947 

1.399291 

29 

38.142 

1.358495 

23 

38.529 

1.407620 

29 

40.974 

1.409287 

30 

39.074 

1.367263 

24 

39.512 

1.418368 

30 

42.043 

1.419366 

31 

40.045 

1.376104 

25 

40.538 

1.429258 

31 

43.159 

1.429547 

32 

41.055 

1.384977 

26 

41.609 

1.440287 

32 

44.321 

1.439816 

33 

42.108 

1.393931 

27 

42.726 

1.451455 

33 

45.532 

1.450171 

34 

43.202 

1.402908 

28 

43.893 

1.462753 

34 

46.796 

1.460606 

35 

44.341 

1.411908 

29 

45.110 

1.474183 

35 

48.112 

1.471107 

36 

45.525 

1.420917 

30 

46.379 

1.485723 

36 

49.482 

1.481668 

37 

46.757 

1.429943 

31 

47.704 

1.497390 

37 

50.912 

1.492299 

38 

48.040 

1.438980 

32 

49.088 

1.509178 

38 

52.404 

1.503000 

39 

49.375 

1.448010 

33 

50.533 

1.521081 

39 

53.960 

1.513757 

40 

50.764 

1.457022 

34 

52.042 

1.533097 

40 

55.583 

1.524562 

41 

52.209 

1.466010 

35 

53.617 

1.545218 

41 

57.277 

1.535424 

42 

53.716 

1.474987 

36 

55.261 

1.557442 

42 

59.047 

1.546353 

43 

55.283 

1.483916 

37 

56.980 

1.569782 

43 

60.895 

1.557327 

44 

56.917 

1.492818 

38 

58.777 

1.582234 

44 

62.828 

1.568371 

45 

58.621 

1.501682 

39 

60.656 

1.594795 

45 

64.850 

1.579485 

46 

60.398 

1.510501 

40 

62.621 

1.607464 

46 

^6.966 

1.590670 

47 

62.253 

1.519279 

41 

64.678 

1.620253 

47 

69.184 

1.601943 

48 

64.190 

1.528014 

42 

66.833 

1.633167 

48 

71.511 

1.613318 

49 

66.216 

1.536723 

TABLE    LYll. 


^143 


TEN  ANNUAL  PREMIUM  (P),  ALSO  A  (P  —  tt),  FOR  ENDOWMENT  INSURANCE  OF  1,000, 

PAYABLE  AT  DEATH  OR  AGE  30,  35, 75. 

4  PER  CENT. 


D  or  70. 

D  or  75. 

D  or  75. 

AGE. 
X. 

P. 

A(P-7r). 

AQE. 

X. 

P. 

A(P_:r). 

AGE. 
X. 

P. 

A  (P  -  tt). 

50 

68.336 

1.545404 

19 

29.505 

1.249176 

43 

51.774 

1.430786 

51 

70.559 

1.554086 

20 

30.074 

1.256198 

44 

53.222 

1.437888 

52 

72.887 

1.562734 

21 

30.667 

1.263328 

45 

54.727 

1.444843 

53 

75.339 

1.571470 

22 

31.285 

1.270560 

46 

56.291 

1.451631 

54 

77.920 

1.580248 

23 

31.927 

1.277873 

47 

57.919 

1.458248 

55 

80.643 

1.589137 

24 

32.596 

1.285289 

48 

59.613 

1.464674 

56 

83.519 

1.598159 

25 

33.293 

1.292792 

49 

61.377 

1.470913 

57 

86.571 

1.607430 

26 

34.017 

1.300356 

50 

63.216 

1.476939 

58 

89.810 

.1.616970 

27 

34.771 

1.307984 

51 

65.133 

1.482745 

59 

93.265 

1.626906 

28 

35.555 

1.315681 

52 

67.138 

1.488374 

60 

96.960 

1.637343 

29 

36.371 

1.323421 

53 

69.230 

1.493740 

30 

37.217 

1.331190 

54 

71.422 

1.498907 

D  or  •; 

'5. 

31 

38.099 

1.339006 

55 

73.722 

1.503878 

32 

39.014 

1.346826 

56 

76.135 

1.508644 

33 

39.966 

1.354664 

57 

78.676 

1.513255 

10 

25.313 

1.191417 

34 

40.956 

1.362511 

58 

81.351 

1.517700 

11 

25.705 

1.197311 

35 

41.984 

1.370324 

59 

84.183 

1.522105 

12 

26.113 

1.203340 

36 

43.050 

1.378103 

60 

87.185 

1.526473 

13 

26.540 

1.209510 

37 

44.159 

1.385851 

61 

90.374 

1.530890 

14 

26.985 

1.215815 

38 

45.311 

1.393554 

62 

93.773 

1.535485 

15 

27.448 

1.222238 

39 

46.508 

1.401190 

63 

97.414 

1.540400 

16 

27.930 

1.228785 

40 

47.750 

1.408741 

64 

101.322 

1.545788 

17 

28.434 

1.235465 

41 

49.040 

1.416198 

65 

105.537 

1.551885 

18 

28.958 

1.242263 

42 

50.382 

1.423557 

^ 

^144 


TABLE    LYIII. 


CONTINUED  ANNUAL  PREMIUM   (P),    ALSO   A(P— tt),  FOR  ENDOWMENT  INSURANCE 


OF  1,000,  PAYABLE  AT  DEATH  OR  AT  THE  END  OF  m  YEARS. 


4  PER  CENT. 


Formula,    P^=  1000 


^x — ^x+m 


:1000 


li+^'-^i-"'! 


AQiE. 
X. 

,  m=5. 

10. 

15. 

20. 

AGE. 
X. 

15 

P. 

A(P-7r). 

P. 

X(P-n). 

P. 

51.732 

A(P-7r). 

P.   A(P_7r). 

15 

180.391 

2.229234 

83.428 

1.861309 

1.612429 

36.3291.407614 

16 

180.303 

.228678 

83.447 

.860046 

51.757 

.610247 

36.3611  .404235 

16 

17 

180.317 

.228095 

83.468 

.858725 

51.783 

.607961 

36.395  .400686 

17  \ 

18 

180.333 

.227483 

83.489 

.857333 

51.813 

.605559 

36.433;  .396956 

18  i 

19 

180.350 

.226842 

83.514 

.855874 

51.845 

.603035 

36.475 

.393033 

19  1 

20 

180.370 

2.226172 

83.543 

1.854341 

51.881 

1.600380 

36.522 

1.388904 

20 

21 

180.391 

.225467 

83.572 

.852734 

51.921 

.597591 

36.572 

.384560 

21 

22 

180.414 

.224724 

83.605 

.851045 

51.964 

.594660 

36.628 

.379985 

22 

23 

180.439 

.223945 

83.641 

.849268 

52.012 

.591575 

36.689 

.375175 

23 

24 

180.467 

.223129 

83.682 

.847402 

52.004 

.588336 

36.755 

.370093 

24 

25 

180.498 

2.222271 

83.724 

1.845446 

52.122 

1.584928 

36.831 

1.364770 

25 

26 

180.532 

.221370 

83.774 

.843387 

52.186 

.581343 

36.912 

.359150 

26 

27 

180.569 

.220425 

83.826 

.841222 

52.254 

.577567 

37.002 

.353220 

27 

28* 

180.611 

.219432 

83.884 

.838949 

52.331 

.573597 

37.101 

.346973 

28 

29 

180.657 

.218388 

83.950 

.836557 

52.416 

.569415 

37.210 

.340389 

29 

30 

180.705 

2.217289 

84.019 

1.834038 

52.509 

1.565009 

37.328 

1.333433 

30 

31 

180.759 

.216135 

84.097 

.831394 

52.610 

.560372 

37.459 

.326094 

31   ! 

32 

180.819 

.214920 

84.182 

.828607 

52.722 

.555482 

37.605 

.318354 

32 

33 

180.886 

.213646 

84.277 

.825679 

52.846 

.550330 

37.763 

.310173 

33 

34 

180.960 

.212308 

84.380 

.822599 

52.982 

.544901 

37.938 

.301516 

34 

35 

181.039 

2.210894 

84.495 

1.819347 

53.131 

1.539171 

38.130 

1.292396 

35 

36 

181.125 

.209405 

84.619 

.815924 

53.295 

.533121 

38.341 

.282731 

36 

37 

181.221 

.207839 

84.756 

.812315 

53.476 

.526732 

38.574 

.272498 

37 

38 

181.329 

.206197 

84.908 

.808520 

53.676 

.520002 

38.829 

.261674 

38 

39 

181.446 

.204462 

85.075 

.804513 

53.894 

.512879 

39.111 

.250205 

39 

40 

181.574 

2.202633 

85.259 

1.800288 

54.135 

1.505348 

39.420 

1.238041 

40 

41 

181.714 

.200706 

85.459 

.795826 

54.400 

.497389 

39.760 

.225149 

41 

42 

181.871 

.198679 

85.682 

.791126 

54.693 

.488973 

40.136 

.211460 

42 

43 

182.041 

.196538 

85.925 

.786154 

55.014 

.480051 

40.547 

.196922 

43 

44 

182.229 

.194281 

86.195 

.780906 

55.367 

.470606 

41.001 

.181469 

44 

45 

182.437 

2.191901 

86.491 

1.775361 

55.756 

1.460599 

41.498 

1.165036 

45 

46 

182.665 

.189389 

86.818 

.769493 

56.184 

.449981 

42.047 

.147534 

46 

47 

182.915 

.186730 

87.177 

.763284 

56.655 

.438712 

42.650 

.128887 

47 

48 

183.190 

.183924 

87.571 

.756711 

57.174 

.426745 

43.313 

.108998 

48 

49 

183.494 

.180960 

88.006 

.749750 

57.746 

.414025 

44.042 

.087771 

49 

50 

183.828 

2.177825 

88.483 

1.742373 

58.375 

1.400488 

44.845 

1.065079 

50 

51 

184.196 

.174508 

89.010 

.734554 

59.069 

.386092 

45.728 

.040832 

51 

52 

184.598 

.170989 

89.590 

.726243 

59.832 

.370731 

46.698 

.014843 

52 

53 

185.041 

.167261 

90.230 

.717419 

60.672 

.354350 

47.765 

0.986987 

53 

54 

185.531 

.163316 

90.935 

.708040 

61.600 

.336868 

48.938  .957080 

54 

55 

186.071 

2.159134 

91.711 

1.698067 

62.621 

1.318187 

50.228'o.  924935 

55 

56 

186.664 

.154692 

92.566 

.687439 

63.746 

.298183 

51.645  .890354 

56 

57 

187.318 

.149973 

93.510 

.676122 

64.986 

.276765 

53.203;  .853083 

57 

58 

188.034 

.144951 

94.550 

.664036 

66.351 

.253779 

54.911 

.812780 

58 

59 

188.825 

.139615 

95.695 

.651135 

67.856 

.229103 

56.790 

.769348 

59 

60 

189.696 

2.133925 

96.959 

1.637341 

69.517 

1.202557 

58.850  0.722272 

60 

61 

190.655 

.127866 

98.354 

.622568 

71.346 

.173961 

61.110  .671219 

61 

62 

191.711 

.121406 

99.892 

.606746 

73.362 

.143121 

63.586  .615708 

62 

63 

192.878 

.114511 

101.592 

.589771 

75.586 

.109825 

66.299  .555336 

63 

64 

194.161 

.107135 

103.467 

.571521 

78.035 

.073755  I 

69.269  .489396 

64 

65 

195.578  .0992521 

105.537 

.551884 

80.733 

.034697  1 

72.515!  .417223 

65 

TABLE    LYIII. 


♦145 


CONTINUED   ANNUAL  PREMIUM  (P),  ALSO  A,  (P  —  tt),  FOR  ENDOWMENT  INSURANCE 
OF  1,000,  PAYABLE  AT  DEATH  OR  AT  THE  END  OF  m  YEARS. 

4  PER  CENT. 


AGE. 

25. 

30. 

35. 

40. 

AGE. 
X. 

X. 

P. 

;i(P-Tr). 

P. 

31.831 

X  (P-tt). 

P. 

A  (P-tt). 

P. 

A  (P-tt). 

15 

27.444 

1.333149 

1.043559 

18.066 

0.863341 

15.486 

0. 673951 

15 

16 

27.484 

.317189 

31.873 

.036501 

18.131 

.853449 

15.568 

.660193 

16 

17 

37.528 

.311979  \ 

21.939 

.0390671 

18.303 

.843015  1 

15.658 

.645629 

17 

18 

37.577 

.306491  i 

31.991 

.031331 

18.381 

.831985 

15.758 

.630304 

18 

19 

37.631 

.300711  i 

33.059 

.013960 

18.368 

.830330 

15.866 

.613843 

19 

20 

37.690 

1.194635 

33.134 

1.004335 

18.463 

0.807995 

15.985 

0.596530 

20 

21 

37.755 

.188305 

33.316 

0.995016 

18.567 

.794948 

16.116 

.578146 

21 

22 

37.836 

.181440 

33.307 

.985387 

18.681 

.781138 

16.359 

.558613 

22 

23 

37.904 

.174316 

33.406 

.975013 

18.807 

.766517 

16.416 

.537883 

23 

24 

37.990 

.166791 

33.51.6 

.964146 

18.945 

.751017 

16.588 

.515847 

24 

25 

38.085 

1.158857 

23.636 

0.952657 

19.096 

0.734593 

16.776 

0.493411 

25 

26 

38.190 

.150480 

33.768 

.940507 

19.363 

.717163 

16.983 

.467475 

26 

27 

38.304 

.141635 

33.913 

.927642 

19.444 

.698666 

17.308 

.440909 

27 

28 

38.430 

.133393 

23.073 

.914015 

19.644 

.679001 

17.455 

.413578 

28 

29 

38.569 

.133425 

23.248 

.899585 

19.864 

.658136 

17.735 

.383395 

29 

30 

38.730 

1.111978 

23.440 

0.884380 

30.103 

0.635906 

18.019 

0.350113 

30 

31 

38.888 

.100936 

23,651 

.868050 

20.366 

.613365 

18.340 

.315656 

31 

32 

39.073 

.089348 

23.883 

.850818 

30.655 

.587083 

18.690 

.378799 

32 

33 

39.374 

.076870 

24.138 

.833515 

30.970 

.560318 

19.073 

.239335 

33 

34 

39.496  .063765 

24.417 

.813067 

31.316 

.531581 

19.489 

.197087 

34 

35 

39.741 

1.049865 

24.734 

0.793378 

31.694 

0.500991 

19.943 

0.151737 

35 

36 

30.009 

035131 

35.059 

.770351 

33.106 

.468388 

30.434 

.103051 

36 

37 

30.303 

.019461 

35.438 

.746875 

33.557 

.433390 

30.969 

.050650 

37 

38 

30.638 

.003853 

35.833 

.731868 

33.050 

.395868 

31.550 

1.994405 

38 

39 

30.984  0.985184 

36.377 

] 

.695175 

33.588 

.355739 

33.178 

.933740 

39 

40 

31.375  0.966381 

36.763 

0.666658 

34.175 

0.313633 

33.859 

1. 868393 

40 

41 

31.805  .946383 

37.394 

.636187 

34.814 

.366373 

33.594 

.797683 

41 

42 

33.378  .935070 

37.877 

.603577 

35.509 

.316641 

34.389 

.731333 

42 

43 

33.796  .903340 

38.513 

.568636 

36.366 

.163073 

35.345 

.638589 

43 

44 

33.366  .878079 

39.311 

.531159 

37.088 

.105373 

36.167 

.548635 

44 

45 

33.991  0.853175 

39.973 

0.490969 

27.980 

0.043087 

37.158 

T.  451173 

45 

46 

34.677 

.834464 

30.805 

.447733 

38.947 

1.975707 

38.333 

.344785 

46 

47 

35.439 

.794803 

31.714 

.401345 

39.994 

.903818 

39.364 

.338400 

47 

48 

36.354 

.76.3008 

33.705 

.351130 

31.136 

.823670 

30.586 

.099681 

48 

49 

37.160 

728914 

33.785 

.397082 

33.350 

.737908 

31.894 

3.959041 

49 

50 

38.151 

0.693356 

34.961 

0.338648 

33.669 

T.  644340 

33.391 

3.797960 

50 

51 

39.338 

.653894 

36.340 

.175599 

35.091 

.543835 

34.784 

.634383 

51 

52 

40.439 

.610479 

37.630 

.107108 

36.630 

.430881 

36.377 

.436511 

52 

53 

41.730 

.564737 

39.138 

.033830 

38.363 

.307496 

38.076 

.306836 

53 

54 

43.155 

.515344 

40.775 

L 952066 

40.038 

.171141 

39.888 

3.963788 

54 

55 

44.713 

0.461934 

43.547 

T.  864096 

41.930 

T.  018384 

41.831 

3.681341 

55 

56 

46.413 

.404115 

44.463 

.767823 

43.947 

3.846337 

I  43.879 

.397940 

56 

57 

48.368 

.341355 

46.533 

.662386 

46.118 

.656098 

46.074 

4.954343 

57 

58 

50.389 

.373978 

48.764 

.544564 

48.443 

.463398 

48.414 

.477131 

58 

59 

53.490 

.198904 

51.171 

.415808 

'  50.936 

.309515 

50.910 

00 

59 

60 

54.886 

0.117735 

53.760 

T.369513 

'  53.583 

3.934498 

60 

61 

57.488 

.038815 

56.547 

.105851 

56.434 

.633349 

61 

62 

60.311 

1.931305 

59.543 

3.934379 

59.461 

.378754 

62 

63 

63.374 

.833148 

63.761 

.734376 

63.709 

4.845098 

63 

64 

66.687 

.703344 

66.314 

.495544 

66.184 

.477131 

1 

64 

65 

70.370 

.566084 

69.930 

.340549 

65 

♦146  TABLE     LIX. 

FIVE  ANNUAL  PBEMIUM  (P),  ALSO  X(P— ?r),  poR  ENDOWMENT  INSURANCE  OF  1,000, 
PAYABLE  AT  DEATH  OR  AT  THE  END  OF  m   YEARS. 

4  PER   CENT. 


AGE. 
X. 

m—\0. 

15. 

20. 

25. 

AGE. 

X, 

P. 

A(P-7r). 

p.   A  (P-tt). 

P. 

106.257 

A  (P-TT). 

P. 

A(P— 7r). 

15 

149.726 

2.142890 

125.469  2.059574 

1.979964 

91.092 

1.904855 

15 

16 

149.745 

.142233 

125.501 

.058828 

106.310 

.979162 

91.174 

.904060 

16 

17 

149.767 

.141547 

125.537 

.058050 

106.370 

.978331 

91.266 

.903252 

17 

18 

149.790 

.140822 

125.577 

.057237 

106.434 

.977471 

91.367 

.902423 

18 

19 

149.816 

.140068 

125.621 

.056390 

106.506 

.976578 

91.477 

.901575 

19 

20 

149.845 

2.139278 

125.669'2. 055504 

106.584 

1.975654 

91.600 

1.900715 

20 

21 

149.877 

.138451 

125.7221  .054583 

106.670 

.974696 

91.733 

.899833 

21 

22 

149.911 

.137579  : 

125.779 

.053612 

106.764 

.973702 

91.878 

.898937 

22 

23 

149.949 

.136667  \ 

125.842 

.052602 

106.869 

.972680 

92.040 

.898035 

23 

24 

149.990 

.135711 

125.912 

.051554 

106.980 

,971610 

92.215 

.897117 

24 

25 

150.036 

2.134709 

125.989 

2.050457 

107.108 

1.970529 

92.409 

1.896195 

25 

26 

150.087 

.133661 

126.074 

.049315 

107.247 

.969407 

92.622 

.895275 

26 

27 

150.142 

.132561 

126.167 

.048127 

107.397 

.968243 

92.853 

.894347 

27 

28 

150.203 

.131407 

126.269 

.046885 

107.563 

.967053 

93.109 

.893429 

28 

29 

150.271 

.130199 

126.382 

.045593 

107.747 

.965833 

93.390 

.892525 

29 

30 

150.343 

2.128929 

126.504 

2.044246 

107.945 

1.964569 

93.694 

1.891620 

30 

31 

150.424 

.127601 

126.639 

.042843 

108.163 

.963278 

94.028 

.890740 

31 

32 

150.513 

.126206 

126.788 

.041385 

108.405 

.961964 

94.396 

.889892 

32 

33 

150.612 

.124745 

126.951 

.039862 

108.669 

.960618 

94.798 

.889077 

33 

34 

151^721 

.123218 

127.132 

.038290 

108.957 

.959240 

95.237 

.888305 

34 

35 

150.839 

2.121609 

127.329 

2.036649 

109.276 

1.957855 

95.717 

1.887577 

35 

36 

150.967 

.119918 

127.543 

.034937 

109.621 

.956430 

96.239 

.886898 

36 

37 

151.110 

.118149 

127.780 

.033162 

110.001 

.954995 

96.810 

.886293 

37 

38 

151.269 

.116299 

128.042 

.031328 

110.419 

.953548 

97.435 

.885774 

38 

39 

151.442 

.114351 

128.327 

.029412 

110.874 

.952086 

98.115 

.885333 

39 

40 

151.632 

2.112306 

128.640 

2.027427 

111.372 

1.950617 

98.855 

1.884991 

40 

41 

151.839 

.110159 

128.983 

.025372 

111.916 

.949142 

99.659 

.884754 

41 

42 

152.671 

.107915 

129.361 

.023244 

112.512 

.947677 

100.536 

.884646 

42 

43 

152.321 

.105547 

129.773 

.021036 

113.161 

.946212 

101,485 

.884657 

43 

44 

152.599 

.103071 

130.226 

.018755 

113.871 

.944766 

102.517 

.884815 

44 

45 

152.904 

2.100467 

130.723 

2.016394 

114.644 

1.943338 

103.634 

1.885123 

45 

46 

153.238 

.097733 

131.266 

.013953 

115.486 

.941934 

104.841 

.885585 

46 

47 

153.606 

.094859 

131.861 

.011427 

116.404 

.940561 

106.146 

.886215 

47 

48 

154.010 

.091843 

132.511 

.008817 

117.401 

.939223 

107.552 

.887010 

48 

49 

154.453 

.088668 

133.223 

.006124 

118.485 

.937929 

109.067 

,887979 

49 

50 

154.940 

2.085333 

134.001 

2.003344 

119.661 

1.936679 

110.695 

1.889115 

50 

51 

155.476 

.081vS29 

134.852 

.000477 

120.937 

.935482 

112.442 

.890421 

61 

52 

156.062 

.078137 

135.778 

1.997507 

122.316 

.934328 

114.310 

.891873 

52 

53 

156.705 

.074250  1136.789 

.994446 

123.809 

.933228 

116.307 

.893467 

53 

54 

157.413 

.070164 

137.894 

.991293 

125.421 

.932178 

118.436 

.895188 

54 

55 

158.191 

2.065863  1 

139.099 

1.988038 

127.161 

1.931181 

120.704 

1.897011 

55 

56 

159.043 

.061328 

140.409 

.984673 

129.032 

.930214 

123.107 

.898894 

56 

57 

159.979 

.056547 

141.836 

.981196 

131.045 

.929276 

125.654 

.900809 

57 

58 

161.002 

.051496 

143.382 

.977582 

133.198 

.928319 

128.338 

.902681 

58 

59 

162.125 

.046164 

145.063 

.973839 

135.510 

.927370 

131.172 

.904511 

59 

60 

163.357 

2.040535 

146.889 

1.969949 

137.980 

1.926372 

134.151 

1.906207 

60 

61 

164.707 

.034576 

148.866 

.965889 

140.616 

.925294 

137,276 

.907713 

61 

62 

166.186 

.028279 

151.005 

.961643 

143.421 

.924088 

140.545 

.908951 

62 

63 

167.809 

.021607 

153.322 

.957195 

146.406 

.922718 

143.966 

.909865 

63 

64 

169.583 

.014521 

155.821 

.952491 

149.573 

.921111 

147.533 

.910359 

64 

65 

171.528J  .007005 

158.520 

.947522 

152.928 

.919214 

151.253 

.910363 

65 

Formula,    Pj 


=  1000  I 


Mx  —  Ma,+m  +  D 


x+m  (    


N*— Na;+5 


1  +  al 


TABLE     LIX. 


*ui 


FIVE  ANNUAL  PREMIUM  (P)  ALSO  A  (P— tt),  FOR  ENDOWMENT  INSURANCE  OF  1,000, 
PAYABLE  AT  DEATH,  OR  AT  THE  END  OF  m  YEARS. 

4  PER  CENT. 


A&E. 
X. 

30. 

35. 

40. 

AOE. 

X. 

P. 

A(P-Tr). 

P. 

A(P-Tr). 

P. 

;.(P-Tr). 

15 

79.184 

1.835168 

69.913 

1.771933 

62.795 

1.716242 

15 

16 

79.306 

834492 

70.088 

.771532 

63.035 

.716335 

16 

17 

79.443 

.833820 

70.281 

.771177 

63.299 

.716526 

,  17 

18 

79.591 

.833154 

70.491 

.770865 

63.588 

.716821 

18 

19 

79.754 

.832495 

70.722 

.770603 

63.903 

.717227 

19 

20 

79.934 

1.831855 

70.976 

1.770409 

64.248 

1.717770 

20 

21 

80.130 

.831226 

71.253 

.770280 

64.625 

.718453 

21 

22 

80.344 

.830618 

71.555 

.770228 

65.034 

.719284 

22 

23 

80.581 

.830045 

71.887 

.770273 

65.482 

.720297 

23 

24 

80.839 

.829502 

72.249 

.770416 

65.969 

.721491 

24 

25 

81.122 

1.829002 

72.645 

1.770675 

66.500 

1.722890 

26 

26 

81.433 

.828559 

73.078 

.771070 

67.078 

.724518 

26 

27 

81.771 

.828166 

73.549 

.771595 

67.704 

.726372 

27 

28 

82.143 

.827845 

74.063 

.772279 

68.385 

.728482 

28 

29 

82.550 

.827609 

74.625 

.773145 

.  69.123 

.730870 

29 

30 

82.991 

1.827444 

75.232 

1.774175 

^  69.919 

1.733517 

30 

31 

83.474 

.827388  ' 

75.894 

.775415 

I  70.781 

.736471 

31 

32 

84.002 

.827446  ! 

76.614 

.776876 

1  71.711 

.739740 

32 

33 

84.578 

.827632 

77.396 

.778571 

i  72.714 

.743326 

33 

34 

85.206 

.827958 

78.242 

.780516 

1  73.793 

.747239 

34 

35 

85.889 

1.828432  ; 

79.158 

1.782714 

74.950 

1.751476 

35 

36 

86.628 

.829058 

80.145 

.785175 

76.186 

.756027 

36 

37 

87.434 

.829875  : 

81.212 

.787932 

77.511 

.760918 

37 

38 

88.310 

.830894  ■ 

82.362 

.790987 

78.925 

.766137 

38 

39 

89.258 

.832112  1 

83.598 

.794336 

80.429 

.771652 

39 

40 

90.283 

1.833548  i 

84.923 

1.797979 

82.025 

1.777457 

40 

41 

91.391 

.835208  i 

86.342 

.801922 

83.713 

.783522 

41 

42 

92.588 

.837119  ! 

87.861 

.806168 

85.499 

.789839 

42 

43 

93.875 

.839260 

89.478 

.810687 

87.378 

.796356 

43 

44 

95,261 

.841661 

91.199 

.815480 

89.354 

.803052 

44 

45 

96.749 

1.844309 

93.025 

1.820524 

91.424 

1.809883 

45 

46 

98.341 

.847203 

94.957 

.825787 

93.587 

.816806 

46 

47 

100.045 

.850342 

96.997 

.831245 

95.841 

.823778 

47 

48 

101.861 

.853702 

99.144 

.836855 

98.185 

.830749 

48 

49 

103.794 

.857277 

101.399 

.842585 

100.618 

.837683 

49 

50 

105.845 

1.861037 

103.760 

1.848385 

103.136 

1.844523 

50 

5t 

108.018 

.864963 

106.226 

.854213 

105.739 

.851239 

51 

52 

110.311 

.869000 

108.794 

.860000 

108.423 

.857772 

52 

53 

112.726 

.873125 

111.462 

.865709 

111.188 

.864088 

53 

54 

115.265 

.877293 

114.230 

.871289 

114.035 

.870148 

54 

55 

117.928 

1.881455 

117.097 

1.876686 

116.963 

1.875917 

55 

56 

120.709 

.885543 

120.055 

.881833 

119.969 

.881341 

56 

57 

123.610 

.889507 

123.109 

.886696 

123.056 

.886392 

57 

58 

126.622 

.893259 

126.256 

.891219 

126.224 

.891042 

58 

59 

129.756" 

.896782 

129.489 

.895309 

129.472 

.895215 

59 

60 

133.004 

1.899981 

132.820 

1.898975 

60 

61 

136.366 

.902797 

136.245 

.902142 

61 

62 

139.842 

.905166 

139.765 

.904755 

62 

63 

143.437 

.907030 

143.392 

.906786 

63 

64 

147.149 

.908303 

147.124 

.908167 

64 

65 

150.985 

.908931 

65 

*148 


TABLE    LX 


TEN  ANNUAL  PREMIUM  (P)   ALSO  a(P  — tt),  FOR  ENDOWMENT  INSURANCE  OF  1,000. 
PAYABLE  AT  DEATH  OR  AT  THE  END  OF  m  YEARS. 

4  PER  CENT. 


AQE. 

mz 

=15. 

20. 

25. 

AQE. 
15 

P. 

A(P-7r). 

P. 

A  (P  -  77). 

P. 

A  (P  -  77). 

15 

69.912 

1.771927 

59.207 

1.685216 

50.757 

1.601961 

16 

69.937 

.770420 

59.243 

.683472 

50.808 

.600017 

16 

17 

69.964 

.768843 

59.281 

.681649 

50.864 

.598000 

17 

18 

69.994 

.767188 

59.324 

.679742 

50.926 

.595895 

18 

19 

70.027 

.765453 

59.371 

.677748 

50.994 

.593706 

19 

20 

70.063 

1.763631 

59.423 

1.675660 

51.069 

1.591429 

20 

21 

70.103 

.761723 

59.480 

.673478 

51.151 

.589058 

21 

22 

70.147 

.759720 

59.542 

.671194 

51.241 

.586594 

22 

23 

70.195 

.757617 

59.611 

.668810 

51.340 

.584037 

23 

24 

70.248 

.755414 

59.685 

.666304 

51.448 

.581376 

24 

25 

70.306 

1.753103 

59.770 

1.663709 

51.567 

1.578620 

25 

26 

70.370 

.750677 

59.861 

.660987 

51.698 

.575763 

26 

27 

70.440 

.748129 

59.961 

.658133 

51.841 

.572794 

27 

28 

70.518 

.745459 

60.071 

.655162 

51.999 

.569729 

28 

29 

70.604- 

.742655 

60.193 

.652058 

52.173 

.566555 

29 

30 

70.696 

1.739709 

60.325 

1.648805 

52.361 

1.563263 

30 

31 

70.799 

.736621 

60.470 

.645411 

52.568 

.559867 

31 

32 

70.912 

.733376 

60.631 

.641875 

52.796 

.556367 

32 

33 

71.037 

.729968 

60.807 

.638180 

53.045 

.552757 

33 

34 

71.174 

.726396 

60.999 

.634316 

53.318 

.549045 

34 

35 

71.325 

1.722638 

61.212 

1.630306 

53.617 

1.545218 

35 

36 

71.489 

.718687 

61.443 

.626103 

53.943 

.541282 

36 

37 

71.670 

.714537 

61.698 

.621728 

54.300 

.537246 

37 

38 

71.870 

.710185 

61.979 

.617169 

54.691 

.533119 

38 

39 

72.090 

.705606 

62.285 

.612419 

55.118 

.528888 

39 

40 

72.331 

1.700792 

62.621 

1.607464 

55.583 

1.524562 

40 

41 

72.595 

.695729 

62.989 

.602305 

56.091 

.520146 

41 

42 

72.887 

.690414 

63.394 

.596938 

56.646 

.515653 

42 

43 

73.206 

.684812 

63.835 

.591346 

57.249 

.511067 

43 

44 

73.558 

.678925 

64.320 

.585530 

57.906 

.506410 

44 

45 

73.944 

1.672733 

64.850 

1.579485 

58.621 

1.501682 

45 

46 

74.369 

.666212 

65.429 

.573190 

59.398 

.496877 

46 

47 

74.835 

.659343 

66.062 

.566645 

60.241 

.492005 

47 

48 

75.346 

.652110 

66.754 

.559836 

61.154 

.487056 

48 

49 

75.908 

.644490 

67.511 

.552765 

62.145 

.482041 

49 

50 

76.525 

1.636458 

68.336 

1.545404 

63.216 

1.476939 

50  1 

51 

77.203 

.627994 

69.237 

.537759 

64.374 

.471757 

51  ' 

52 

77.946 

.619053 

70.218 

.529794 

65.622 

.466457 

52 

53 

78.762 

.609619 

71.288 

.521507 

66.969 

.461029 

53 

54 

79.658 

.599658 

72.453 

.512870 

68.418 

.455442 

54  i 

55 

80.643 

1.589137 

73.722 

1.503878 

69.978 

1.449674 

55 

56 

81.721 

.578003 

75.099 

.494476 

71.651 

.443648 

56 

57 

82.905 

.566227 

76.598 

.484655 

73.447 

.437335 

57 

58 

84.201 

.553741 

78.221 

.474329 

75.367 

.430617 

58 

59 

85.624 

.540512 

79.985 

.463526 

77.424 

.423490 

59 

60 

87.185 

1.526473 

81.897 

1.452135 

79.624 

1.415803 

60 

61 

88.894 

.511543 

83.968 

.440093 

81.973 

.407452 

61 

62 

90.767 

.495666 

86.209 

.427329 

84.480 

.398315 

62 

63 

92.822 

.478764 

88.635 

.413754 

87.157 

.388268 

63 

64 

95.070 

.460703 

91.258 

.399238 

90.014 

.377135 

64 

65 

97.534 

.441409 

94.093 

.383658 

93.062 

.364752 

65 

1 

^'OBMULA,  Pa,= 

=1000 1^- 

)  ~  1  +  a 

9  * 

0! 

TABLE     LX. 


*149 


TEN  ANNUAL  PREMIUM  (P),  ALSO  A  (P— tt),   FOR  ENDOWMENT  INSURANCE  OP  1,000 
PAYABLE  AT  DEATH  OR  AT  THE  END  OF  m  YEARS. 

4  PER  CENT. 


AGE. 

15 

30. 

35. 

40. 

AQE. 

P. 

A  (P  -  tt). 

P. 

A  (P  -  tt). 
1.450095 

P. 

A(P-Tr). 

44.122 

1.523169 

38.956 

34.990 

1.384237 

15 

16 

44.194 

.521124 

39.057 

.448114 

35.127 

.382584 

16 

17 

44.274 

.519013 

39.169 

.446104 

35.278 

.380957 

17 

18 

44.362 

.516833 

39.290 

.444056 

35.442 

.379355 

18 

19 

44.459 

.514582 

39.424 

.441976 

35.622 

.377787 

19 

20 

44.565 

1.512267 

39.571 

1.439877 

35.820 

1.376278 

20 

21 

44.681 

.509880 

39.731 

.437760 

36.035 

.374833 

21 

22 

44.808 

.507425 

39.906 

.435626 

36.269 

.373455 

22 

23 

44.948 

.504910 

40.099 

.433496 

36.526 

.372179 

23 

24 

45.101 

.502328 

40.308 

.431367 

36.805  » 

.371008 

24 

25 

45.269 

1.499686 

40.538 

1.429258 

37.109 

1.369963 

25 

26 

45.453 

.496993 

40.790 

.427181 

37.441 

.369069 

26 

27 

45.654 

.494238 

41.063 

.425131 

37.800 

.368328 

27 

28 

45.875 

.491442 

41.362 

.423140 

38.191 

.367770 

28 

29 

46.117 

.488608 

41.689 

.421222 

38.616 

.367421 

29 

30 

46.379 

1.485723 

42.043 

1.419366 

39.074 

1.367263 

30 

31 

46.667 

.482818 

42.430 

.417615 

39.571 

.367350 

31 

32 

46.982 

.479895 

42.850 

.415977 

40.108 

.367691 

32 

33 

47.327 

.476963 

43.307 

.414470 

40.688 

.368294 

33 

34 

47.702 

.474033 

43.804 

.413112 

41.313 

.369173 

34 

35 

48.112 

1.471107 

44.341 

1.411908 

41.984 

1.370324 

35 

36 

48,556 

.468193 

44.922 

.410868 

42.703 

.371747 

36 

37 

49.041 

.465316 

45.541 

.409858 

43.475 

.373458 

37 

38 

49.569 

.462496 

46.230 

.409390 

44.301 

.375458 

38 

39 

50.142 

.459726 

46.963 

.408964 

45.182 

.377712 

39 

40 

50.764 

1.457022 

47.750 

1.408741 

46.120 

1.380204 

40 

41 

51.437 

.454392 

48.596 

.408730 

47.116 

.382904 

41 

42 

52.168 

.451863 

49.504 

.408944 

48.174 

.385801 

42 

43 

52.956 

.449417 

50.475 

.409344 

49.291 

.388829 

43 

44 

53.808 

.447077 

51.513 

.409933 

50.471 

.391960 

44 

45 

54.727' 

1.444843 

52.620 

1.410688 

51.715 

1.395134 

45 

46 

55.715 

.442699 

53.798 

.411560 

53.021 

.398287 

46 

47 

56.778 

.440651 

55.049 

.412525 

54.393 

.401363 

47 

48 

57.918 

.438669 

56.374 

.413523 

55.828 

.404288 

48 

49 

59.140 

.436753 

57.776 

.414515 

57.330 

.407009 

49 

50 

60.446 

1.434853 

59.255 

1.415426 

58.899 

1.409433 

50 

51 

61.841 

.432953 

60.815 

.416198 

60.536 

.411521 

51 

52 

63.326 

.430981 

62.456 

.416730 

62.243 

.413174 

52 

53 

64.907 

.428896 

64.179 

.416959 

64.021  . 

.414331 

53 

54 

66.586 

.426630 

65.988 

.416797 

65.876 

.414920 

54 

55 

68.369 

1.424120 

67.887 

1.416166 

67.810 

1.414878 

55 

56 

70.255 

.421252 

69.875 

.414943 

69.824 

.414104 

56 

57 

72.252 

.417951 

71.959 

.413074 

71.928 

.412545 

57 

58 

74.359 

.414073 

74.144 

.410457 

74.126 

.410143 

58 

59 

76.589 

.409583 

76.431 

.406912 

76.421 

.406736 

59 

60 

78.943 

1.404301 

78.834 

1.402431 

60 

61 

81.430 

.398116 

81.358 

.396865 

61 

62 

84.057 

.390910 

84.011 

.390105 

62 

63 

86.837 

.382544 

86.810 

.382053 

63 

64 

89.779 

.372844 

89.764 

.372557 

64 

65 

92.898 

.361648 

65 

^150 


TABLE    LXI. 


LIMITED  OR  m  ANNUAL  PREMIUMS  (P),  ALSO  A  (P  —  tt),  FOR  LIFE  POLICIES  OF  1,000. 

4  PER  CENT. 


AQE. 
X. 

m  : 

=  5. 

10. 

15. 

20. 

AGE. 

X. 

p. 

A  (P  -  tt). 

P. 

P. 

A(P_:r). 

P. 

A(P_7r). 

15 

47.841 

1.569080 

26.657 

19.725 

0.952279 

16.357 

0.747458 

15 

16 

48.636 

.575656 

27.103 

20.057 

.957224 

16.634 

.751210 

16 

17 

49.465 

.582385 

27.568 

20.404 

.962251 

16.925 

.754982 

17 

18 

50.327 

.589248 

28.051 

20.765 

.967323 

17.227 

.758723 

18 

19 

51.224 

.596246 

28.555 

21.141 

.972434 

17.543 

.762431 

19 

20 

52.158 

1.603385 

29.079 

21.533 

0.977591  ' 

17.872 

0.766115 

20 

21 

53.129 

.610649 

29.625 

i  21.942 

.982773 

18.215 

.769739 

21 

22 

54.139 

.618034 

30.193 

1  22.367 

.987966  ; 

18.573 

.773296 

22 

23 

55.188 

.625547 

30.784 

1  22.810 

.993176  ; 

18.947 

.776774 

23 

24 

56.279 

.633170 

31.398 

23.271 

.998377 

19.336 

.780144 

24 

25 

57.412 

1.640910 

32.038 

23.751 

1.003564 

19.742 

0.783410 

25 

26 

58.590 

.648762 

32.703 

24.252 

.008732 

20.166 

.786546 

26 

27 

59.810 

.656696 

33.393 

24.772 

■  .013840  ' 

20.607 

.789489 

27 

28 

61.079 

.664734 

34.111 

25.314 

.018900 

21.067 

.792273 

28 

29 

62.395 

.672861 

34.857 

25.878 

.023891 

21.548 

.794857 

29 

30 

63.757 

1.681044 

35.631 

26.464 

1.028767 

22.048 

0.797184 

30 

31 

65.171 

.689305 

36.435 

27.074 

.033544 

22.570 

.799272 

31 

32 

66.636 

.697631 

37.270 

27.710 

.038195 

23.115 

.801067 

32 

33 

68.154 

.706006 

38.136  ■ 

28.371 

.042690 

23.684 

.802534 

33 

34 

69.726 

.714424 

39.036 

29.058 

.047022 

24.278 

.803655 

34 

35 

71.352 

1.722864 

39.969 

29.774 

1.051141 

24.897 

0.804364 

35 

36 

73.032 

.731309 

40.935 

30.517 

.055026 

25.544 

.804637 

36 

37 

74.771 

.739775 

41.938 

31.292 

.058665 

26.220 

.804432 

37 

38 

76.569 

.748241 

42.979 

32.098 

.062044 

26.926 

.803723 

38 

39 

78.426 

.756679 

44.057 

32.937 

.065094 

27.665 

.802425 

39 

40 

80.342 

1.765086 

45.174 

33.810 

1.067800 

28.437 

0.800490 

40 

41 

82.319 

.773437 

46.331 

34.719 

.070119 

29.246 

.797884 

41 

42 

84.361 

.781742 

47.532 

35.667 

.072033 

30.093 

.794523 

42 

43 

86.463 

.789955 

48.775 

36.653 

.073469 

30.981 

.790341 

43 

44 

88.631 

.798083 

50.063 

37.682 

.074407 

31.912 

.785266 

44 

45 

90.864 

1.806100 

51.398 

38.755 

1.074798 

32.891 

0.779236 

45 

46 

93.162 

.813987 

52.781 

39.875 

.074582 

33.919 

.772138 

46 

47 

95.527 

.821727 

54.214 

41.045 

.073707 

35.001 

.763885 

47 

48 

97.960 

.829300 

55.700 

42.267 

.072118 

36.141 

.754371 

48 

49 

100.461 

.836691 

57.241 

43.545 

.069761 

37.343 

.743502 

49 

50 

103.031 

1.843872 

58.839 

44.884 

1.066531 

38.613 

0.731121 

50 

51 

105.672 

.850829 

60.498 

46.287 

.062413 

39.956 

.717154 

51 

52 

108.382 

.857524 

62.219 

47.760 

.057275 

41.378 

.701387 

52 

53 

111.165 

.863946 

64.008 

49.307 

.051033 

42.887 

.683659 

53 

54 

114.022 

.870073 

65.868 

50.936 

.043625 

44.490 

.663842 

54 

55 

116.957 

1.875879 

1  67.806 

52.653 

1.034937 

46.198 

0.641682 

55 

56 

119.965 

.881320 

69.822 

54.464 

.024810 

48.016 

.616969 

56 

57 

123.054 

.886386 

71.927 

56.381 

.013174 

49.959 

.589480 

57 

58 

126.221 

.891022 

74.124 

58.410 

0.999852 

52.035 

.558900 

58 

59 

129.472 

.895215 

76.421 

60.564 

.984707 

54.259 

.524954 

59 

60 

132.811 

1.898927 

78.829 

62.855 

0.967553 

56.646 

0.487280 

60 

61 

136.241 

.902120 

81.355 

65.296 

.948227 

59.209 

.445480 

61 

62 

139.764 

.904747 

84.010 

67.901 

.926461 

61.965 

.399033 

62 

63 

143.391 

.906781 

86.809 

70.689 

.902085 

64.934 

.347603 

63 

64 

147.124 

.908167 

89.764 

73.679 

.874801 

68.135 

.290458 

64 

65 

150.971 

.908858 

92.889 

76.889 

.844309 

71.588 

.226806 

65 

Formula,     Pg.  =  1000 


Na;  —  Na;+OT        1  -t-  «: 


■m—1 


TABLE    LXII. 


*151 


NET  VALUE  OR  RESERVE  ON  TEN  PAYMENT  LIFE  POLICIES  OP  1,000. 

4  PER  CENT. 


r 

Age  of 

Entry. 

1st  Year. 

2d  Year. 

3d  Year. 

Age  of 

Entry. 

6m. 

12m. 

l^m.d. 

6m. 

12m. 

|m.d. 

6m. 

12m. 

^m.d. 

15 

23.965 

21.272 

.224 

45.724 

43.520 

.184 

68.478 

66.779 

.142 

15 

16 

24.409 

21.716 

.224 

46.619 

44.418 

.183 

69.838 

68.154 

.140 

16 

17 

24.869 

22.169 

.225 

47.541 

45.346 

.183 

71.247 

'69.580 

.139 

17 

18 

25.346 

22.642 

.225 

48.504 

46.315 

.182 

72.712 

71.059 

.138 

18 

19 

25.845 

23.135 

.226 

49.503 

47.316 

.182 

74.231 

72.590 

.137 

19 

20 

26.360 

23.641 

.227 

50.535 

48.349 

.182 

75.804 

74.180 

.135 

20 

21 

26.896 

24.166 

.228 

51.609 

49.427 

.182 

77.439 

75.826 

.134 

21 

22  1 

27.454 

24.715 

.228 

52.724 

50.541 

.182 

79.133 

77.532 

.133 

22 

23  ! 

28.030 

25.277 

.229 

53.877 

51.692 

.182 

80.887 

79.299 

.132 

23 

24 

28.631 

25.863 

.231 

55.076 

52.891 

.182 

82.706 

81.122 

.132 

24 

25 

29.255 

26.472 

.232 

56.314 

54.119 

.183 

84.583 

83.010 

.131 

25 

26 

29.895 

27.088 

.234 

57.591 

55.390 

.183 

86.527 

84.961 

.131 

26 

27 

30.566 

27.739 

.236 

58.923 

56.715 

.184 

88.539 

86.969 

.131 

27 

28 

31.259 

28.407 

.238 

60.290 

58.062 

.186 

90.606 

89.040 

.130 

28 

29 

31.969 

29.080 

-.241 

61.696 

59.454 

.187 

92.744 

91.177 

.131 

29 

30 

32.712 

29.793 

.243 

63.164 

60.904 

.188 

94.962 

93.389 

.131 

30 

31 

33.479 

30.524 

.246 

64.674 

62.390 

.190 

97.244 

95.662 

.132 

31 

32 

34.272 

31.273 

.250 

66.231 

63.918 

.193 

99.591 

97.994 

.133 

32 

33 

35.090 

32.044 

.254 

67.832 

65.485 

.196 

102.000 

100.380 

.135 

33 

34 

35.934 

32.832 

.258 

69.475 

67.082 

.199 

104.478 

102.837 

.137 

34 

35 

36.801 

33.633 

.264 

71.168 

68.733 

.203 

107.032 

105.363 

.139 

35 

36 

37.704 

34.473 

.269 

72.922 

70.437 

.207 

109.663 

107.954 

.142 

36 

37 

38.633 

35.328 

.275 

74.717 

72.167 

.213 

112.351 

110.597 

.146 

37 

38 

39.585 

36.192 

.283 

76.551 

73.932 

.218 

115.100 

113.288 

.151 

38 

39 

40.568 

37.079 

.291 

78.434 

75.731 

.225 

117.919 

116.050 

.156 

39 

40 

41.576 

37.977 

.300 

80.364 

77.577 

.232 

120.802 

118.854 

.162 

40 

41 

42.621 

38.912 

.309 

82.347 

79.452 

.241 

123.752 

121.720 

.169 

41 

42 

43.685 

39.837 

.321 

84.360 

81.351 

.251 

126.751 

124.620 

.178 

42 

43 

44.784 

40.794 

.333 

86.429 

83.288 

.262 

129.818 

127.572 

.187 

43 

44 

45.910 

41.756 

.346 

88.531 

85.244 

.274 

132.931 

130.556 

.198 

44 

45 

47.063 

42.729 

.361 

90.675 

87.222 

.288 

136.095 

133.570 

.210 

45 

46 

48.247 

43.713 

.378 

92.855 

89.217 

.303 

139.307 

136.616 

.224 

46 

47 

49.458 

44.701 

.396 

95.072 

91.229 

.320 

142.561 

139.679 

.240 

47 

48 

50.701 

45.702 

.417 

97.326 

93.250 

.340 

145.856 

142.762 

.258 

48 

49 

51.968 

46.696 

.439 

99.606 

95.275 

.361 

149.179 

145.841 

.278 

49 

50 

53.269 

47.699 

.464 

101.918 

97.297 

.385 

152.529 

148.922 

.301 

50 

51 

54.593 

48.688 

.492 

104.247 

99.309 

.411 

155.900 

151.994 

.326 

51 

52 

55.949 

49.678 

.523 

106.608 

101.319 

.441 

159.298 

155.058 

.353 

52 

53 

57.336 

50.665 

.556! 

108.995 

103.317 

.473 

162.703 

158.080 

.385 

53 

54 

58.755 

51.641 

.593 

111.391 

105.273 

.510 

166.102 

161.064 

.420 

54 

55 

60.194 

52.583 

.634 

113.792 

107.195 

.550 

169.489 

163.977 

.459 

55  • 

56 

61.673 

53.524 

.679 

116.210 

109.074 

.595 

172.867 

166.838 

.502 

56 

57 

63.173 

54.418 

.730 

118.620 

110.895 

.644 

176.221 

169.620 

.550 

57 

58 

64.713 

55.302 

.784 

121.053 

112.680 

.698 

179.563 

172.321 

.603 

58 

59 

66.289 

56.158 

.844 

123.486 

114.392 

.758 

183.858 

174.904 

.663 

59 

60 

67.898 

56.967 

.911 

125.902 

116.008 

.825 

186.106 

177.374 

.728 

60 

61 

69.541 

57.726 

.985 

128.316 

117.552 

.897 

189.308 

179.709 

.800 

61 

62 

71.236 

58.463 

1.064 

130.741 

119.008 

.978^ 

192.458 

181.898 

.880 

62 

63 

72.972 

59.134 

1.153 

133.141 

120.340 

1.067 

195.525 

183.901 

.969 

63 

64 

74.756 

59.748 

1.251 

135.531 

121.549 

1.165 

198.523 

185.734 

1.066 

64 

65 

76.592 

60.295 

1.358 

137.914 

122.644 

1.272 

201.446 

187.359 

1.174 

65 

*152 


TABLE    LXII. 


NET  VALUE  OR  RESERVE  ON  TEN  PAYMENT  LIFE  POLICIES  OF  1,000. 

4  PER  CENT. 


1 

A^eof 
Entry. 

4th  Year. 

5th  Year. 

6th  Year. 

% 

Age  of 

Entry. 

6m. 

12m. 

^m.d. 

6m. 

12m. 

^m.d. 

6m. 

12m. 

|m.d. 

15 

92.268 

91.100 

.097 

117.145 

116.533 

.051 

143.157 

143.124 

.003 

15 

16 

94.116 

92.974 

.095 

119.500 

118.923 

.048 

146.039 

146.052 

.001 

16 

17 

96.031 

94.914 

.093 

121.939 

121.397 

.045 

149.028 

149.091 

.005 

17  I 

18 

98.017 

96.925 

.091 

124.474 

123.971 

.042 

152.133 

152.243 

.009 

18  1 

19 

100.080 

99.015 

.089 

127.102 

126.635 

.039  1 

155.350 

155.510 

.013 

19 

20 

102.218 

101.177 

.087 

129.826 

129.396 

.036 

158.687 

158.899 

.018 

20 

21 

104.434 

103.417 

.085 

132.652 

132.261 

.033 

162.144 

162.402 

.022 

21 

22 

106.735 

105.744 

.083 

135.579 

135.221 

.030 

165.724 

166.034 

.026 

22 

23 

109.112 

108.141 

.081 

138.605 

138.286 

.027 

169.432 

169.794 

.030 

23 

24 

111.573 

110.627 

.079 

141.743 

141.461 

.024  173.265 

173.671 

.034 

24 

25 

114.124 

113.199 

.077 

144.983 

144.729 

.021'  177.224 

177.681 

.038 

25 

26 

116.752 

115.840 

.076 

148.325 

148.107 

.018 

181.317 

181.824 

.042 

26 

27 

119.470 

118.578 

.074 

151.787 

151.602 

.015 

185.549 

186.104 

.046 

27 

28 

122.275 

121.400 

.073 

155.357 

155.203 

.013  1  189.915 

190.515 

.050 

28 

29 

125.171 

124.308 

.072 

159.039 

158.913 

.010  194.414 

195.059 

.054 

29 

30 

128.167 

127.313 

.071 

162.842 

162.740 

.009  199.053 

199.734 

.057 

30 

31 

131.248 

130.399 

.071 

166.749 

166.664 

.007  1203.824 

204.550 

.060 

31 

32 

134.412 

133.560 

.071 

170.768 

170.706 

.005'!  208.739 

209.502 

.064 

32 

33 

137.666 

136.816 

.071 

174.906 

174.860 

.00411  213.791 

214.585 

.066 

33 

34 

141.016 

140.160 

.071 

179.157 

179.119 

.003  218.977 

219.800 

.069 

34 

35 

144.460 

143.587 

.073 

183.522 

183.487 

.003 

224.299 

225.142 

.070 

35 

36 

147.996 

147.104 

.074 

187.999 

187.960 

.003 

229.761 

230.627 

.072 

36 

37 

151.612 

150.688 

.077 

192.583 

192.539 

.004 

235.350 

236.223 

.  .073 

37 

38 

155.312 

154.358 

.079 

197.271 

197.206 

.005 

241.064 

241.943 

.073 

38 

39 

159.102 

158.096 

.084 

202.065 

201.977 

.007 

246.908 

247.781 

.073 

39 

40 

162.970 

161.912 

.088 

206.961 

206.835 

.010 

252.869 

253.730 

.072 

40 

41 

166.924 

165.798 

.094 

211.956 

211.784 

.014 

258.952 

259.788 

.070 

41 

42 

170.945 

169.737 

.101 

217.037 

216.804 

.019 

265.135 

265.934 

.067 

42 

43 

175.044 

173.741 

.109 

222.209 

221.902 

.026 

271.428 

272.179 

.063 

43 

44 

179.204 

177.789 

.118 

227.457 

227.063 

.033 

277.812 

278.498 

.057 

44 

45 

183.426 

181.884 

.129 

232.781 

232.279 

.042 

284.283 

284.890 

.051 

45 

46 

187.705 

186.014 

.141 

238.169 

237.543 

.052 

290.831 

291.338 

.042 

46 

47 

192.034 

190.174 

.155 

243.613 

242.839 

.065 

297.442 

297.831 

.032 

47 

48 

196.406 

194.350 

.171 

249.106 

248.162 

.079 

304.112 

304.362 

.021 

48 

49 

200.806 

198.530 

.190 

254.634 

253.497 

.095 

310.827 

310.916 

.007 

49 

50 

205.238 

202.715 

.210 

260.197 

258.839 

.113 

317.571 

317.464 

.009 

50 

51 

209.691 

206.890 

.233 

265.770 

264.153 

.135 

324.326 

324.000 

.027 

51 

52 

214.154 

211.032 

.260 

271.348 

269.444 

.159 

331.080 

330.497 

.049 

52 

53 

218.614 

215.139 

.290 

276.911 

274.676 

.186 

337.812 

336.940 

.073 

53 

54 

223.054 

219.177 

.323 

282.442 

279.839 

.217 

344.509 

343.311 

.100 

54 

55 

227.461 

22^.138 

.360 

287.929 

284.914 

.251 

351.148 

349.577 

.131 

55 

56 

231.845 

227.030 

.401 

293.372 

289.891 

.290 

357.717 

355.720 

.166 

56 

57 

236.176 

230.806 

.447 

298.726 

294.720 

.334 

364.181 

361.716 

.205 

57 

58 

240.453 

234.461 

.499 

304.002 

299.418 

.382 

370.545 

367.548 

.250 

58 

59 

244.654 

237.982 

.556 

309.170 

303.938 

.436 

376.764 

373.168 

.300 

59 

60 

248.770 

241.338 

.619 

314.208 

308.248 

.497 

382.812 

378.548 

.355 

60 

61 

252.785 

244.505 

.690 

319.091 

312.323 

.564 

388.672 

383.666 

.417 

61 

62 

256.687 

247.467 

.768 

323.817 

316.156 

.638 

394.325 

388.484 

.487 

62 

63 

260.456 

250.201 

.855 

328.348 

319.687 

.722 

399. 742 

392.987 

.563 

63 

64 

264.089 

252.680 

.951 

332.690 

322.936 

.813 

404.905 

397.110 

.650 

64 

65 



267.582 

254.917 

1.055 

336.816 

325.825 

.916 

409.779 

400.845 

.745 

65 

TABLE    LXII. 


*lo3 


NET  VALUE  OR  RESERVE  ON  TEN  PAYMENT  LIFE  POLICIES  OF  1,000. 

4  PER  CENT. 


Age  of 

Entry. 

7th  Year. 

8th  Year. 

9th  Year.* 

Age  of 
Entry. 

6m. 

12in. 

^m.d. 

6m. 

12m. 

Jm.d. 

6m. 

12m. 

l^m.d. 

15 

170.354 

170.927 

.048 

198.794 

200.004 

.101 

228.535 

230.408 

.156 

15 

16 

173.789 

174.422 

.053 

202.805 

204.084 

.107 

233.143 

235.100 

.163 

16 

17 

177.351 

178.043 

.058 

206.963 

208.315 

.113 

237.928 

239.972 

.170 

17 

18 

181.047 

181.800 

.063 

211.280 

212.709 

.119 

242.889 

245.018 

.177 

18 

19 

184.883 

185. 700 

.068 

215.755 

217.255 

.125 

248.030 

• 

250.251 

.185 

19 

20 

188.855 

189.732 

.073 

220.390 

221.969 

.132 

253.363 

255.677 

.193 

20 

21 

192.970 

193.912 

.079 

225.196  1226.855 

.138 

258.882 

261.284 

.200 

21 

22 

197.235 

198.244 

.084 

230.169 

231.902 

.144 

264.593 

267.091 

.208 

22 

23 

201.646 

202.713 

.089 

235.311 

237.125 

.151 

270.505 

273.102 

.216 

23 

24 

206.203 

207.338 

.095 

240.633 

242.530 

.158 

276.622 

279.316 

.225 

24 

25 

210.920 

212.121 

.100 

246.136 

248.113 

.165 

282.943 

285.735 

.233 

25 

26 

215.792 

217.057 

.105 

251.819 

253.878 

.172 

289.472 

292.363 

.241 

26 

27 

220.826 

222.155 

.111 

257.688 

259.828 

.178 

296.208 

299.195 

.249 

27 

28 

226.017 

227.409 

.116 

263.737 

265.953 

.185 

303.156 

306.248 

.258 

28 

29 

231.365 

232.813 

.121 

269.971 

272.273 

.192 

310.323 

313.516 

.266 

29 

30 

236.878 

238.391 

.126 

276.404 

278.785 

.198 

317.708 

320.999 

.274 

30 

31 

242.557 

244.129 

.131 

283.022 

285.480 

.205 

325.307 

328.699 

.283 

31 

32 

248.398  250.024 

.135 

289.828 

292.363 

.211 

333.121 

336.609 

.291 

32 

33 

254.400  1  256.079 

.140 

296.821 

299.427 

.217 

341.153 

344.743 

.299 

33 

34 

260.560  1262.285 

.144 

304.003 

306.684 

.223 

349.401 

353.083 

.307 

34 

35 

266.885 

268.658 

.148 

311.372 

314.117 

.229 

357.863 

361.639 

.315 

35 

36 

273.370 

275.179 

.151 

318.925 

321.736 

.234 

366.537 

370.403 

.322 

36 

37 

280.007 

281.852 

.154 

326.658 

329.527 

.239 

375.418 

379.371 

.329 

37 

38 

286.793 

288.665 

.156 

334.566 

337.488 

.244 

384.502 

388.537 

.336 

38 

39 

293.729 

295.620 

.158 

342.646 

345.615 

.247 

393.784 

397.896 

.343 

39 

40 

300.807 

302.709 

.159 

350.891 

353.898 

.251 

403.258 

407.444 

.349 

40 

41 

308.022  309.926 

.159 

359.297 

362.337 

.253 

412.918 

417.169 

.354 

41 

42 

315.362  1317.257 

.158 

367.850 

370.911- 

.255 

422.753 

427.062 

.359 

42 

43 

322.827  324.700 

.156 

376.548 

379.622 

.256 

432.755 

437.114 

.363 

43 

44 

330.401  332.241 

.153 

385.377 

388.450 

.256 

442.913 

447.313 

.367 

44 

45 

338.077 

339.866 

.149 

394.325 

397.385 

.255 

453.216 

457.648 

.369 

45 

46 

345.842 

347.566 

.144 

403.381 

406.416 

.253 

463.653 

468.109 

.371 

46 

47 

353.687 

355.328 

.137 

412.538  415.533 

.250 

474.207 

478.668 

.372 

47 

48 

361.602 

363.142 

.128 

421.773 

424.705 

.244 

484.862 

489.319 

.371 

48 

49 

369.566 

370.975 

.117 

431.071 

433.925 

.238 

495.601 

500.036 

.370 

49 

50 

377.563 

378.824 

.105 

440.415 

443.167 

.229 

506.405. 

510.803 

.366 

50 

51 

385.577 

386.656 

.090 

449.782 

452.411 

.219 

517.257 

521.605 

.362 

51 

52 

393.588 

394.459 

.073 

459.162 

461.645 

.207 

528.140 

532.417 

.356 

52 

53 

401.582 

402.216 

.053 

468.531 

470.838 

.192 

539.026 

543.206 

.348 

53 

54 

409.537  1409.895 

.030 

477.859 

479.955 

.175 

549.892 

553.961 

.339 

54 

55 

417.420 

417.458 

.003 

487.124 

488.984 

.155 

560.721 

564.652 

.328 

55 

56 

425.224 

424.906 

.026 

496.313 

497.898 

.132 

571.484 

575.247 

.314 

56 

57 

432.919 

432.195 

.060 

505.387 

506.653 

.105 

582.148 

585.716 

.297 

57 

58 

440.485 

439.297 

.099 

514.323 

515.225 

.075 

592.693 

596.038 

.279 

58 

59 

447.881 

446.174 

.142 

523.091 

523.587 

.041 

603.093 

606.177 

.257 

59 

60 

455.090 

452.802 

.191 

531.660 

531.689 

.002 

613.315 

616.112 

.233 

60 

61 

462.076 

459.132 

.245 

540.006  539.524 

.040 

623.336 

625.793 

.205 

61 

62 

468.830 

465.165 

.305 

548.100  547.026 

.090 

633.118 

635.201 

.174 

62 

63 

475.305 '470.815 

.374 

555.898,554.171 

.144 

642.635 

644.290 

.138 

63 

64 

481.476  476.078 

.450 

563.376  560.911 

.205 

651.853 

653.031 

.098 

64 

65 

487.316  480.897 

.535 

570.499  567.212 

.274 

660.750 

661.399 

.054 

65 

Note.     The  last  Premium  at  the  beginning  of  the  10th  Year  changes  the  Policy  to  the  Paid-up  class. 


*154 

TABLE    LXIII. 

GENERAL  VALUATION  OF  ANNUAL  PREMIUM  POLICIES  OF  1,000. 
INTEREST,  4  PER  CENT. 

I.  Common  Life  Policies. — The  Net  Value  or  Reserve  is  already  computed  in  the 
column  (V,  6n3.)  for  the  middle  of  each  Policy  Year,  and  in  the  column  (V,  12m.)  for 
the  end  of  each  Policy  Year,  when  the  next  Annual  Premium  is  just  due  and  unpaid. 
For  any  other  time  of  year,  a  correction  derived  from  the  column  of  half  monthly  or 
15  days  difference  (|^m.  d.)  is  to  be  added  or  subtracted,  according  as  the  Reserve  is 
increasing  or  decreasing  in  the  direction  of  the  given  interval. 

For  example,  if  the  Age  of  Entry,  x,  of  a  common  Life  Policy  of  11000  be  35  years, 
the  4  per  cent.  Reserve  at  the  middle  of  the  24th  Policy  Year  (V||,  6m.)  is  given  $362.47, 
and  at  the  end  of  the  same  Policy  Year,  $362.37.  Hence,  at  the  end  of  3  months  in 
the  same  year,  the  Reserve  i?  $362.52,  and  at  the  end  of  the  9th  month,  $362.42. 

Formulas,    (V,  12m.)  =  1000  ]  1  -  1 +  ^"  i .  .,  =  ^^^.   - 

(V,  6m.)  =  i  \ (Vr\  12m.)  +77^4- (VS,  Urn.)}.       B^  =  ^^-^1^. 

IL  General  Valuation. — For  Endowment  Insurances  and  all  other  Annual 
Premium  Policies,  the  Reserve  V  is  first  found  from  the  Table,  and  corrected  for  the 
elapsed  fraction  of  a  year,  when  required,  as  if  for  a  common  Life  Policy.  The  remain- 
ing part  and  process  is  thus  indicated  : 

General  Formula,  Reserve  =  V  4-  (Pa-  —  ttx)  •  B^  •/*+„. 

Middle  of  Policy  Year,     Reserve  =  (V,  6m.)  +  (Pa,  —  tt^)  •  (B/)". 
End       "      "         "         Reserve  =  (V,  12m.)  +  (Pa;  —  tt^,)  •  B^. 

V     Pure  Endowment,  Reserve  =:  — rp^  •  B^  •  fx+n- 

Here  n  -\-  m-  denotes  the  expired  (n)  added  to  the  unexpired  (m)  years  of  the  whole 
period  of  simple  endowment.     In  all  cases, 

X  =  the  Age  of  Entry  or  of  original  Insurance. 
h  =  fraction  elapsed  of  the  current  Policy  Year. 
f  =  h-{-{l—h)  vjJx+n-h    Table  LXIV. 
At  12  montiis,  or  the  end  of  the  year,  /=  1,  since  A  =  1. 

Example  1.     End  of  the  Year. — A  Ten  Premium  Endowment  Insurance  of  $1000,  payable  at 
Death  or  Age  50,  is  contracted  at  the  Age  of  30.     Required  the  Net  Value  at  the  end  of  the  9th  Year. 
x  =  dO;    n  +  h  =  8  yrs.  13m.  1.648805  =  a(P  -  n),     Table  LVIL 

V  =      92.685,        1.060738  =  /.B30,  Table  LXIII. 

+  512.322  . . .  .3.709543       Sum.  Table  LXXXIL 

Reserve  =  feoXOOT  on  $1000  Insured. 
Example  3.    Intermediate  Months  and  Term  Policies. — An  Insurance  of  $1000  is  entered  at  the 
age  of  38,  for  the  Term  of  7  years.     Required  the  Net  Value  at  the  end  of  4  years  and  8J  months 
(5th  year). 

a;  =  38 ;    a  +  n  +  A  =  43  yrs.  8^  m.  1 .05327  =  A  (tt  -  P),      Table  UII. 

1.99387  =   lf\z,  Table  LXIV. 

Adjusted  V  =      68.993,        0.76363  =  1B\»,  Table  LXIII. 

-64.531  ■...1.80977         Sum,  Table  LXXXIL 

Net  Value  =      $4,462  on  $1000  Insured. 
In  this  case,  (P  —  n)  being  negative,  since  P  is  less  than  tt,  the  computed  term  is  subtractive,  which 
is  a  general  characteristic  of  Simple  Term  Policies. 

Example  3.  Middle  of  the  Year.—K  Fifteen  Premium  Insurance  of  $1000  for  the  whole  Life  is 
entered  at  the  Age  of  42.  Required  the  Net  Value  at  the  end  of  7  years  and  6  months,  (8th  Policy 
Year). 

V,  6m.         1.07203  =  ?.(P-7r),     Table  LXI. 
133.75         0.99521   =  ?^(B/),  Table  LXIIL 

+  116.75  . . .  .2.06724         Sum,  Table  LXXXIL 

Reserve  =  $250.50  on  $1000  Insured. 
Note  1.     Five,  Ten,  or  Limited  Premium  Policies  can  be  valued  by  this  method  only  till  one  year 
after  the  last  Annual  Premium  is  paid.     After  the  beginning  of  this  year,  the  Policy  being  Paid-up, 
the  Reserve  is  more  easily  found  from  the  proper  Single  Premium  Table. 

Note  2.  Although  six  decimals  are  given,  yet  in  practice  five,  and  in  many  cases,  four  decimals 
will  be  suflBcient  for  logarithms  or  anti-logarithms.  Thus  the  last  of  the  six  decimals  can  generally  be 
omitted,  as  in  the  last  Examples. 


TABLE     LXIII. 


*155 


GENERAL  VALUATION   OF  ANNUAL   PREMIUM   POLICIES    OF  1,000. 

4  PER  CENT. 


n. 

10. 

11. 

o  o 

n. 

V. 

6m. 

V. 

12m. 

^m.d 

6m. 

AB. 

13m. 

V. 

6m. 

V. 

13m. 

im.d 

6m. 

AB. 
12m. 

0 

6.742 

3.70E 

.253 

0.010043 

0.019857 

6.914 

3.875 

.353 

0.010046 

0.019866 

0 

1 

10.527 

7. 570 

.246 

.331118 

.330938 

10.873 

7.917 

.346 

.331136 

.330948 

1 

2 

14.470 

11.597 

.239 

.507337 

.517159 

14.999 

13.137 

.339 

.507349 

.517176 

2 

3 

18.582 

15.792 

.233 

.643484 

.653311 

19.393 

16.505 

.333 

.643504 

.653337 

3 

4 

22.860 

20.154 

.226 

.749687 

.759530 

33.763 

31.065 

.325 

.749714 

.759553 

4 

5 

27.312 

24.696 

.218 

0.839344 

0.849083 

38.415 

35.811 

.317 

0.839378 

0.849133 

5 

6 

31.94? 

29.425 

.310 

.916653 

.936496 

33.359 

30.754 

.309 

.916693 

.926543 

6 

7 

36.774 

34.349 

.203 

.985188 

.995039 

38.301 

35.893 

.301 

.985338 

.995096 

7 

8 

41.797 

39.470  .194 

1.046973 

1.056830 

43.543 

41.340 

.193 

1.047033 

1.056898 

8 

"  9 

47.020 

44.796 

.185 

.103449 

.113314 

48.995 

46.796 

.183 

.103530 

.113395 

9 

10 

52.450 

50.331 

.177 

1.155649 

1.165534 

54.659 

53.568 

.174 

1.155734 

1.165619 

10 

11 

58.094 

56.083 

.168 

.304335 

.314330 

60.545 

58.568 

.165 

.304436 

.314333 

11 

12 

63.959 

62.060 

.158 

.350088 

.359984 

66.661 

64.799 

.155 

.350305 

.360113 

12 

13 

70.051 

68.268 

.149 

.393356 

.303363 

73.010 

71.367 

.145 

.393491 

.303411 

13 

14 

76.377 

74.712 

.139 

.334498 

.344418 

79.603 

77.983 

.135 

.334654 

.344587 

14 

15 

83.944 

81.403 

.138 

1.373803 

1.383736 

86.441 

84.945 

.125 

1.373983 

1.383933 

15 

16 

89.759 

88.340 

.118 

.411508 

.431458 

93.533 

93.167 

.114 

.411713 

.431679 

16 

17 

96.824 

95.534 

.108 

.447810 

.45777711100.888 

99.655 

.103 

.448043 

.458038 

17 

18 

104.151 

102.995 

.096 

.483875 

.493860 

108.505 

107.403 

.093 

.483143 

.493150 

18 

19 

111.741 

110.713 

.086 

.516846 

.536854 

116.393 

115.438 

.080 

.517149 

.537178 

19 

20 

119.598 

118.710 

.074 

1.549843 

1.559873 

134.559 

133.736 

.069 

1.550184 

1.560339 

20 

21 

127. 735 

126.986 

.063 

.581968 

.593033; 

133.013 

133.333 

.057 

.583353 

.593434 

21 

22 

136.156 

135.552 

.050 

.613315 

.633396 

141.753 

141.318 

.045 

.613749 

.633861 

22 

23 

144.865 

144.403 

.039 

.643964 

.654076 

150.786 

150.399 

.033 

.644454 

.654599 

23 

!24 

153.864 

153.552 

.036 

.673993 

.684137 

160.110 

159.867 

.030 

.674545 

.G84739 

24 

25 

163.155 

162.983 

.014 

1. 703464 

1.713648 

169.734 

169.647 

.007 

1.704083 

1.714306 

25 

126 

172.742 

172.727 

.001 

.733434 

.743657 

179.669 

179.737 

.006 

.733134 

.743389 

26 

27 

182.640 

182.779 

.012 

.760957 

.771333 

189.911 

190.133 

.018 

.761737 

.773043 

27 

28 

192.845 

193.137 

.024 

.789083 

.799398 

300.460 

300.834 

.031 

.789948 

.800318 

28 

29 

203.354 

203.798 

.037 

.816861 

.837331 

311.315 

211.843 

,.044 

.817839 

.838359 

29 

30 

214.169' 

214.766 

.050 

1.844335 

1.854765 

333.486 

333.175 

.057 

1.845413 

1.855904 

30 

31 

225.299 

226.057 

.063 

.871543 

.883034 

333.965 

334.803 

.070 

.873745 

.883313 

31 

32 

236.735 

237.640 

.075 

.898536 

.909093 

345.753 

346.748 

.083 

.899867 

.910509 

32 

33 

248.479: 

249.543 

.089 

.935335 

.935967 

357.850 

358.997 

.096 

.936815 

•937545 

33 

34 

260.531 

261.746 

.101 

.951973 

.963703 

370.348 

371.546 

.108 

.953634 

.964459 

34 

35 

272.884 

274.248 

.114 

1.978511 

1.989336 

383.948 

384.396 

.131 

1.980356 

1.991385 

35 

36; 

385,536 

287.050 

.126 

2.004974 

2.015903 

395.943 

397.534 

.133 

2.007035 

3.018069 

36 

37' 

298.483 

300.141 

.138 

.031403 

.043447 

309.333 

310.957 

.145 

.033681 

.044851 

37 

38 

311.714 

313.513 

.150 

.057833 

.069003 

333.785 

334.659 

.156 

.060360 

.071668 

38 

39 

325.225 

327.164 

.162 

.084301 

.095609 

336.618 

338.633 

.167 

.087107 

.098568 

39 

40 

339.007 

341.075 

.172 

3.110853 

3.133313 

350.708 

353.840 

.178 

3.113964 

2.135593 

40 

41 

353.044 

355.240 

.183 

.137537 

.149156 

365.047 

367.300 

.188 

.140976 

.153789 

41 

42 

367.331 

369.647 

.193 

.164369 

.176183 

379.633 

381.991 

.197; 

.168190 

.180304 

42 

43 

381.852 

384.283 

.203 

.191433 

.303436 

394.433 

396.898 

.306' 

.195653 

.307887 

43 

10.     IT  =  9.7739. 

11.    Tr  =  9.9535. 

Continued  on  Page  *199. 


*156 


TABLE    LXIII 


GENERAL  VALUATION  OF  ANNUAL  PREMIUM  POLICIES  OF  1,000. 

4  PER  CENT. 


a;  =  12. 

13. 

H 

n. 
0 

V. 

6ni. 

V. 

12m. 

im.d. 

6m. 

AB. 

12m. 

V. 

6m. 

V. 

12m. 

im.d. 

A(B/). 
6m. 

AB. 

12m. 

0 

7.100 

4.058 

.254 

0.010050 

0.019872 

7.292 

4.244 

.254 

0.010055 

0.019882 

1 

11.243 

8.285 

.247 

.321134 

.330901 

11.621 

8.657 

.247 

.321147 

.330980 

1 

2 

15.553 

12.680 

.239 

.507365 

.517198 

16.125 

13.253 

.239 

.507382 

.517221 

2 

3 

20.039 

17.257 

.232 

.042526 

.652365 

20.815 

18.037 

.232 

.642549 

.652393 

3 

4 

24.711 

22.022 

.224 

.749741 

.759585 

25.698 

23.019 

.223 

.74977r  .759622 

4 

5 

29.574 

26.984 

.216 

0.839313 

0.849164 

30.779 

28.200 

.215 

0.839352 

0.849210 

5 

6 

34.634 

32.143 

.208 

.916736 

.926594 

36.065 

33.589 

.206 

.916786 

.926651 

6 

7 

39.898 

37.510 

.199 

.985293 

.995158 

41.559 

39.189 

.197 

.985353 

.995228 

7 

8 

45.370 

43.088 

.190 

1.047098 

1.056973 

47.268 

45.007 

.188 

1.047172 

1.057057 

8 

■  9 

51.056 

48.883 

.181 

.103600 

.113485 

53.201 

51.055 

.179 

.103687 

.113583 

9 

10 

56.966 

54.906 

.172 

1.155828 

1.165724 

59.365 

57.336 

.169 

1.155932 

1.165839 

10 

11 

63.104 

61.161 

.102 

.204546 

.214453 

65.766 

63.855 

.159 

.204667 

.214587 

ill 

12 

69.479 

67.654 

.152 

.250333 

.260253 

72.410 

70.625 

.149 

.250474 

.260407 

12 

13 

76.096 

74.396 

.142 

.293639 

.303572 

79.  .304 

77.643 

.138 

.293803 

.303753 

13 

14 

82.962 

81.386 

.131 

.334825 

.344775 

86.452 

84.922 

.128 

.335013 

.344980 

14 

15 

90.082 

88.636 

.121 

1.374178 

1.384145 

93.866 

92.470 

.116 

1.374394:1.384379 

15 

16 

97.465 

96.153 

.109 

.406004 

.416049 

101.545 

100.279 

.105 

.412186^  .422194 

16 

17  105.113 

103.930 

.099 

.448301 

.458309 

109.494 

108.309 

.094 

.448586  .458615 

17 

18  113.030 

111.988 

.087 

.483430 

.493465 

117.726 

110.743 

.082 

.483758 

.493813 

18 

19|131.229 

120.328 

.075 

.517482 

.527537 

126.246 

125.409 

.070 

.517846 

.527927 

19, 

20  129.714 

128.958 

.063 

1.550559 

1.560640 

135.057 

134.365 

.058 

1.550971 

1.561083 

20^ 

21138. 488 

137.877 

.051 

.582776  .5928881 

144.162 

143.619 

.045 

.583243 

.593388 

21 

22  147.557 

147.094 

.039 

.614227 

.624372 

153.561 

153.163 

.033 

.614755 

.624939 

22 

231156.917 

156.599 

.027 

.644995 

.655179 

163.261 

163.020 

.020 

.645589 

.655812 

23 

24  [166.579 

166.417 

.014 

.675152 

.685375 

173.276 

173.191 

.007 

.675816 

.686081 

24 

25:176.553 

176.547 

.001 

1.704760 

1.715025 

183.600 

183.669 

.006 

1.705505 

1.715821 

25 

26  186.836 

186.982 

.012 

.733883 

.744199 

194.232 

194.450 

.019 

.734721 

.745091 

26 

27  197.424 

197.725 

.025 

.762581 

.772951 

205.175 

205.553 

.032 

.763519 

.773949 

27 

281208.322 

208.777 

.038 

.790901 

.801331 

216.434 

216.976 

.045 

.791949 

.802440 

28 

29  219.537 

220.154 

.051 

.818892 

.829383 

228.006 

228.695 

.057 

.820062 

.830629 

29 

30  231.060 

231.825 

.064 

1.846599 

1.857166 

239.886 

240.737 

.071 

1.847906 

1.858548 

30 

31  243.893 

243.819 

.077 

.874069 

.884711 

252.080 

253.084 

.084 

.875524 

.886254 

31 

321255.0.38 

256.115 

.090 

.901.340 

.912070 

264.579 

265.733 

.090 

.902903 

.913788 

32 

33 

267.485 

268.713 

.102 

.928458 

.939283 

277.379 

278.685 

.109 

.930202 

.941191 

33 

34 

280.234 

281.612 

.115 

.955459 

.966388 

290.477 

291.929 

.121 

.957407 

.968511 

34 

35 

293.278 

294.802 

.127 

1.982387 

1.993431 

303.864 

305.459 

.133 

1.984021 

1.995791 

35 

36 

306.610 

308.277 

.139 

2.009283 

2.020453! 

317.534 

319.270 

.145 

2.011765 

2.023073 

36 

37 

320.226 

322.032 

.151 

.036186 

.047494i 

.331.477 

333.344 

.150 

.038944 

.050405 

37 

38 

334.111 

336.049 

.162 

.063143 

.074604 

345.680 

347.675 

.100 

.066204 

.077833 

38 

39 

348.256 

350.322 

.172 

.090195 

.101824 

360.133 

362.251 

.170 

.093591, 

.105404 

39 

40 

362.652 

364.839 

.182 

2.117388 

2.129201 

374.825 

377.059 

.186 

2.121154' 

2.133168 

40 

41 

377.284 

379.587 

.192 

.144770 

.156784- 

389.742 

392.085 

.195 

.148942 

.101177 

41 

42 

392.140 

394.552 

.201 

.172391 

.1846261 

404.864 

407.303 

.203 

.177014 

.189496 

42 

43 

407.201 

409.708 

.209 

.200307 

.212789 

420.173 

422.703 

.211 

.205430 

.318178 

43 

■  ■■■..— — y . '  —  • 

12.   77  =  10.1419. 

13.   -n-  =  10.3400. 

Continued  on  Page  *198. 


*157 


TABLE    LXIII. 


GENERAL  VALUATION  OF  ANNUAL  PREMIUM  POLICIES  OF  1,000. 

4  PER  CENT. 


n. 

14. 

15. 

V. 

6m. 

V. 

12m. 

^m.d. 

A(B/). 
6m. 

aB. 

12m. 

V. 

6m. 

V. 

12m. 

^m.d. 

A(B/). 
6m. 

aB. 

12m. 

n. 

0 

7.490 

4.432 

.255 

0.010062 

0.019895 

7.701 

4.636 

.255 

0.010067 

0.019906 

1 

ol 

1 

12.013 

9.047 

.247 

.321158 

.330997 

12.432 

9.462 

.248 

.321169 

.331013 

1 

2 

16.724 

13.852 

.239 

.507400 

.517244 

17.358 

14.488 

.239 

.507417 

.517268 

2 

3 

21.627 

18.855 

.231 

.642573 

.652424 

22.483 

19.713 

.231 

.642600 

.652458 

3 

4 

26.731 

24.058 

.223 

.749805 

.759663 

27.815 

25.150 

.222 

.749841 

.759706 

4 

5 

32.038 

29.470 

.214 

0.839395 

0.849260 

33.357 

30.799 

.213 

0.839442 

0.849317 

5 

6 

37.556 

35.094 

.205 

.916839 

.926714 

39.117 

36.668 

.204 

.916898 

.926783 

6 

7 

43.289 

40.937 

.196 

.985419 

.995304 

45.101 

42.768 

.194 

.985492 

.995388 

7 

8 

49.248 

47.011 

.186 

1.047252 

1.057148 

51.319 

49.104 

.185 

1.047340 

1.057247 

8 

9 

55.439 

53.318 

.177 

.103783 

.113690 

57.775 

55.680 

.175 

.103889 

.113809 

9 

10 

61.865 

59.865 

.167 

1.156045 

1.165965 

64.477 

62.509 

.164 

1.156169 

1.166102 

10 

11 

68.539 

66.664 

.156 

.204800 

.214733 

71.432 

69.589 

.154 

.204946 

.214896 

11 

12 

75.462 

73.712 

.146 

.250628 

.260578 

78.643 

76.931 

.143 

.250798 

.260765 

12 

13 

82.641 

81.022 

.135 

.293982 

.303949 

86.121 

84.545 

.131 

.294179 

.304164 

13 

14 

90.086 

88.602 

.124 

.335220 

.345205 

93.867 

92.422 

.120 

.335448 

.345456 

14 

15 

97.797 

96.444 

.113 

1.374633 

1.384641 

101.885 

100.583 

.108 

1.374897 

1.384926 

15 

16 

105.780 

104.569 

.101 

.412461 

.422490: 

110.190 

109.030 

.097 

.412760 

.422815 

16 

17 

114.048 

112.979 

.089 

.448897 

.458952 

118.784 

117.772 

.084 

.449239 

.459320 

17 

18 

122.605 

121.682 

.077 

.484112 

.494193 

127.671 

126.805 

.072 

.484499 

.494611 

18 

19 

131.452 

130.675 

.065 

.518246 

.528358 

136.856 

136.141 

.060 

.518687 

.528832 

19 

20 

140.596 

139.969 

.052 

1.551425 

1.561570 

146.338 

145.768 

.048 

1.551927 

1.562111 

20 

21 

150.035 

149.553 

.040 

.583758 

.593942 

156.122 

155.711 

.034 

.584324 

.594547 

21 

22 

159.777 

159.453 

.027 

.615336 

.625559 

166.224 

165.971 

.021 

.615971 

.626236 

22 

23 

169.835 

169.668 

.014 

.646239 

.656504 

176.639 

176.541 

.008 

.646953 

.657269 

23 

24 

180.203 

180.190 

.001 

.676545 

.686861 

j 

187.365 

187.422 

.005 

.677350 

.687720 

24 

25 

190.881 

191.024 

.012 

1.706326 

1.716696 

198.401 

198.615 

.018 

1.707231 

1.717661 

25 

26 

201.869 

202.167 

.025 

.735643 

.746073 

209.760 

210.138 

.031 

.736654 

.747145 

26 

27 

213.177 

213.639 

.039 

.764549 

.775040 

221.432 

221.960 

.044 

.765681 

.776248 

27 

28 

224.798 

225.408 

.051 

.793100 

.803667 

233.416 

234.107 

.058 

.794368 

.805010 

28 

29 

236.728 

237.501 

.064 

.821350 

.831992 

245.717 

246.561 

.070 

.822764 

.833494 

29 

30 

248.975 

249.900 

.077 

1.849341 

1.860071 

258.324 

259.321 

.083 

1.8509221.861747 

30 

31 

261.526 

262.604 

.090 

.877126 

.887951 

271.237 

272.386 

.096 

.878887 

.889816 

31 

32 

274.381 

275.611 

.102 

.904746 

.915675 

284.448 

285.745 

.108 

.906709 

.917753 

32 

33 

287.535 

288.911 

.115 

.932249 

.943293 

297.953 

299.394 

.120 

.934435 

.945605 

33 

34|30d.979 

302.499 

.127 

.959679 

.970849 

311.742 

313.325 

.132 

.962110 

.973418 

34 

35 '.314. 708 

316.369 

.138 

1.987078 

1.998386 

325.807 

327.522 

.143 

1.989783 

».001244 

35 

36  328.710 

330.502 

.149 

2.014495 

2.025956 

340.133 

341.979 

.154 

2.017502 

.029131  36 

37 

342.972 

344.895 

.160 

.041978 

.053607 

.354.713 

356.681 

.164 

.045316 

.057129  37 

38 

357.488 

359.533 

.170 

.069572 

.081385 

369.533 

371.619 

.174 

.073276 

.085290 

38 

39 

372.243 

374.404 

.180 

.097325 

.109339 

384.581 

386.776 

.183 

.101434 

.113669 

39 

40 

387.223 

389.494 

.189 

2.125294 

2.137529 

399.834 

402.127 

.191 

2.129850 

2.142332 

40 

41 

402.409 

404.777 

.197 

.153532 

.166014 

415.278 

417.662 

.199 

.158584 

.171332 

41 

42 

417.784 

420.243 

.205 

.182103 

.194851 

430.888 

433.348 

.205 

.187701 

.200749 

42 

43 

433.326 

435.860 

.211 

.211067 

.224115 

446.645 

449.177 

Ml 

.217272 

.230642 

43 

14.   TT  =  10.5480. 

15.   7r  =  10.7660. 

Continued  on  Page  *197. 


♦158 


TABLE    LXIII 


GENERAL  VALUATION  OF  ANNUAL  PREMIUM  POLICIES  OF  1,000. 

4  PER  CENT. 


n. 

X  =   16. 

17. 

.s  " 
n. 

V. 

6m. 

V. 

12in. 

^in.d. 

6m. 

12m. 

V. 

6m. 

V. 

12m. 

^mA. 

6m. 

AB. 

12m. 

0 

7.922 

4.849 

.256 

0.010072 

0.019916 

8.155 

5.073 

.257 

0.010079 

0.019930 

0 

1 

12.871 

9.898 

.248 

.321182 

.331033 

13.329 

10.349 

.248 

.321196 

.331054 

1 

2 

18.021 

15.148 

.239 

.507438 

.517296 

18.711 

15.837 

.239 

.507462 

.517327 

2 

3 

23.376 

20.609 

.231 

.642630 

.652495 

24.307 

21.540 

.231 

.642663 

.652538 

3 

4 

28.944 

26.285 

.222 

.749881 

.759756 

30.120 

27.465 

.221 

.749926 

.759811 

4 

5 

34.731 

32.181 

.213 

0.839494 

0.849379 

36.163 

33.624 

.212 

0.839552 

0.849448 

5 

6 

40.743 

38.310 

.203 

.916964 

.926860 

42.440 

40.020 

.202 

.917036 

.926943 

6 

7 

46.990 

44.675 

.193 

.985573 

.995480 

.   48.958 

46.660 

.192 

.985661 

.995581 

7 

8 

53.476 

51.282 

.183 

1.047437 

1.057357 

55.725 

53.554 

.181 

1.047544 

1.057477 

8 

9 

60.210 

58.143 

.172 

.104004 

.113937 

1  62.745 

60.701 

.170 

.104131 

.114081 

9 

10 

67.196 

65.255 

.162 

1.156306 

1.166256 

70.026 

68.114 

.159 

1.156456 

1.166423 

10 

11 

74.441 

72.632 

.151 

.205106 

.215073 

77.575 

75.800 

.148 

.205283 

.215268 

11 

12 

81.954 

80.281 

.139 

.250985 

.260970 

85.394 

83.752 

.137 

.251192 

.261200 

12 

13 

89.736 

88.195 

.128 

.294397 

.304405 

93.489 

91.991 

.125 

.294639 

.304668 

13 

14 

97.792 

96.394 

.117 

.335702 

.345731 

101.873 

100.519 

.113 

.335977 

.346032 

14 

15 

106.134 

104.880 

.105 

1.375185 

1.385240 

110.550 

109.344 

.101 

1.375502 

1.385583 

15 

16 

114.769 

113.663 

.092 

.413090 

.423171 

119.522 

118.464 

.088 

.413451 

.423563 

16 

17 

123.699 

122.739 

.080 

.449613 

.459725 

128.794 

127.888 

.075 

.450028!  .460173 

17 

18 

132.925 

132.117 

.067 

.484927 

.495072 

138.365 

137.607 

.063 

.4854001  .495584 

18 

19 

142.451 

141.789 

.055 

.519175 

.529359 

148.245 

147.646 

.050 

.519711 

.529934 

19 

20 

152.281 

151.779 

.042 

1.552479 

1.562702 

158.443 

158.004 

.037 

1.553083'l.563348 

20 

21 

162.431 

162.087 

.029 

.584944 

.595209 

168.957 

168.675 

.024 

.585625 

.595941 

21 

22 

172.894 

172.706 

.016 

.616668 

.626984 

179.786 

179.660 

.010 

.617439 

.627809: 22 

23 

183.669183.638 

.003 

.647741 

.658111 

190.928 

190.960 

.003 

.648610 

.659040  23 

24 

194.758 

194.883 

.010 

.678238 

.688668 

202.394 

202.593 

.017 

.679211 

.689702  24 

25 

206.169 

206.460 

.024 

1.708224 

1.718715 

214.178 

214.527 

.029 

1.709317 

1.719884  25 

26 

217.896  218.336 

.037 

.737768 

.748335 

226.277 

226.791 

.043 

.738994 

.749636  26 

27 

229.935 

230.540 

.050 

.766929 

.777571 

238. 696 

239.364 

.056 

.768299 

.779029  27 

28 

242.294 

243.052 

.063 

.795761 

.806491 

251.422 

252.245 

.069 

.797295 

.808120  28 

29 

254.959 

255.872 

.076 

.824322 

.835147 

264.458 

265.435 

.081 

.826034 

.836963  29 

30 

267.932 

268.997 

.089 

1.852659 

1.863588 

277.797 

278.922 

.094 

1.854571 

1.865615 

30, 

31 

281.206 

282.419 

.101 

.880825 

.891869 

291.429 

292.701 

.106 

.882958 

.894128 

31' 

32 

294.772 

296.131 

.113 

.908869 

.920039 

305.352 

306.766 

.118 

.911245 

.922553 

32 

33 

308.627 

310.127 

.125 

.936840 

.948148 

319.550 

321.098 

.129 

.939484 

.950945 

33 

34 

322.756 

324.390 

.136 

.964785 

.976246 

334.013 

335.693 

.140 

.967730 

.979359 

34 

35' 

337.149 

338.914 

.147 

1.992758 

2.004387 

348. 733 

350.536 

.150 

1.996032 

2.007845 

35 

36 

351.797 

353.685. 

.157; 

2.020809 

.032622 

363.694 

365.616 

.160 

2.024446 

.036460 

36 

37: 

366.686 

368.692 

.167 

.048988 

.061002 

378.885 

380.918 

.169 

.053025 

.065260 

37 

38 

381.804 

383.920 

.176 

.077349 

.089584 

394.285 

396.416 

.178 

.081832 

.094314 

38 

39 

397.128 

399.342 

.185 

.105954 

.118436 

409.875 

412.099 

.185 

.110930 

.123678 

39 

40 

412.644 

414.950 

.192 

2.134865 

2.147613 

425.636 

427.936 

.192 

2.140385 

2.153433 

40 

41 

428.327  430.709 

.198 

.164146 

.177194 

441.543 

443.915 

.198 

.170267 

.183637 

41 

42 

444. 158^46. 612 

.205 

.193867 

.207237 

457.584 

460.017 

.203 

.200646 

.214371 

42 

43 

460.121462.635 

.209 

.224097 

.237822 

473.731476.208 

.206 

.2316061  .245724 

43 

16.   TT  =  10.9953. 

17.   77  =  11.2364. 

Continued  on  Page  *196. 


♦159 


/ 


TABLE    LXIII 


GENERAL  VALUATION  OF  ANNUAL  PREMIUM  POLICIES  OP  1,000. 

4  PER  CENT. 


'•si 

o  o 

n. 
0 

18. 

19. 

s§ 

V. 

6m. 

V. 

13m. 

-Jm.d. 

A(B/). 
6m. 

AB. 

12m. 

V. 

6m. 

V. 

13m. 

\mA. 

A(B/). 
6m. 

AB. 

12m. 

II 
n. 

8.396 

5.303 

.358 

0.010087 

0.019945 

8.651 

5.545 

.259 

0.010096 

0.019961  0 

1 

13.806 

10.818 

.349 

.331213 

.331078 

14.304 

11.308 

.250 

.321231 

.331106'  1 

2 

19.439 

16.551 

.340 

.507488 

.517363 

30.180 

17.395 

.240 

.507516 

.517401  2 

3 

35.374 

33.506 

.331 

.643700 

.652585 

36.384 

33.518 

.331 

.642741 

.652637 

3 

4 

31.346 

38.696 

.331 

.749975 

.759871 

33.638 

39.981 

.221 

.750030 

.759937 

4 

5 

37.655 

35.135 

.311 

0.839615 

0.849522 

39.313 

36.690 

.210 

0.839685 

0.849605 

5 

6 

44.307 

41.798 

.301 

.917116 

.927036 

46.051 

43.656 

.300 

.917202 

.927135 

6 

7 

51.007 

48.737 

.190 

.985758 

.995691 

53.145 

50.878 

.189 

.985865 

.995815 

7 

8 

58.064 

55.911 

.179 

1.047661 

1.057611 

60.501 

58.368 

.178 

1.047789 

1.057756 

8 

9 

65.381 

63.361 

.168 

.104371 

.114238 

68.130 

66.135 

.166 

.104425 

.114410 

9 

10 

73.969 

71.087 

.157 

1.156633 

1.166607 

76.031 

74.171 

.155 

1.156805 

1.166813 

10 

11 

80.839 

79.080 

.146 

.205478 

.215486 

84.211 

82.496 

.143 

.205695 

.215734 

11 

12 

88.965  87.361 

.134 

.351422 

.3614511 

92.683 

91.113 

.131 

.251671 

.261726 

12 

13 

97.393  95.933 

.133 

.294902 

.3049571 

101.449 

100.030 

.118 

.295191 

.305272 

13 

14 

106.113104.803 

.109 

.336281 

.346363 

110.516 

109.245 

.106 

.336613 

.346725 

14 

15 

115.13o'll3.969 

.097 

1.375850 

1.385962 

119.884 

118.768 

.093 

1.376333 

1.386378 

15 

16 

134.450133.441 

.084 

.413851 

.4239961 

139.557 

128.589 

.081 

.414393 

.434476 

16 

17 

134.071sl33.310 

.073 

.450485 

.460669 

139.539 

138.733 

.067 

.450988 

.461211 

17 

18 

144.000:143.300 

.058 

.485920 

.496143 

149.844 

149.199 

.054 

.486489 

.496754 

18 

19 

154.350153.710 

.045 

.520298 

.530663 

160.468 

159.981 

.041 

.520942 

.531258 

19 

20 

164.817164.435 

.033 

1.553745 

1.564061 

171.409 

171.081 

.037 

1.554477 

1.564847 

20 

21 

175.701175.477 

.019 

.586377 

.596747 

183.668 

182.500 

.014 

.587205 

.597635 

21 

22 

186.901 

186.834 

.006 

.618288 

.628718 

194.355 

194.254 

.000 

.619219 

.629710 

22 

23 

198.435 

198.537 

.009 

.649563 

.660054 

306.163 

206.313 

.013 

.650611 

.661178 

23 

24 

310.370 

310.533 

.031 

.680282 

.690849 

318.387 

218.705 

.026 

.681462 

.692104 

24 

25 

333.430  333.848 

.035 

1.710520 

1.721162 

330.935 

231.409 

.040 

1.711842 

1.722572 

25 

26 

334.91l!335.485 

.048 

.740340 

.751070 

343. 795 

244.426 

.053 

.741823 

.752648, 26 

27 

347.704  348.433 

.061 

.769808 

.780633 

356.968 

257.754 

.065 

.771467 

.783396|27 

28 

360.806  361.690 

.074 

.798981 

.809910 

370.446 

371.383 

.078 

.800838 

.811883  28 

29 

374.313  375.345 

.086 

.827919 

.838963 

384.222 

385^05 

.090 

.829993 

.841163  29 

30 

387.915  389.094 

.098 

1.856675 

1.867845 

298.288 

399.516 

.102 

1.858989 

1.870397 

30 

31 

301.907  303.331 

.110 

.885303 

.896611 

312.636 

313.999 

.114 

.887884 

.899345 

31 

32 

316.179  317.636 

.131 

.913859 

.925320 

337.250 

338.746 

.125 

.916736 

.938365 

32 

33 

330.715i333.305 

.133 

.942396  .9540251 

342. 123 

343.744 

.135 

.945599 

.957413 

33 

34 

345.510 

347.334 

.143 

■ 

.9709691  .982782^ 

357.241 

358.983 

.145 

.974533 

.986547 

34 

35 

360.547 

363.381 

.153  1.999634'3.011648' 

372.591 

374.444 

.154 

2.003593 

3.015838 

35 

36 

375.816 

377.761 

.163  3.038445 

.040680! 

388.152 

390. 104 

.163 

.032847 

.045329 

36 

37 

391.395 

393.338 

.170:  .057468 

.069950 

403.906 

405.951 

.170 

.062359 

.075107 

37 

38 

406.964|409.101 

.178 

.086766 

.099514 

419.830 

431.953 

.177 

.092197 

.105245 

38 

39 

433.805 

435.018 

.184 

.116406 

.129454 

435.904 

438.100 

.1«3 

.122435 

.135805 

39 

40 

438.794 

441.080 

.191 

2.146461 

3.159831 

452.113 

454.370 

.188 

2.153143  2.166868 

40 

41 

454.916 

457.363 

.196 

.176999 

.190734 

468.428 

470.730 

.192 

.184407  .198525 

41 

42 

471.145 

473.537 

.199 

.208106 

.333334  484.831 

487.155 

.195 

.316320  .230869 

42 

43 

487.451 

489.874 

.302 

.239874 

.354433  501.270 

1 1 

503.639 

.197 

.248971  .263989 

43 

18.   77  =  11.4897. 

19.   TT  =  11.7560. 

Continued  on  Page  *195. 


'160 


TABLE     LXIII 


GENERAL  VALUATION  OF  ANNUAL  PREMIUM  POLICIES  OF  1,000. 

4  PER   CENT. 


&e 

a:=20. 

21. 

Is 

Ms 

V. 

V. 

|^m.d. 

A(B/). 

AB. 

V. 

V. 

1     ^ 

^(B/). 

AB. 

n. 
0 

6m. 

12m. 

6m. 

12m. 

6m. 

12m. 

^m.d. 

6m. 

12m. 

n. 
0 

8.915 

5.795 

.260 

0.010105 

0.019980 

9.193 

6.056 

.261 

0.010115 

0.020000 

1 

14.833 

11.816 

.251 

.321250 

.331135 

15.368 

12.350 

.252 

.321271 

.331167 

1 

2 

20.963 

18.073 

.241 

.507547 

.517443 

21.783 

18.887 

.241 

.507581 

.517488 

2 

3 

27.340 

24.572 

.231 

.642785 

.652692 

28.445 

25.672 

.231 

.642834 

.652754 

3 

4 

33.963 

31.318 

.220 

.750089 

.760009 

35.360 

32.718 

.220 

.750153 

.760086 

4 

5 

40.839 

38.323 

.210 

0.839761 

0.849694 

42.535 

40.023 

.209 

0.839844 

0.849794 

5 

6 

47.972 

45.586 

.199 

.917298 

.927248 

49.976 

47.599 

.198 

.917402 

.927369 

6 

7 

55.370 

53.118 

.188 

.985981 

.995948 

57.692 

55.454 

.186 

.986110 

.996095 

7 

8 

63.041 

60.928 

.176 

1.047932 

1.057917 

65.682 

63.581 

.175 

1.048088 

1.058096 

8 

9 

70.986 

69.008 

.165 

.104596 

.114604 

73.957 

72.002 

.163 

.104784 

.114813 

9i 

1 

10 

79.212 

77.380 

.153 

1.157008 

1.167037 

82.524 

80.717 

.151 

1.157229 

1.167284 

10 

11 

87.731 

86.045 

.141 

.205930 

.215985 

91.392 

89.737 

.138 

.206189 

.216270 

11 

12 

96.546 

95.012 

.128 

.251946 

.262027 

100.563 

99.058 

.125 

.252246 

.262358 

12 

13 

105.663 

104.278 

.115 

.295508 

.305620 

110.038 

108.689 

.112 

.295859 

.306004 

13 

14 

115.085 

113.855 

.102 

.336981 

.347126 

119.821 

118.622 

.100 

.337387 

.347571 

14 

15 

124.810 

123.730 

.090 

1.376658 

1.386842 

129.917 

128.882 

.086 

1.377124 

1.387347 

15 

16 

134.848 

133.930 

.077 

.414777 

.425000 

140.340 

139.468 

.073 

.415307 

.425572 

16 

17 

145.211 

144.455 

.063 

.451538 

.461803 

151.086 

150.374 

.059 

.452142 

.462458 

17 

18 

155.894 

155.297 

.050 

.487113 

.497429 

162.152 

161.601 

.046 

.487803 

.498173 

18 

19 

166.896 

166.459 

.036 

.521653 

.532023 

173.540 

173.149 

.033 

.522437 

.532867 

19 

20 

178.218 

177.941 

.023 

1.555284 

1.565714 

185.259 

185.039 

.018 

1.556169 

1.566660 

20 

21 

189.869 

189.761 

.009 

.588113 

.598604 

197.303 

197.236 

.006 

.589113 

.599680 

21 

22 

201.842 

201.888 

.004 

.620244 

.630811 

209.667 

209.769 

.009 

.621372 

.632014 

22 

23 

214.136 

214.348 

.018 

.651766 

.662408 

222.359 

222.619 

.022 

.653034 

.663764 

23 

24 

226.754 

227.124 

.031 

.682757 

.693487 

235.372 

235.794 

.035 

.684184 

.695009 

24 

25 

239.687 

240.213 

.044 

1.713298 

1.724123 

248. 694 

249.264 

.047 

1.714898 

1.725827 

25 

26 

252.932 

253.615 

.057 

.743453 

.754382 

262.321 

263.048 

.061 

.745248 

.756292 

26 

27 

266.485 

267.319 

.070 

.773293 

.784337 

276.254 

277.130 

.073 

.775303 

.786473 

27 

28 

280.337 

281.319 

.082 

.802880 

.814050 

290.482 

291.505 

.085 

.805126 

.816434 

28 

29 

294.482 

295.610 

.094 

.832273 

.843581 

304. 994 

306.152 

.097 

.834784 

.846245 

29 

30 

308.910 

310.173 

.105 

1.861535 

1.872996 

319.775 

321.068 

.108 

1.864338 

1.875967 

30 

31 

323.606 

325.003 

.116 

.890725 

.902354 

334. 818 

336.239 

.118 

.893850 

.905663 

31 

32 

338.562 

340.085 

.127 

.919901 

.931714 

350.110 

351.651 

.128 

.923383 

.935397 

32 

33 

353.764 

355.408 

.137 

.949123 

.961137 

365.635 

367.289 

.138 

.952997 

.965232 

33 

34 

369.200 

370.956 

.146 

.978450 

.990685 

381.374 

383.128 

.146 

.982763 

.995245 

34 

35 

384.848 

386.703 

.155 

2.007951 

2.020433 

397.307 

399.157 

.154 

2.012748 

2.025496 

35 

36 

400.689 

402.639 

.162 

.037692 

.050440 

413.415 

415.342 

.161 

.043024 

.056072 

36 

37 

416.702 

418.730 

.169 

.067741 

.080789 

429.672 

431.673 

.167 

.073668 

.087038 

37 

38 

432.867 

434.967 

.175 

.098175 

.111545 

446.067 

448.130 

.172 

.104750 

.118475 

38 

39 

449.165 

451.328 

.180 

.129065 

.142790 

462.568 

464.677 

.176 

.136361 

.150479 

39 

40 

465.572 

467.779 

.184 

2.160496 

2.174614 

479.148 

481.289 

.178 

2.168593 

2.183142 

40 

41 

482.055 

484.295 

.187 

.192564 

.207113 

495.786 

497.952 

.180 

.201539 

.216557 

41 

42 

498.596 

500.861 

.189 

.225357 

.240375 

512.452 

514.623 

.181 

.235303 

.250842 

42: 

43 

515.166 

517.'436 

.189 

.258982 

.274521 

529.117 

531.281 

.180 

.270003 

.286112 

43 

20.   n  =  12.0361. 

21.   77  =  12.3304. 

Continued  on  Page  *194. 


TABLE    LXIII. 


*161 


GENERAL  VALUATION  OF  ANNUAL  PREMIUM  POLICIES  OF  1,000. 

4  PER  CENT. 


&l 

22. 

23. 

si 

Pk(M 

V. 

V. 

-i.m.d. 

^(B/). 

AB. 

V. 

V. 

im.d 

^(B/). 

AB. 

|{S 

n. 
0 

6m. 

12m. 

^ 

6m. 

12m. 

6m. 

12m. 

g-m.u.. 

6m. 

12m. 

0 

9.487 

6.333 

.263 

0.010126 

0.020022 

9.792 

6.619 

.264 

0.010138 

0.020045 

1 

15.941 

12.909 

.253 

.321294 

.331201 

16.537 

13.489 

.254 

.321320 

.331240 

1 

2 

22.642 

19.736 

.242 

.507619 

.517539 

23.539 

20.623 

.243 

.507659 

.517592 

2 

3 

29.601 

26.825 

.231 

.642886 

.652819 

30.804 

28.018 

.232 

.642946 

.652896 

3 

4 

36.819 

34.174 

.220 

.750225 

760175 

38.336 

35.689 

.221 

.750303 

.760270 

4 

5 

44.305 

41.796 

.209 

0.839936 

0.849903 

46.149 

43.643 

.209 

0.840037 

0.850022 

5 

6 

52.068 

49.699 

.197 

.917517 

.927502 

54.241 

51.872 

.197 

.917645 

.927653 

6 

7 

60.107 

57.876 

.186 

.986253 

.996261 

62.618 

60.398 

.185 

.986411 

.996440 

7 

8 

68.432 

66.348 

.174 

1.048262 

1.058291 

71.293 

69.222 

.17311.048451 

1.058506 

8 

9 

77.053 

75.117 

.161 

.104989 

.115044 

80.271 

78.354 

.160 

.105215 

.115296 

9 

10 

85.974 

84.191 

.149 

1.157471 

1.167552 

89.556 

87.792 

.147 

1.157737^1.167849 

10 

11 

95.199 

93.568 

.136 

.206473 

.216585 

99.151 

97.544 

.134 

.206786 

.216931 

11 

12 

104.734 

103.259 

.123 

.252579 

.262724 

109.055 

107.601 

.121 

.252947 

.263131 

12 

13 

114.575 

113.252 

.110 

.296246 

.306430 

119.278 

117.989 

.107 

.296672 

.306895 

13 

14 

124.733 

123.574 

.097 

.337834 

.348057 

129.831 

128.707 

.094 

.338322 

.348587 

14 

15 

135.220 

134.225 

.083 

1.377634 

1.387899 

140.711 

139.749 

.080 

1.378193 

1.388509 

15 

16 

146.031 

145.197 

.070 

.415889 

.426205 

151.916 

151.117 

.067 

.416533 

.426903'  16 

17 

157.164 

156.492 

.056 

.452809 

.463179 

163.447 

162.810 

.053 

.453544 

.4639741  17 

18 

168.622 

168.112 

.042 

.488563 

.498993 

175.312 

174.848 

.039 

.489397 

.499888 

18 

19 

180.413 

180.073 

.028 

.523297 

.533788 

187.505 

187.197 

.026 

.524243 

.534810 

19 

20 

192.529 

192.345 

.015 

1.557142 

1.567709 

200.026 

199.888 

.012 

1.558215 

1.568857 

20 

21 

204.969 

204.954 

.001 

.590214 

.600856 

212.876 

212.898 

.002 

.591423 

.602153 

21 

22 

217.738 

217.882 

.012 

.622611 

.633341 

226.046 

226.228 

.015 

.6239771  .634802 

22 

23 

230.825 

231.128 

.025 

.654431 

.665256 

239.535 

239.877 

.028 

.6559661  .666895 

23 

24 

244.229 

244.690 

.038 

.685753 

.696682 

253.338 

253.833 

.041 

.687479;  .698523 

24 

25 

257.944 

258.558 

.051 

1.716659 

1.727703 

267.445 

268.091 

.054 

1.718697 

1.729767 

25 

26 

271.962  272.726 

.064 

.747223 

.758393 

281.851 

282.645 

.066 

.749394 

.760702 

26 

27 

286.277 

287.188 

.076 

.777512 

.788820 

296.544 

297.476 

.078 

.779944 

.791405 

27 

28 

.300.877 

301.925 

.087 

.807598 

.819059 

311.510 

312.579 

.089 

.810319 

.821948 

28 

29 

315.748 

316.932 

.099 

.837546 

.849175 

326.742 

327.938 

.100 

.840586 

.852399 

29 

30 

330.883 

332.194 

.109 

1.867421 

1.879234 

342.223 

343.543 

.110 

1.870813 

1.882827 

30 

31 

346.268 

347.701 

.119 

.897288 

.909302 

357.944 

359.378 

.120 

.901068 

.913303 

31 

32 

361.888 

363.435 

.129 

.927211 

.939446 

373.879 

375.414 

.128 

.931424 

.943906 

32 

33 

377.722 

379.370 

.137 

.957261 

.969743 

390.012 

391.644 

.136 

.961956 

.974704 

33 

34 

393.753 

395.496 

.145 

.987510 

2.000258 

406.320 

408.031 

.143 

.99273512.005783 

34 

35 

409.958 

411.780 

.152 

2.018029 

2.031077 

422. 782 

424.567 

.149 

2.023842 

2.037212 

35 

36 

426.316 

428.211 

.158 

.048896 

.062266 

439.381 

441.229 

..154 

.055353 

.069078 

36 

37 

442.809 

444. 767 

.163 

.080185 

.093910 

456.089 

457.983 

.158 

.087359 

.101477 

37 

38 

459.411 

461.415 

.167 

.111987 

.126105 

472.876 

474.803 

.161 

.119955 

.134504 

38 

39 

476.092 

478.129 

.170 

.144395 

.158944 

489.722 

491.674 

.163 

.153236 

.168254 

39 

40 

492.831 

494.893 

.172 

2.177503 

2.192521 

506.597 

508.  .554 

.163 

2.187309 

2.202848 

40 

41 

509.599 

511.666 

.172 

.211417 

.226956 

523.469 

525.419 

.162 

.222292 

.238401 

41 

42 

526.366 

528.425 

.172 

.246253 

.262362 

540.309 

542.232 

.160 

.258311 

.275049 

42 

43 

543.098 

545.131 

.169 

.282139 

.298877 

557.069 

558.941 

.156 

.295499 

.312921 

43 

22.    TT  =  12.6399 

23.    7r  =  12.9656 

Continued  on  Page  *193. 


*163 


TABLE    LXIII, 


GENERAL  VALUATION  OF  ANNUAL  PREMIUM  POLICIES  OF  1,000. 

4  PER  CENT. 


s 

n. 

x  =  24. 

25. 

n. 
0 

V. 

6m. 

V. 

12m. 

|m.d 

A(B/). 
6m. 

AB. 

12m. 

V. 

6m. 

V. 

12m. 

|m.d. 

6m. 

AB. 

12m. 

1  0 

10.112 

6,916 

.366 

0.010153 

0.020073 

10.450 

7.231 

.368 

0.010167 

0.020100 

1 

17.161 

14.097 

.255 

.331348 

.331381 

17.814 

14.738 

.357 

.321380 

.331330 

1 

2 

24.473 

21.542 

.244 

.507704 

.517654 

25.450 

22.504!  .246 

.507754 

.517721 

2 

3 

32.057 

29.264 

.233 

.643009 

.652976 

33.370 

30.567 

.334 

.643080 

.653065 

3 

4 

39.922 

37.271 

.221 

.750390 

.760375 

41.572 

38.908 

.222 

.750486 

.760494 

4 

5 

48.067 

45.555 

.209 

0.840150 

0.850158 

50.064 

47.550 

.209 

0.840275 

0.850304 

5 

6 

56.500 

54.137 

.197 

.917787 

.927816 

58.857 

56.495 

.197 

.917941 

.927996 

6 

7 

65.233 

63.021 

.184 

.986583 

.996638 

67.958 

65.752 

.184 

.986772 

.996853 

7 

8 

74.271 

72.214 

.171 

1.04865911.058740 

77.370 

75.319 

.171 

1.048886 

1.058998 

8 

9 

83.618 

81.714 

.159 

.105462 

.115574 

87.096 

85.205 

.158 

.105735 

.115880 

9 

10 

93.277 

91.531 

.146 

1.158031 

1.168176 

97.137 

95.399 

.145 

1.158357 

1.168541 

10 

11 

103.247 

101.655 

.133 

.207134 

.217318 

107.498 

105.929 

.131 

.207515 

.217738 

11 

12 

113.537 

112.112 

.119 

.253351 

.263574 

118.1961116. 794 

.117 

.353793 

.264058 

12 

13 

124.161 

133.903 

.105 

.297138 

.307403 

129.225 

127.987 

.103 

.397648 

.307964 

13 

14 

135.114 

134.018 

.091 

.338857 

.349173 

140.583 

139.510 

.089 

.339450 

.349820 

14 

15 

146.394 

145.461 

.078 

1.378811 

1.389181 

152.271 

151.363 

.076 

1.379493 

1.389923 

15 

16 

158.000 

157.333 

.064 

.417242 

.427672 

164.299 

163.565!  .061 

.418019 

.438510 

16 

17 

169.945169.350 

.050 

.454350 

.464841 

176.659 

176.084!  .048 

.455238 

.465805 

17 

18 

182.220181.783 

.036 

.490314 

.500881 

189.350 

188.947 

.034 

.491325 

.501967 

18 

19 

194.824 

194.557 

.022 

.535385 

.535927 

302.376 

202.136 

.020 

.536430 

.537160 

19 

20 

207.759 

307.654 

.009 

1.559392 

1.570133 

215.726 

215.648 

.007 

1.560689 

1.571514 

20 

21 

221.018  321.073 

.005 

.593756 

.603581 

339.400 

229.483 

.007 

.594319 

.605148 

21 

22 

334.596  234.812 

.018 

.635477 

.636406 

343.391 

243.630 

.030 

.627139 

.638173 

22 

23 

348.4911248.861 

.031 

.657656 

.668700 

357.691 

258.083 

.033 

.659516 

.670686 

23 

24 

363.693 

363.315 

.044 

.689379 

.700549 

372.295 

272.837 

.045 

.691469 

.703777 

24 

25 

377.194 

377.866 

.056 

1.730729 

1.733037 

287.188 

287.870 

.057 

1.733075 

1.734536 

25 

26 

291.985 

392.795 

.068 

.751784 

.763245 

302.359 

303.179 

.068 

.754415 

.766044 

26 

27 

307.051307.999 

.079 

.783631 

.794350 

317.798 

318.749 

.079 

.785567 

.797380 

27 

28 

333.384  323.461 

.090 

.813313 

.835126 

333.493 

334.567 

.089 

.816606 

.838630 

28 

29 

337.969  339.170 

.100 

.843930 

.855944 

349.427 

350.618 

.099 

.847607 

.859842 

29 

30 

353.794  355.109 

.110 

1.874543 

1.886778 

365.580 

366.874 

.108 

1.878649 

1.891131 

30 

31 

369.835:371.253 

.118 

.905339 

.917711 

381.934 

383.325 

.116 

.909810 

.922558 

31 

32 

386.076,387.591 

.136 

.936064 

.948812 

398.466 

399.937 

.133 

.941170 

.954318 

32 

33 

403.4931404.087 

.133 

.967123 

.980171 

415.152 

416.699 

.129 

.973813 

.986183 

33 

34 

419.064420.733 

.139 

.998488 

3.011858 

431.979 

433.589 

.134 

3.004816 

3.018541 

34 

35 

435.773  437.506 

.144 

3.030237 

3.043962 

448.915 

450.573 

.138 

3.037274 

2.051392 

35! 

36 

452.593  454.372 

.148 

-.062461 

.076579 

465.931 

467.633 

.141 

.070288 

.084837 

36 

37 

469.492  471.304 

.151 

.095258 

.1098071 

483.008 

484.734 

.143 

.103951 

.118969 

37 

38 

486.450  488.287 

.153 

.128724 

.1437421 

500.113 

501.834 

.143 

.1383761 

.153915 

38 

39 

503.437  505.279 

.153 

.162967 

.178506 

517.317 

518.930 

.143 

.173681 

.189790 

39 

40 

520.422  532.357 

.153 

2.198106 

3.214315 

534.286 

535.973 

.141 

2.209996 

3.336734 

40 

41 

537.373539.183 

.151 

.234268 

.251006 

551.376 

553.910 

.136 

.247454 

.364876 

41 

42 

554.3461556.003 

.146 

.271587 

.289009! 

568.188 

569.797 

.134 

.286206 

.304387 

42 

43 

571.042|572.773 

.144 

.310212 

.328393' 

584.997 

586.538 

.138 

.326408 

.345409 

43 

24.   TT  =  13.3082. 

26.   -n  =  13.6687. 

Continued  on  Page  *192. 


^   ♦lea 


TABLE    LXIII. 


GENERAL  VALUATION  OP  ANNUAL  PREMIUM  POLICIES  OF  1,000. 

4  PER  CENT. 


■u 

26. 

27. 

Is 

V. 

V. 

|-m.d. 

A(B/). 

AB. 

V. 

V. 

^m.d. 

A(B/-). 

AB. 

n. 
0 

6in. 

12m. 

6m. 

12m. 

6m. 

12m. 

6m. 

12m. 

n. 

10.800 

7.551 

.271 

0.010184 

0.020134 

11.170 

7.892 

.273 

0.010199 

0.020166 

0 

1 

18.492 

15.384 

.259 

.321413 

.331380 

19.208 

16.075 

.261 

.321450 

.331435'  1 

2 

26.469 

23.505 

.247 

.507809 

.517794 

i  27.532 

24.541 

.249 

.507870 

.517878'  2 

3 

34.731 

31.907 

.235 

.643160 

.653168 

36.151 

33.313 

.237 

.643247 

.653276 

3 

4 

43.284 

40.613 

.223 

.750593 

.760622 

1  45.076 

42.391 

.224 

.750708 

.760763 

4 

5 

53.143 

49.623 

.210 

0.840410 

0.850465 

:  54.313 

51.787 

.210 

0.840558 

0.850639 

5 

6 

61.309 

58.947 

.197 

.918111 

.928192 

63.865 

61.496 

.197 

.918295 

.928407 

6| 

7 

70.790 

68.583 

.184 

.986978 

.997090 

73.737 

71.530 

.184 

.987207 

.997352 

7 

8 

80.586 

78.541 

.170 

1.049138 

1.059283 

1  83.928 

81.877 

.171 

1.049416 

1.059600 

8 

9 

90.700 

88.810 

.158 

.106038 

.116222 

94.444 

92.564 

.157 

.106371 

.116594 

9 

10 

101.138 

99.416 

.143 

1.158714 

1.168937 

105.302 

103.591 

.143 

1.159104 

1.169369Jl0 

11 

111.913 

110.361 

.129 

.207932 

.218197 

116.495 

114.952 

.129 

.208388 

.218704J 11 

12 

123.022 

121.635 

.116 

.254277 

.264593 

128.024 

126.647 

.115 

.254813 

.265183  12 

13 

134.463 

133.242 

.102 

.298213 

.308583 

139.886 

138.677 

.101 

.298835 

.309265  13 

14 

146.236 

145.181 

.088* 

.340102 

.350532 

|152.093 

151.062 

.086 

.340818 

.351309  14 

15 

158.352 

157.473 

.073 

1.380240 

1.390731 

'l64.639 

163.768 

.073 

1.381062 

1.391629  15 

16 

170.802 

170.082 

.060 

.418875 

.429442 

177.520 

176.823 

.058 

.419817 

.430459  16 

17 

183.585 

183.040 

.045 

.456215 

.466857 

190.740 

190.209 

.044 

.457288 

.468018  17 

18 

196.707 

196.324 

.032 

.492434 

.503164 

204.290 

203.923 

.031 

.493657 

.504482  18 

19 

210.154 

209.935 

.018 

.527690 

.538515 

|218.168 

217.965 

.017 

.529076 

.540005  19 

20 

223.927 

223.871 

.005 

1.562115 

1.573044 

1232.368 

232.324 

.004 

1.563685 

1.574729  20 

21 

238.021 

238.121 

.008 

.595831 

.606875 

i246.883 

246.993 

.009 

.597605 

.608775 

21 

22 

252.424 

252.679 

.021 

.628947 

.640117 

i261.704 

261.967 

.022 

.630946 

.642254 

22 

23 

267.134 

267.540 

.034 

.661562 

.672870 

276.820 

277.225 

.034 

.663813 

.675274 

23 

24 

282.136 

282.683 

.046 

.693769 

.705230 

292.218 

292.763 

.045 

.696300 

.707929 

24 

25 

297.418 

298.104 

.057 

1.725657 

1.737286 

307.888 

308.566 

.057 

1.728499 

1.740312 

25 

26 

312.970 

313.787 

.068 

.757310 

.769123 

323.817 

324.620 

.067 

.760494 

.772508: 26 

27 

328.778 

329.720 

.079 

.788807 

.800821 

339.990 

340.911 

.077 

.792370 

.804605  27 

28 

344.829 

345.888 

.088 

.820227 

.832462 

356.384 

357.410 

.085 

.824213 

.836695  28 

29 

361.099 

362.262 

.097 

.851654 

.864136 

372.983 

374.107 

.094 

.856110 

.868858 

29 

30 

377.573 

378.834 

.105 

1.883169 

1.895917 

389.761 

390.967 

.100 

1.888145 

1.901193 

30 

31 

394.224 

395.566 

.112 

.914853 

.927901 

406.697 

407.979 

.107 

.920406 

.933776 

31 

32 

411.033 

412.450 

^.118 

.946793 

.960163 

423.774 

425.122 

.112 

.952978 

.966703 

32 

33 

427.981 

429.463 

.123 

.979071 

.992796 

440.965 

442.359 

.116 

.985959 

2.000077 

33 

34 

445.041 

446.570 

.127 

2.011781 

2.025899 

458.235 

459.664 

.119 

2.019452 

.034001 

34 

35 

462.181 

463.744 

.130 

2.045025 

2.059574 

475.567 

477.021 

.121 

2.053555 

2.068573 

35 

36 

479.382 

480.970 

.132 

.078901 

.093919 

492.928 

494.387 

.122 

.088383 

.103922 

36  i 

37 

496.612 

498.205 

.133 

.113520 

.129059 

510.287 

511.739 

.121 

.124057 

.140166 

37 

38 

513.840 

515.426 

.132 

.149004 

.165113 

527.612 

529.037 

.119 

.160709 

.177447 

38 

39 

531.034 

532.593 

.130 

.185481 

.202219 

544.856 

546.227 

.114 

.198475 

.215897 

39 

40 

548.147 

549.653 

.126 

2.223088 

2.240510 

562.020 

563.366 

.112 

2.237507 

2.255688 

401 

41 

565.183 

566.664 

.123 

.261976 

.280157 

579.081 

580.347 

.106 

.277963 

.296964  41 

42 

582.115 

583.516 

.117 

.302300 

.321301 

595.966 

597.137 

.098 

.320028 

.339946  42 

43 

598.872 

600.180 

.109 

.344246 

.364164 

612.658 

613.731 

.089 

.363895 

.384806 

43 

26.   77  =  14.0485. 

27.   TT  =  14.4479. 

Continued  on  Page  *1W 


nu 


TABLE      LXIII, 


GENEKAL  VALUATION  OF  ANNUAL  PREMIUM  POLiaES  OF  1,000. 

4  PER   CENT. 


li 

n. 
0 

a;  =  28. 

29. 

■si 

n. 

V. 

6m. 

V. 

12m. 

|m.d. 

MB/). 

6m. 

AB. 
12m. 

V. 

6m. 

V. 

12m. 

im.d. 

MB/). 

6m. 

AB. 
12m. 

11.559 

8.248 

.276 

0.010220 

0.020205 

11.958 

8.604 

.279 

0.010244 

0.020252 

0 

1 

19.949 

16.782 

.264 

.3214941  .331502 

20.718 

17.519 

.267 

.321541 

.331570 

1 

2 

28.637 

25.623 

.251 

. 507938;  .517967 

29.788 

26.746 

.254 

.508011 

.518066 

2 

3 

37.633 

34.774 

.238 

.643342 

.653397 

39.177 

36.295 

.240 

.643446 

.653527 

3 

4 

46.944 

44.244 

.225. 

.750835 

.760916 

48.885 

46.163 

.227 

.750973 

.761085 

4 

5 

56.572 

54.031 

.212 

0.840720 

0.850832 

58.918 

56.361 

.213 

0.840900 

0.851045 

5 

6 

66.522 

64.144 

.198 

.918500 

.928645 

69.275 

66.877 

.200 

.918728 

.928912 

6 

7 

76.793 

74.573 

.185 

.987462 

.997646 

79.964 

77.739 

.185 

.987740 

.997963 

7 

8 

87.394 

85.346 

.171 

1.049723 

1.059946 

90.998 

88.946 

.171 

1.050056 

1.060321 

8 

9 

98.338 

96.461 

.156 

.106733 

.116998 

102.375 

100.492 

.157 

.107131 

.117447 

9 

10 

109.620 

107.911 

.142 

1.159532 

1.169848 

114.091 

112.378 

.143 

1.160006 

1.170376 

10 

11 

121.240 

119.699 

.128 

.208894 

..219264 

126.148 

124.605 

.129 

.209451;  .219881 

11 

12 

133.197 

131.826 

.114 

.255403 

.265833 

138.554 

137.192 

.113 

.256051 

.266542 

12 

13 

145.502 

144.309 

.099 

.299517 

.310008 

151.305 

150.106 

.100 

.300268 

.310835 

13 

14 

158.147 

157.116 

.086 

.341605 

.352172 

164.397 

163.375 

.085 

.342472 

.353114 

14 

15 

171.130 

170.275 

.071 

1.381968 

1.392610 

177.833 

176.979 

.071 

1.382962 

1.393692 

15 

16 

184.455 

183.767 

.057 

.420851 

.431581 

191.604 

190.917 

.057 

.421991 

.432816 

16 

17 

198.114 

197.591 

.044 

.458471;  .469296 

205.709 

205.189 

.043 

.459769 

.470698 

17 

18 

212.N102 

211.744 

.030 

.495000 

.505929 

220.141 

219.782 

.030 

.496479 

.507523;  18 

19 

226;  415 

226.217 

.017 

.530601 

.541645 

:234.893 

234.691 

.017 

.532280 

.543450119 

20 

241.044 

241.003 

.003 

1.565412 

1.576582 

249.956  249.909 

.004 

1.567312 

1.578620 

20 

21 

255.984 

256.096 

.009 

.599556 

.610864 

265.319  265.417 

.008 

.601703 

.613164 

21 

22 

271.221 

271.476 

.021 

.633147 

.644608 

280.969  281.209 

.020 

.635569 

.647198 

22 

23 

286.741 

287.137 

.033 

.666291 

.677920 

:296.895i297.269 

.031 

.669018 

.680831 

23 

24 

1 

302.535 

303.065 

.044 

.699086 

.710899 

313.084  313.586 

.042 

.702150 

.714164 

24 

25 

318.591 

319.248 

.055 

1.731624 

1.743638 

329.520  330.143 

.052 

1.735062 

1.747297 

25 

26 

334.893 

335.668 

.065 

.763995 

.776230 

1346.184  346.912 

.061 

.767850 

.780332 

26 

27 

351.417 

352.298 

.073 

.796292 

.808774 

363.053;363.882 

.069 

.800610 

.813358 

27 

28 

368.148 

369.128 

.082 

.828602 

.841350 

380.105  381.017 

.076 

.833434 

.846482 

28 

29 

385.059 

386.122 

.089 

.861016 

.874064 

397.318 

398.307 

.082 

.866418 

.879788 

29 

30 

402.131 

403.270 

.095 

1.893624 

1.906994 

414.674 

415.729 

.088 

1.899651 

1.913376 

30 

31 

419.344 

420.549 

.100 

.926514 

.940239 

432.145 

433.248 

.092 

.933238 

.947356 

31 

32 

436.670 

437.923 

.104 

.959786 

.973904 

449.698 

450.836 

.095 

.967285 

.981834 

32 

33 

454.079 

455.366 

.107 

.993546 

2.008095 

467.312 

468.477 

.097 

2.001896 

2.016914 

33 

34 

471.548 

472.861 

.109 

2.027894 

.042912| 

484.958 

486.127 

.097 

.037188 

.052727 

34 

35 

489.048 

490.365 

.110 

2.062946 

2.078485; 

502.601 

503.762 

.097 

2.073287 

2.089396 

35 

36 

506.544 

507.855 

.109 

.098824 

.114933 

520.208 

521.342 

.095 

.110325 

.127063 

36 

37 

524.007 

525.290 

.107 

.135663 

.152401; 

537.733 

538.813 

.090 

.148443 

.165865 

37 

38 

541.388 

542.617 

.102 

.173599 

.191021 

555.179 

556.233 

.088 

.187797 

.205978 

38 

39 

558.690 

559.893 

.100 

.212786 

.230967 

572.518 

573.491 

.081 

.228543 

.247544 

39 

40 

575.885 

577.009 

.094 

2.253382 

2.272383 

589.679 

590.555 

.073 

2.270870 

2.290788 

40 

41 

592.906 

593.933 

.086 

.295074 

.315492 

606.644 

607.420 

.065 

.314975 

.335886 

41 

42 

609.730 

610.658 

.077 

.339556 

.360467 

623.386  624.041 

.055 

.361067 

.383074 

42 

43 

626.334 

627.142 

.067 

.385539 

.407546 

639.875  640.396 

.043 

.409383 

.432587 

43 

28.   n  =  14.8689. 

29.   TT  =  15.3125. 

Continued  on  Page  *190, 


*165 


TABLE     LXIII. 


GENERAL  VALUATION  OP  ANNUAL  PREMIUM  POLICIES   OF  1,000. 

4  PER  CENT. 


n. 


30. 


V. 

6in. 


Y. 

12m. 


0 
1 
2 
3 

4 

5 
6 

7 
8 
9 

10 
11 
12 
13 

14  170.865 


15 
16 
17 
18 
19 

20 
21 
22 
23 
24 

25 
26 
27 

28 
29 

30 
31 
32 
33 
34 

35 
36 
37 
38 
39 

40 
41 

42 
43 


12.386 
21.535 
31.005 
40.798 
5J3.917 

61.364 
72.146 
83.276 
94.751 
106.569 

118.730 
131.245 
144.106 
157.311 


8.992 
18.300 
27.931 

37.885 
48.171 

58.778 
69.734 
81.039 
92.685 
104.674 

117.007 
129.704 
142.729 
156.114 
169.836 

183.895 
198.291 
213.010 
228.048 
243.399 

259.041 
274.970 
291.170 
307.629 
324.329 

340.676  341.243 
357.691358.361 
374.892  375.644 
392.254  393.085 
409.761410.658 


^m.d 


184. 755 
198.982 
213.540 
228.419 
243.613 

259.109 
274.895 
290.960 
307.289 
323.868 


427. 
445. 
462. 
480. 
498. 

516. 
533. 
551. 

568. 
586. 


383  428.329 
089  446.070 
857463.864 
655  481.667 
450!499.455 

211517.188 
889  534.810 
485J552.382 
975,569.789 
285587.002 


603.397|604.013 
620.285'620.778 
636.916,637.275 
653.269  653.483 


.283 
.270 
.256 
.243 
.229 


6ni. 


AB. 

12m. 


0.010266  0.020295 
.321589  .331644 
.508090  .5181711 
.643557  .6536691 
.751126    .761271 


.216  0.841100 
,201  .918977 
,186  .988043 
,172 1 1.050422 
,158    .107571 


.144 
.128 
.115 
.100 
.086 

.072 
.058 
.044 
.031 
.018 

.006 
.006 
.017 
.028 
.038 

.047 
.056 
.063 
.069 
.075 

.079 
.082 
.084 
.084 
.084 

.081 
.077 
.075 
.068 
.060 

.051 
.041 
.030 
.018 


1.160528 
.210061 
.256763 
.301095 
.343424 


0.851284 
.929200 
.998308 

1.060738 
.117941 

1.170958 
.220552 
.267330 
.311737 
.354154 


1.384058  1, 
.423244  , 
.461199  , 
.498107  , 
.534126  . 

1.5694031. 
.604066  . 
.638235  . 

.672018  . 
.705520  . 


1.738846 
.772095 
.805364 

.838755 
.872360 


394883 
434173 
472243 
509277 
545434 

580864 
615695 
650048 
684032 

717755 


1.751328 

.784843 
.818412 
.852125 
.886085 


1.9062861.920404 
.940644  .955193 
.975538  .990556 


2.011089 
.047424 

2.084677 
.122991 
.162522 
.203430 
.245902 

2.290138 
.336347 
.384768 
.435645 


2.026628 
.063533 

2.101415 
.140413 
.180703 
.222431 
.265820 

2.3110491 
.358354 

.407972! 
.460158' 


31. 


V. 
6m. 


12.832 
22.387 
32.268 
42.480 
53.022 

63.901 
75.132 
86.712 
98.637 
110.908 

123.536 
136.514 
149.839 
163.515 
177.532 

191.888 
206.578 
221.592 
236.924 
252.561 

268.490 
284. 700 
301.178 
317.907 
334.868 

352.037 
369.394 
386.914 
404. 580 
422.362 

440. 228 
458.157 
476.116 
494.074 
511.995 

529.834 
547.590 
565.238 
582.706 
599.972 


V. 

12m. 


9.392 
19.111 
29.155 
39.534 
50.238 

61.293 
72.701 
84.452 
96.550 
108.995 

121.807 
134.950 
148.456 
162.303 
176.490 

191.016 
205.869 
221.044 
236.533 
252.318 

268.391 
284.738 
301.346 
318.198 
335.266 

352.538 
369.979 
387.578 
405.311 
423.142 

441.043 

458.999 
476.963 
494.913 
512.807 

530.589 
548.320 
565.886 
583.254 
600.420 


4m.d. 


30. 


71  =  15.7791. 


617.014  617.337 
633.796|633.984 
650.297  650.338 
666.477  666.345 


6m. 


.287  0.010293 
.273  .321644 
.259  .508176 
.246  .643685 
.2321  .751298 

.21710.841319 
.2031  .919249 
.188'  .988376 


,174 
.159 


1.050828 
.108057 


.144  1.161100 
,130    .210734 


.115 
.101 

.087 

.073 
.059 
.046 
.033 
.020 

.008 
.003 
.014 
.024 
.033 

.042 
.049 
.055 
.061 
.065 

.068 
.070 
.071 
.070 
.068 

.063 
.061 
.054 
.046 
.037 

.027 
.016 
.003 
.011 


.257548 
.302002 
.344474 

1.385262 
.424624 
.462774 
.499897 
.536159 

1.571705 
.606667 
.641167 
.675317 
.709230 

1.743013 

.776768 

.810600 

.844609 

,  .878902 

1.913595 

.948795 

.984625 

2.021214 

.058699 

2.097223 
.136945 
.178025 
.220653 
.265029 


AB. 
12m. 


Wei 
'  O  «  , 


0.020348  0 

.331725  1', 

.518288;  2 1 

.6538301  31 

.761482  4i 

0.851542 

.929514 

.998692 
1.061198 

.118487 

1.171591  lOi 
.221301  11 


.268190 
.312732 
.355299 


12i 

13 

14 


15 
16 


1.396191 
.435668 
.473944' 17  j 
.511205!  18 

.547620119 

1.583334  20 

.618480^21 
.653181  22 
.687552123 
.721712  24 


1.755761 
.789816 
.823970 
.858334 
.893020 

1.928144 
.963813 

2.000164 
037323 
075437 

2.114645 
.155126 
.197026 
.240571 
.285940 


25 
26 
27 
28 
29 

30 
31 
32 
33 
34 

35 
36 
37 
38 
39 


■>.311364  2.338371  40 
.3598971  .3831011 41 
.4108741  .435387  42 
.4645941  .490558,43 


31. 


7T  =  16.2712. 


Continued  on  Page  *189. 


•=166 


TABLE    LXIIl. 


GENERAL  VALUATION  OF  ANNUAL  PREMIUM  POLICIES  OF  1,000. 

4  PER  CENT. 


li 

x  =  Z2. 

33. 

m 

o  o 

0^>* 

n. 
0 

V. 

6in. 

V. 
12in. 

9.811 

^m.d. 

A  (BO. 
6m. 

AB. 
12m. 

V. 

6m. 

V. 

12m. 

^m.d. 

A(B/). 
6m. 

AB. 

12m. 

n. 
0 

13.301 

.291 

0.010321 

0.020402 

13.789 

10.240 

.296 

0.010352 

0.020464 

1 

23.275 

19.950'  .277 

.321703 

.331815 

24.200 

20.821 

.282 

.321772 

.331917 

1 

2 

33.584 

30.428|  .263 

.508275 

.518420 

34.946 

31.733 

.268 

.508385 

.518569 

2 

3 

44.226 

41.2331  .249 

.643826 

.654010 

46.037 

43.004 

.253 

.643981 

.654204 

3 

4 

55.208 

52.394  .235 

.751485 

.761708 

57.488 

54.634 

.238 

.7516881  .761953 

4 

5 

66.547 

63.909  .220 

0.841558 

0.851823 

69.294 

66.615 

.223 

0.841819(0.852135 

5 

6 

78.235 

75.772  .205 

.919547 

.929863 

81.450 

78.948 

.209 

.919877 

.930247 

6 

7 

90.274 

87.985  .191 

.988745 

.999115 

93.961 

91.636 

.194 

.989152 

.999582 

7 

8 

102.661 

100.548 

.176 

1.051275 

1.061705 

106.836 

104.697 

.178 

1.051765 

1.062256 

8 

9 

115.410 

113.481 

.161 

.108589 

.119080 

120.066 

118.097 

.164 

.109174 

.119741 

9 

10 

128.510 

126.749 

.147 

1.161730 

1.172297 

133.650 

131.865 

.149 

1.162424 

1.173066 

10 

11 

141.961 

140.383 

.131 

.211474 

.222116 

147.592 

145.982 

.134 

.212287 

.223017 

11 

12 

155.767 

154.361 

.117 

.258409 

.269139 

161.883 

160.445 

.120 

.259359 

.270184 

12 

13 

169.916 

168.682 

.103 

.303003 

.313828 

176.518 

175.254 

.105 

.304103 

.315032 

13 

14 

184.409 

183.346 

.089 

.345627 

.356556 

191.495 

190.397 

.091 

.346896 

.357940 

14 

15 

199.238 

198.340 

.075 

1.386588 

1.397632 

206.801 

205.867 

.078 

1.388047:1.399217 

15 

16 

214.395 

213.659 

.061 

.426142 

.437312 

222.432 

221.659 

.064 

.427811 

.439119 

16 

17 

229.872 

229.295 

.048 

.464505 

.4758131 

238.374 

237.751 

.052 

.466411 

.477872 

17 

18 

245.657 

245.229 

.036 

.501868 

.513329 

254.613 

254.137 

.040 

.504037 

.515666 

18 

19 

261.737 

261.455 

.024 

.538396 

.5500251 

271.139 

270.803 

.028 

.540858 

.552671 

19 

20 

278.101 

277.957 

.012 

1.574238 

1.586051 

287.937 

287.734 

.017 

1.5770251.589039 

20 

21 

294.734 

294.722 

.001 

.609529 

.621543 

304.994 

304.915 

.007 

.612675 

.624910 

21 

22 

311.623 

311.734 

.009 

.644392 

.6566271 

322.284 

322.315 

.003 

.647942 

.660424 

22 

23 

328.744 

328.964 

.018 

.678949 

.691431 

339.788 

339.924 

.011 

.682949 

.695697 

23 

24 

346.077 

346.400 

.027 

.713315 

.726063; 

357.483 

357.704 

.018 

.717813 

.730861 

24 

25 

363.598 

364.006 

.034 

1.747600 

1.760648 

375.344 

375.646 

.025 

1.752653 

1.766023 

25 

26 

381.284 

381.771 

.041 

.781914 

.795284 

393.354 

393.724 

.031 

.787576 

.801301 

26 

27 

399.117 

399.673 

.046 

.816360 

.830085 

411.483 

411.903 

.035 

.822702 

.836820 

27 

28 

417.068 

417.673 

.050 

.851053 

.865171 

429.697 

430.153 

.038 

.858152 

.872701 

28 

29 

435.103 

435.744 

.053 

.886109 

.900658 

447.975 

448.459 

.040 

.894042 

.909060 

29 

30 

453.202 

453.870 

.056 

1.921640 

1.936658 

466.285 

466.773 

.041 

1.930498 

1.946037 

30 

31 

471.333 

472.0051  .056 

.957771 

.973310 

484.592 

485.073 

.040 

.967657 

.983766 

31 

32 

489.460 

490.125!  .055 

.994634 

2.010743 

502.863 

503.315 

.038 

2.005660 

2.022398 

32 

33 

507.551 

508.188 

.053 

2.032368 

.049106 

521.048 

521.444 

.033 

.044655 

.062077 

33 

34 

525.559 

526.139 

.048 

.071118 

.088540 

539.151 

539.520 

.031 

.084802 

.102983 

34 

35 

543.483 

544.038 

.046 

2.111045 

2.129226 

557.143 

557.428  .024 

2.126267 

2.145268 

35 

36  561.299 

561.770 

.039 

.152310 

.171311 

574.951 

575.135  .015 

.169242 

.189160 

36 

37 

578.932 

579.303 

.031 

.195106 

.215024 

592.554 

592.635;  .007 

.213929 

.234840 

37 

38 

596.362 

596,631 

.022 

.239632 

.260543 

609.927 

609.882 

.004 

.260544 

.282551 

38 

39 

613.565 

613.710 

.012 

.286102 

.308109 

627.037 

626.853 

.015 

.309326 

.332530 

39 

40 

630.507 

630.514 

.001 

2.334755 

2.357959 

643.858 

643.526 

.028 

2.360524 

2.385037 

40 1 

41 

647.164 

647.023 

.012 

.385839 

.410352 

660.355 

659.845  .043 

.414439 

.440403 

41 

42 

663.497 

663.182 

.026 

.439653 

.465617 

676.495 

a75.808|  .057 

.471378 

.498915 

42 

43 

679.481 

678.989 

.041 

.496504 

.524041 

692.273 

1 

691.399  .073 

.531660 

.560916 

43 

32.   7r  =  16.7902. 

33.   7r  =  17.3376. 

Continued  on  Page  *188. 


TABLE    LXIII. 


*167 


GENERAL  VALUATION  OP  ANNUAL  PREMIUM  POLICIES  OF  1,000, 

4  PER  CENT. 


o  » 

n. 
0 

34. 

35. 

n. 

V. 

6m. 

V. 
12m. 

|-m.d. 

6m. 

AB. 

12m. 

V. 

6m. 

V. 

12ra. 

\mA. 

6m. 

AB. 

12m. 

14.303 

10.691 

.301 

0.010390 

0.020535 

14.834 

11.144 

.308 

0.010430 

0.020614 

0 

1 

25.161 

21.716 

.287 

.321849 

.332033 

!  26.162 

22.655 

.292 

.321929 

.332152 

1 

2 

36.367 

33.103 

.272 

.508504 

.518727 

I  37.855 

34.532 

.277 

.508630 

.518895 

2 

3 

47.936 

44.853 

.257 

.644147 

.654412 

i  49.912 

46.767 

.262 

.644328 

.654644 

3 

4 

59.863 

56.958 

.242 

.751910 

.762226 

62.327 

59.363 

.247 

.752158 

.762528 

4 

5 

72.146 

69.419 

.227 

0.842109 

0.852479 

75.103 

72.320 

.232 

0.842429 

0.852859 

5 

6 

84.786 

82.238 

.212 

.920241 

.930671 

88.252 

85.659 

.216 

.920641 

.931132 

6 

7 

97.793 

95.434 

.197 

.989597 

1.000088 

101.763 

99.3441  ,202 

.990087 

1.000654 

7 

8 

111.161 

108.973 

.182 

1.052304 

.062871 

115.637 

113.406  .186 

1.052897 

.063539 

8 

9 

124.886 

122.884 

.167 

.109819 

.120461 

129.876 

127.822  .171 

.110527 

.121257 

9 

10 

138.973 

137.147 

.152 

1.163186 

1.173916 

144.470 

142.593 

.156 

1.164025 

1.174850 

10 

11 

153.411 

151.759 

.138 

.213183 

.224008 

159.417 

157.717 

.142 

.214167 

.225096 

11 

12 

168.198 

166.722 

.123 

.260402 

.271331 

174.711 

173.182 

.127 

.261550 

.272594 

12 

13 

183.329 

182,021 

.109 

.305313 

.316357 

190.344 

188.981 

.114 

.306646 

.317816 

13 

14 

198.794 

197.652 

.095 

.348294 

.359464 

206.306 

205.108 

.100 

.349830 

.361138 

14 

15 

214.586 

213.606 

.082 

1.389652 

1.400960 

222.587 

221.542 

.087 

1.391418 

1.402879 

15 

16 

230.693 

229.865 

.069 

.429649 

.441110 

239.172 

238.277 

.075 

.431673 

.443302 

16 

17 

247.101 

246.421 

.057 

.468509 

.480138 

256.049 

255.297 

.063 

.470818 

.482631 

17 

18 

263.797 

263.259 

.045 

.506425 

.518238 

273.205 

272.589 

.051 

.509051 

.521065 

18 

19 

280.770 

280.365 

.034 

.543567 

.555581 

290. 624 

290.135 

.041 

.546545 

.558780 

19 

20 

298.002 

297.724 

.023 

1.580090 

1.592325 

308.282 

307.905 

.031 

1.583463 

1.595945 

20 

21 

315.471 

315.304 

.014 

.616140 

.628622 

326.158 

325.888 

.022 

.619955 

.632703 

21 

22 

333.157 

333.095 

.005 

.651852 

.664600 

344.230 

344.047 

.015 

.656156 

.669204 

22 

23 

351.035 

351.059 

.002 

.687352 

.700400 

362.470 

362.370 

.008  .692203 

.705573 

23 

24 

369.080 

369.186 

.009 

.722768 

.736138 

380. 864 

380.833 

.003 

.728218 

.741943 

24 

25 

387.276 

387.452 

.015 

1.758212 

1.771937 

399.377 

399.398 

.002 

1.764332 

1.778450 

25 

26 

405.593 

405.819 

.019 

.793810 

.807928 

417.979 

418.036 

.005 

.800678 

.815227 

26 

27 

423.996 

424.258 

.022 

.829689 

.844238 

436. 646 

436.731 

.007 

.837379 

.852397 

27 

28 

442.463 

442.753 

.024 

.865967 

.880985 

455. 345 

455.435 

.008 

.874572 

.890111 

28 

29 

460.962 

461.256 

.025 

.902777 

.918316 

474.041 

474.123 

.007 

.912399 

.928508 

29 

30 

479.458 

479.745 

.024 

1.940256 

1.956365 

492. 700 

492. 754 

,004 

1.951007 

1.967745 

30 

31 

497.918 

498.176 

.021 

.978550 

.995288 

511.273 

511.268 

.000 

.990549 

2.007971 

31 

32 

516.292 

516.493 

.017 

2.017807 

2.035229 

529. 760 

529.728 

.003 

2.031191 

.049372 

32 

33 

534.582 

534.756 

.015 

.058192 

.076373 

548.135 

548.017 

.010 

.073102 

.092103 

33 

34 

552.760 

552.849 

.007 

.099872 

.118873 

566.321 

566.101 

,018 

.116479 

.136397 

34 

35 

570.752 

570.739 

.001 

2.143040 

2.162958 

584.299 

583.973 

.027 

2.161527 

2.182438 

35 

36 

588.537 

588.420 

.010 

.187901 

.208812 

602.041 

601.586 

.038 

.208464 

.230471 

36 

37 

606.090 

605.846 

.020 

.234671 

.256678 

619.514 

618.918 

.050 

.257533 

.280737 

37 

38 

623.377 

622.997 

.032 

.283591 

.306795 

636.694 

635.946 

.062 

.308985 

.333498 

38 

39 

640.372 

639.838 

.044 

.334912 

.359425 

653.541 

652.612 

.077 

.363125 

.389089 

39 

40 

657.040 

656.326 

.060 

2.388935 

2.414899 

670.026 

668.915 

.093 

2.420261 

2.447798 

40 

41 

673.347 

672.454 

.074 

.445970 

.473507 

686.138 

684.837 

.108 

.480714 

.509970 

41 

42 

689.288 

688.207 

.090 

.506334 

.535590 

701.846 

700.332 

.126 

.544876 

.576033 

42 

43 

704.829 

703.535 

.108 

.570419 

.601576 

717.128 

715.399 

.144 

.613161 

.646384 

43 

34.   -rr  =  17.9149. 

35.   77  =  18.5241. 

Continued  on  Page  *187. 


*168 


TABLE    LXIII 


GENERAL  VALUATION  OF  ANNUAL  PREMIUM  POLICIES  OF  1,000. 

4  PER  CENT. 


li 

n. 
0 

x  =  36. 

37. 

3  3 

O  4> 

n. 

V. 

6m: 

V. 
12m. 

^m.d. 

6m. 

AB. 

12m. 

V. 

6m. 

V. 

12m. 

^m.d. 

A(B/).   AB. 
6m.    12m. 

15.403 

11.640 

.314 

0.010470 

0.020693 

15.999 

12.152 

.321 

0.0105140.020779 

1 

ol 

1 

37.229 

23.651 

.298 

.322014 

.332279 

28.334 

24.671 

.305 

.322111 

.3324271  1 

2 

39.420 

36.024 

.283 

.508769 

.519085 

41.037 

37.559 

.290 

.5089271  .519297 

2 

3 

51.976 

48.762 

.268 

.644531 

.654901 

54.111 

50.817 

.275 

.644756!  .655186 

3 

4 

64.897 

61.866 

.253 

.752432 

.762862 

67.564 

64.465 

.258 

.752730 

.763221 

4 

5 

78.194 

75.355 

.237 

0.842778 

0.853269 

81.388 

78.467 

.243 

0.843164 

0.853731 

5i 

6 

91.857 

89.194 

.222 

.921079 

.931646 

95.583 

92.854 

.227 

.921563 

.932205 

6 

7 

105.887 

103.414 

.206 

.990627 

1.001269 

110.152 

107.605 

.212 

.991219 

1.001949 

7! 

8 

120.287 

117.993 

.191 

1.053548 

.064278 

125.084 

122.718 

.197 

1.054267 

.065092 

8 

9 

135.044 

132.930 

.176 

.111307 

.122132 

140.378 

138.193 

.182 

.112164 

.123093 

di 

10 

150.161 

148.225 

.161 

1.164947 

1.175876 

156.027 

154.016 

.168 

1.165963 

1.177007 

10 

11 

165.627 

163.864 

.147 

.215250 

.226294 

172.022 

170.182 

.153 

.216443 

.227613 

11 

12 

181.436 

179.841 

.133 

.262814 

.273984 

188.355 

186.683 

.139 

.264205 

.275513 

12 

13 

197.578 

196.150 

.119 

.308111 

.319419 

205.013 

203.498 

.126 

.309724 

.321185 

13 

14 

214.043 

212.769 

.106 

.351522 

.362983 

221.981 

220.620 

.113 

.353385 

.365014 

14 

15 

230.814 

229.693 

.093 

1.393363 

1.404992 

239.250 

238.035 

.101 

1.395503 

1.407316 

15 

16 

247.882 

246.905 

.081 

.433899 

.445712 

256.804 

255.727 

.090 

.436349 

.448363 

16 

17 

265.231 

264.391 

.070 

.473358 

.485372 

274.626 

273.680 

.079 

.476151 

.488386!  17 ! 

18 

282.846 

282.135 

.059 

.511939 

.524174 

292.693 

291.862 

.069 

.515119 

.527601  18 

19 

300.703 

300.105 

.050 

.549824 

.562306 

310.985 

310.262 

.060 

.553436 

.566184  19 

20 

318.781 

318.291 

.041 

1.587179 

1.599927 

329.474 

328.842 

.053 

1.591271 

1.604319  20 

21 

337.055 

336.654 

.033 

.624155 

.637203 

348.138 

347.589 

.046 

.628783 

.642153  21 

22 

355.502 

355.184 

.026 

.660898 

.674268 

366.957 

366.480 

.040 

.666115 

.6798401 22 

23 

374.103 

373.855 

.021 

.697539 

.711264 

385.901 

385.476 

.035 

.703415 

,717533 

23 

24 

392.825 

392.629 

.016 

.734219 

.748337 

404.933 

404.546 

.032 

.740831 

.755380 

24 

25 

411.636 

411.478 

.013 

1.771075 

1.785624 

424.032 

423.674 

.030 

1.778499!l.793517  25 

26 

430.514 

430.383 

.011 

.808238 

.823256 

443.166 

442.812 

.029 

.816565!  .83210426 

27 

449.423 

449.298 

.010 

.845849 

.8613881  462.295 

461.933 

.030 

.855180!  .871289  27 

28 

468.331 

468.197 

.011 

.884053 

.900162  481.387 

480.996 

.033 

.894500  .911238  28 

29 

487.200 

487.037 

.014 

.923002  .9397401500.390 

1 

499.939 

.038 

.934684j  .952106|29 

30 

505.981 

505.760 

.018 

1.962852,1.980274 

519.305 

518.827 

.040 

1.97590611.994087 

30 

31 

524.677 

524.428 

.021 

2.003772 

2.021953 

538.106 

537.540 

.047 

2.0183382.037339 

31 

32 

543.259 

542.923 

.028 

.045934 

.064935 

556.714 

556.043 

.056 

.062183 

.082101 

32 

33 

561.650 

561.211 

.037 

.089535 

.109453 

575.109 

574.329 

.065 

.107650 

.128561 

33  i 

34 

579.830 

579.284 

.046 

.134785 

.155696 

593.263 

592.351 

.076 

.154962 

.176969 

34 

35 

597.774 

597.097 

.056 

2.181902 

2.203909 

611.140 

610.085 

.088 

2.204363 

2.227567 

35 

36 

615.443 

614.624 

.068  .231131 

.254335 

628.718 

627.507 

.101 

.256110 

.280623 

36 

37 

632.817 

631.843 

.081 

.282725 

.307238 

645.956 

644.559 

.116 

.310510 

.336474 

37 

38 

649*853 

648.697 

.096 

.336990 

.362954 

602.822 

661.240 

.132 

.367873 

.395410 

38 

39 

666.523 

665.183 

.112 

.394235 

.421772 

679.308 

677.532 

.148 

.428524 

.457780 

39 

40 

682.817 

681.285 

.128 

2.454784 

2.484040 

695.381 

693.385 

.166 

2.492857 

2.524014 

40 

41 

698.702 

696.954 

.146 

.519028 

.550185 

711.016(708.802 

.185 

.561287 

.594510!  411 

42 

714.156 

712.191 

.164 

.587383 

.620606 

726.2061723.764 

.203 

.634256 

.669739 

42 

43 

_ 

729.168 

726.980 

.182 

.660287 

.695770 

740.936  738.264 

.22^ 

.712260 

.750216 

43 

36.   71=19.1663. 

37.   77  =  19.8452. 

Continued  on  Page  *186. 


*169 


TABLE    LXIII. 


GENERAL  VALUATION  OF  ANNUAL  PREMIUM  POLICIES  OF  1,000. 

4  PER  CENT. 


38. 

39.            !|.g 

n. 

V. 

6m. 

V. 

12m. 

^m.d. 

A(B/). 
6m. 

aB. 

12m. 

V. 

6m. 

V. 
12m. 

^m.d. 

6m. 

AB. 

12m. 

n. 

0 

16.618 

12.673 

.329 

0.010568 

0.020884 

17.267 

13.214 

.338 

0.010624 

0.020994 

0| 

1 

29.477 

25.719 

.313 

.322221 

.332591 

30.671 

26.807 

.322 

.32234] 

.332771 

l! 

2 

42.710 

39.140 

.298 

.509102 

.519532 

44.463 

40.800 

.305 

.509289 

.519780 

2 

3 

56.329 

52.956 

.281 

.645002 

.655493 

58.638 

55.156 

.290 

.645272 

.655839 

3 

4 

70.324 

67.130 

.266 

.753060 

.763627 

73.192 

69.908 

.274 

.753423 

.764065 

4 

5 

84.694 

81.695 

.250 

0.843589 

0.854231 

88.130 

85.032 

.258 

0.844054 

0.854784 

5 

6 

99.442 

96.627 

.235 

.922094 

.932824 

103.440 

100.527 

.243 

.922678 

.933503 

6 

7 

114.557 

111.926 

.219 

.991873 

1.002698 

119.120 

116.393 

.227 

.992591 

1.003520 

7| 

8 

130.040 

127.591 

.204 

1.055056 

.065985 

135.165 

132.617 

.212 

1.055925 

.066969 

8 

9 

145.881 

143.609 

.189 

.113110 

.124154 

151.564149.191 

.198 

.114148 

.125318 

9 

10 

162.072 

159.973 

.175 

1.167081 

1.178251 

168.310166.109 

.183 

1.168310 

1.179618 

10 

11 

178.606176.677 

.161 

.217755 

.229063 

185.390183.350 

.170 

.219199 

.230660 

11 

12 

195.469 

193.699 

.147 

.265736 

.277197 

202.788  200.906 

.157 

.267421 

.279050 

12 

13 

212.647 

211.033 

.135 

.311500 

.323129 

220.493  218.761 

.144 

.313455 

.325268 

13 

14 

230.128 

228.661 

.122 

.355434 

.367247 

238.491236.901 

.133 

.357689 

.369703 

14 

15 

247.897 

246.571 

.110 

1.397858 

1.409872 

256.764  255.307 

.121 

1.400447 

1.412682 

15 

16  265.939 

264.745 

.100 

.439043 

.451278 

275.288  273.949 

.112 

.442008 

.454490 

16 

17 

284.2281283.150 

.090  !  .479227 

.491709 

294.042  292.815 

.102 

.482615 

.495363 

17 

18 

302.7451301.777 

.081  .518622 

.531370 

312.999  311.864 

.095 

.522478 

.535526 

18 

19 

321.462  320.585 

.073 

.557414 

.570462 

332.135  331.086 

.087 

.561795 

.575165119 

1 

20 

340.355 

339.564 

.066 

1.595779 

1.609149 

351.431350.455 

.081 

1.600738 

1.614463 

20 

21 

359.407  358.687 

.060 

.633875 

.647600 

370.853 

369.931 

.077 

.639481 

.653599 

21 

22  378.582 

377.916 

.055 

.671860 

.685978 

390.367 

389.484 

.074 

.678190 

.692739 

22 

23  397.850 

397.221 

.052 

.709891 

.724440 

409.950 

409.096 

.071 

.717019 

.732037 

23 

241417. 183 

416.584 

.050 

.748111 

.763129 

429.567 

428.717 

.071 

.756129 

.771668 

24 

25  436.553 

435.957 

.050 

1.786675 

1.802214 

449.180 

448.323 

.071 

1.795684 

1.811793 

25 

26 

455.916 

455.314 

.050 

.825739 

.841848 

468.755 

467.867 

.074 

.835850 

.852588 

26 

27 

475.244 

474.611 

.053 

.865464 

.882202 

488.238 

487.290 

.079 

.876794 

.894216 

27 

28 

494.480 

493.787 

.058 

.906012 

.923434 

507.633 

506.656 

.081 

.918699 

.936880 

28 

29 

513.628 

512.908 

.060 

.947560 

.965741 

526.909 

525.842 

.089 

.961745 

.980746 

29 

30 

532.661 

531.851 

.068 

1.990136 

2.009137 

545.988 

544.813 

.098 

2.006139 

2.026057 

30 

31 

551.497 

550.581 

.076 

2.034395 

.054313 

564.847 

563.562 

.107 

.052097 

.073008 

31 

32 

570.117 

569.092 

.085 

.080097 

.101008 

583.461 

582.040 

.118 

.099845 

.121852 

32 

33 

588.496 

587.337 

.097 

.127619 

.149626 

601.791 

600.222 

.131 

.149635 

.172839 

33 

34 

606.593 

605.288 

.109 

.177207 

.200411 

619.814 

618.085 

.144 

.201726 

.226239 

34 

35 

624.388 

622.925 

.122 

2.229119 

2.253632 

637.486 

635.568 

.160 

2.256427 

2.282391 

35 

36 

641.837 

640.187 

.137 

.283663 

.309627 

654.780 

652.671 

.176 

.314055 

.341592 

36 

37 

658.911 

657.073 

.153 

.341154 

.368691 

671.683 

669.375 

.192 

.374935 

.404191 

37 

38 

675.600 

673.565 

.170 

.401915 

.431171 

688.162 

685.629 

.211 

.439466 

.470623 

38 

39 

691.870 

689.613 

.188 

.466343 

.497500 

704.192 

701.436 

.230 

.508066 

.541289 

39 

40 

707.697 

705.219 

.207 

2.534855 

2.568078 

719.767 

716.777 

.249 

2.581178 

2.616661 

40 

41 

723.073 

720.366 

.226 

.607893 

.643376 

734.870 

731.643 

.269 

.659303 

.697259 

41 

42 

737.986 

735.044 

.245 

.685955 

.723911 

749.505 

746.047 

.288 

.742974 

.783620 

421 

43 

752.436 

749.265 

.264 

.769575 

.810221 

763.667 

759.967 

.308 

.832813 

.876419 

43  i 

38.   TT  =  20.5624. 

39.    7r  =  21.3199. 

i 

Continued  on  Page  *185. 


♦170 


TABLE     LXIII 


GENERAL  VALUATION  OF  ANNUAL  PREMIUM  POLICIES  OP  1,000. 

4  PER  CENT. 


11 

n. 

a;  =  40. 

41. 

n. 

V. 

6m. 

V. 

13m. 

im.d. 

MB/). 

6m. 

AB. 

13m. 

V. 

6m. 

V. 

13m. 

l^m.d. 

6m. 

AB. 

13m. 

0 

17.948 

13.775 

.348 

0.010687 

0.031117 

18.673 

14.379 

.358 

0.010752 

0.031343 

0 

1 

31.936 

37.956 

.331 

322469 

.333960 

33.338 

39.130 

.343 

.322612 

.333179 

1 

2 

46.291 

43.504 

.316 

509497 

.530064 

48.193 

44.388 

.335 

.509727 

.520369 

2 

3 

61.039 

57.453 

.399 

645569 

.656311 

63.542 

59.839 

.309 

.645894 

.656624  3 

4 

76.177 

73.780 

.383 

753819 

.764549 

79.273 

75.751 

.394 

.754258 

.765083  4 

5 

91.691 

88.483 

.267 

0 

844568 

0.855393 

95.386 

93.054 

.378 

0.845131 

0.856060  5 

6 

107.582 

104.561 

.252 

923321 

.934350 

111.873 

108.734 

.363 

.924029 

.9350731  6 

7 

123.842 

131.003 

.237 

993381 

1.004435 

138.723 

125.755 

.347 

.994251 

1.0054211  7 

8 

140.461 

137.798 

.222 

1 

056883 

.068053 

145.931 

143.140 

.333 

1.057934 

.069242;  8 

9 

157.431 

154.943 

.207 

115290 

.136598 

163.481 

160.855 

.319 

.116549 

.128010  9 

10 

174.739 

173.414 

.194 

1 

169663 

1.181134 

181.358 

178.894 

.305 

1.171153 

1.182782  10 

11 

192.370 

190.305 

.180 

230789 

.333418 

199.551 

197.241 

.193 

.222539 

.234352  11 

12 

210.312 

308.299 

.168 

369376 

.381089 

218.044 

215.881 

.180 

.271315 

.283329  12 

13 

238.551 

236.682 

.156 

315604 

.337618 

336.822 

334.795 

.169 

.317968 

.330203  13 

14 

247.069 

345.335 

.145 

360168 

.373403 

355.856 

353.950 

.159 

.362898 

.375380  14 

15 

265.842 

364.337 

.135 

1 

403398 

1.415780 

375.136 

373.335 

.149 

1.406438 

1.419186  15 

16 

384.846 

383.345 

.125 

445375 

.458033 

394.605 

292.909 

.141 

.448873 

.461921  16 

17 

304.058 

303.650 

.117 

486345 

.499393 

314.369 

312.661 

.134 

.490455 

.503825  17 

18 

323.450 

333.139 

.110 

536738 

.540098 

334.095 

332.563 

.128 

.531402 

.545127  18 

19 

343.004 

341.757 

.104 

566616 

.580341 

354.053 

352.576 

.133 

.571924 

.586042  19 

20 

362.686 

361.494 

.099 

1 

606300 

1.630318 

374.105 

372.667 

.130 

1.612218 

1.626767  20 

21 

382.462 

381.309 

.096 

645659 

.660308 

394.337 

393.819 

.117 

.652462 

.667480  21 

22 

402.306 

401.183 

.094 

685160 

.700178 

414.383 

413.981 

.117 

.693837 

.708376  22 

23 

422.186 

431.067 

.093 

724871 

.740410 

434.538 

433.137 

.118 

.733534 

.749633  23 

24 

442.061 

440.935 

.094 

764965 

.781074 

454.651 

453.309 

.130 

.774703 

.791441  24 

25 

461.899 

460.741 

.096 

1 

805614 

1.833353 

474.673 

473.167 

.135 

1.816556 

1.833978  25 

26 

481.643 

480,434 

.102 

846991 

.864413 

494.600 

493.066 

.138 

.859374 

.877455  26 

27 

501.297 

500.049 

.104 

889385 

.907466 

514.407 

513.781 

.136 

.903047 

.922048  27 

28 

520.831 

519.493 

.112 

933678 

.951679 

534.011 

533.374 

.145 

.948091 

.968009  28 

29 

540.166 

538.717 

.131 

977383 

.997301 

553.390 

551.540 

.154 

.994628 

2.015539j29 

30 

559.277 

557.717 

.130 

3 

033618 

3.044539 

573.517 

570.537 

.166 

3.042891 

2.064898' 30 

31 

578.141 

576.443 

.141 

071613 

.093620 

591.353 

589.310 

.178 

.093137 

.116341*31 

32 

596.716 

594.868 

.154 

131633 

.144826 

609.871 

607.565 

.193 

.145630 

.170143  32 

33 

614.979 

612.970 

.167 

173906 

.198419 

638.031 

635.530 

.308 

.300684 

.336648!  33| 

34 

632.890 

630.688 

.184 

338776 

.254740 

645.801 

643.104 

.335 

.358631 

.386158 

34 

35 

650.414 

648.020 

.199 

3 

386553 

2.314089 

663.169 

660.368 

.243 

3.319769 

3.349035 

35 

36 

667.544 

664.947 

.316 

347561 

.376817 

680.103 

676.970 

.361 

.384531 

.415688 

36 

37 

684.244 

681.420 

.335 

413303 

.443360 

696.574 

693.311 

.280 

.453338 

.486551 

37 

38 

700.490 

697.438 

.354 

480898 

.514121 

713.576 

708.975 

.300 

.536608 

.562091 

38 

39 

716.371 

712.984 

.374 

554090 

.589573 

738.097 

734.351 

.321 

.604873 

.643839 

39 

40 

731.577 

728.049 

.394 

2 

633383 

2.670338 

743.134 

739.051 

.340 

3.688661 

3.739307 

40 

{41 

746.408 

743.646 

.314 

716010 

.756656 

757.687 

753.356 

.361 

.778594 

.833300 

41 

'42 

760.760 

756.753 

.334 

805894 

.849500 

771.778 

767.333 

.379 

.875305 

.933097 

42 

43 

774.657 

770.439 

.351 

903565 

.949357 

785.440 

780.679 

.397 

.979538 

3.039839 

43 

40.    7r  =  32.1306. 

41.   77  =  33.9667. 

Continued  on  Page  *184. 


TABLE     LXIII. 


*in 


GENERAL  VALUATION  OF  ANNUAL  PREMIUM  POLICIES  OF  1,000. 

4  PER  CENT. 


42. 

43. 

V. 

V. 

Jm.d. 

^(B/). 

AB. 

V. 

V. 

Jm.d. 

^(B/). 

AB. 

n. 

6m. 

12m. 

6m. 

12m. 

6m. 

12m. 

6m. 

12m. 

n. 

!o 

19.415 

14.966 

.371 

0.010831 

0.021398 

20.212 

15.613 

.383 

0.010911 

0.021553 

0 

1  1 

34.587 

30.345 

.354 

.322771 

.333413 

36.021 

31.620 

.367 

.322941 

.333671  1 

2 

50.160 

46.113 

.337 

.509978 

.520708 

52.225 

48.020 

.350 

.510255 

.521080  2 

3 

66.122 

62.267 

.321 

.646255 

.657080 

68.821 

64.812 

.334 

.646649 

.657578 

3 

4 

82.469 

78.808 

.305 

.754740 

.765669 

85.802 

81.982 

.318 

.755270 

.766314 

4 

5 

99.196 

95.722 

.289 

0.845753 

0.856797 

103.158 

99.524 

.303 

0.846437 

0.857607 

5 

61116.293 

113.001 

.274 

.924809 

.935979 

il20.882 

117.430 

.288 

.925665 

.936973 

6 

7il33.752 

130.639 

•259 

.995207 

1.006515 

1138.959 

135.677 

.274 

.996260 

1.007721 

7 

8|151.557 

148.613 

.245 

1.059092 

.070553 

157.372 

154.258 

.259 

i.060366 

.071995 

8 

9  169.696 

166.916 

.232 

.117934 

.129563 

;i76.112 

173.155 

.246 

.119458 

.131271 

9 

10  188.155 

185.530 

.219 

1.172793 

1.184606 

195.159 

192.354 

.234 

1.174597 

1.186611 

10 

11 

206.917 

204.442 

.206 

.224464 

.236478 

214.500 

211.835 

.222 

.226579 

.238814 

11 

12 

225.968 

223.631 

.195 

.273558 

.285793 

234.105 

231.565 

.212 

.276028 

.288510 

12 

13 

245.280 

243.066 

.185 

.320571 

.333053 

'253.953 

251.532 

.202 

.323439 

.336187 

13 

14 

264.832 

262.734 

.175 

.365905 

.378653 

:274.018 

271.694 

.194 

.369217 

.382265 

14 

15 

284.595 

282.594 

.167 

1.409896 

1.422944 

294.271 

292.038 

.186 

1.413707 

1.427077 

15 

16 

304.546 

302.634 

.159 

.452837 

.466207 

314.693 

312.537 

.180 

.457198 

.470923 

16 

17 

324.661 

322.826 

.153 

.494977 

.508702 

335.248 

333.150 

.175 

.499957 

.514075 

17 

18 

344.910 

343.131 

.148 

.536551 

.550669 

'355.903 

353.845 

.172 

.542225 

.556774 

18 

19 

365.255 

363.515 

.145 

.577775 

.592324 

376,628 

374.601 

.169 

.584217 

.599235 

19 

20 

385.669 

383.961 

.142 

1.618845 

1.633863 

397.389 

395.368 

.168 

1.626145 

1.641684 

20 

21 

406.121 

404.417 

.142 

.659955 

.675494 

418.148 

416.118 

.169 

.668214 

.684323 

21 

22 

426.568 

424.857 

.143 

.701297 

.717406 

438.866 

436.803 

.172 

.710624 

.727362  22 

23 

446.976 

445.232 

.145 

.743062 

.759800 

459.486 

457.360 

.177 

.753574 

.770996  23 

24 

467.288 

465.481 

.151 

.785436 

.802858 

480.013 

477.856 

.180 

.797270 

.815451  24 

25 

487.508 

485.671 

.153 

1.828620 

1.846801 

500.415 

498.163 

.188 

1.841914 

1.860915 

25 

26 

507.603 

505.673 

.161 

.872808 

.891809 

520.607 

518.241 

.197 

.887733 

.907651 

26 

27 

527.494 

525.451 

.170 

.918222 

.938140 

540.567 

538.084 

.207 

.934959 

.955870 

27 

28 

547.155 

544.997 

,180 

.965089 

.986000 

560.268 

557.641 

.219 

.983833 

2.005840 

28 

29 

566.561 

564.261 

.192 

2.013644 

2.035651 

579.667 

576.884 

.232 

2.034619 

.057823 

29 

30 

585.670 

583.217 

.204 

2.064148 

2.087352 

598.742  595.790 

.246 

2.087587 

2.112100 

30 

31 

604.460 

601.840 

.218 

.116868 

.141381 

!617.447 

614.294 

.263 

.143058 

.169022 

31 

132 

622.885 

620.067 

.235 

.172122 

.198086 

635.750 

632.395 

.280 

.201358 

.228895 

32 

33 

640.914 

637.897 

.251 

.230233 

.257770 

653.639 

650.074 

.297 

.262822 

.292078 

33 

34 '658. 535 

655.311 

.269 

.291532 

.320788 

671.081667.278 

.317 

.327854 

.359011 

34 

35 '675.716 

672.257 

.288 

2.356424 

2.387581 

688.048  684.007 

.337 

2.396883 

2.430106 

35 

36  692.438 

688.736 

.308 

.425333 

.458556 

704.530 

700.243 

.357 

.470359 

.505842 

36 

37  708.664 

704.729 

.328 

.498706 

.534189 

720.515 

715.977 

.378 

.548788 

.586744137 

38 

724.410 

720.228 

.348 

.577049 

.615005 

736.004 

731.222 

.398 

.632712 

.673358!  38 

39 

739.667 

735.244 

.369 

.660903 

.701549 

750.994 

745.955 

.420 

.722756 

.7663621 39 

40 

754.432 

749.757 

.390 

2.750890 

2.794496 

765.507 

760.249 

.438 

2.819556 

2.866348*40 

41 

768.729 

763.837 

.408 

.847643 

.894435 

779.578 

774.098 

.457 

.923851 

.974162  41 

42 

782.589 

777.479 

.426 

.951901 

3.002212 

793.262 

787.616 

.471 

3.036438 

3.090542;  42 

43 

796.069 

790.795 

.440 

3.064459 

.118563 

806.697 

800.969 

.477 

.158109 

.216302 

43' 

42.    TT  =  23.8627. 

43.    7r  =  24.8099. 

Continued  on  Page  *183. 


*172 


TABLE     LXIII 


GENERAL  VALUATION   OF  ANNUAL  PREMIUM  POLICIES   OF  1,000. 

4  PER  CENT. 


Is 

x  =  44. 

45. 

m 

o  « 

n. 

V. 

6m. 

V. 

12m. 

Jm.d. 

A(B/). 
6m. 

AB. 
12m. 

V. 

6m. 

V. 

12m. 

im.d. 

^  (B/). 
6m. 

AB. 
12m., 

0 « 

n. 

0 

21.037 

16.261 

.398 

0.011001 

0.021731 

21.906 

16.936 

.414 

0.011103 

0.021928 

0 

1 

37.498 

32.921 

.381 

.323134 

.333959 

39.044 

34.276'  .397  .323343 

.334272'  1 

2 

54.356 

49.979 

.365 

.510559 

.521488 

56.580 

52.007 

.381  .510895 

.521939  2 

3 

71.607 

67.422 

.349 

.647085 

.658129 

74.502 

70.122 

.365  .647564 

.658734  3 

4 

89.239 

85.242 

.333 

.755854 

.767024 

92.806 

88.613 

.349  .756496 

.7678041  4 

1 

5 

107.243 

103.432 

.318 

0.847188 

0.858496 

111.472 

107.455 

.335 

0.848016 

0.859477 

5 

6 

125.607 

121.969 

.303 

.926608 

.938069 

130.4871 126. 643'  .320 

.927646 

.939275 

6 

7 

144.313 

140.844 

.289 

.997420 

1.009049 

149. 838146.1571  .307 

.998696 

1.010509 

7 

8 

163.349 

160.041 

.276 

1.061769 

.073582 

169.508:165.983  .294 

1.063313 

.075327 

8 

9 

182.700 

179.545 

.263 

.121134 

.133148 

189.479  186.100;  .282 

'           1 

.122976 

.135211 

9 

10 

202.346 

199.335 

.251 

1.176579 

1.188814 

209. 725J206. 4741  .271 

1.178762 

1.191244 

10 

11 

222.263 

219.378 

.240 

.228909 

.241391 

230.222 

227.093 

.261 

.231476 

.2442241 11 

12 

242.426 

239.661 

.230 

.278749 

.291497 

250.941 

247.913 

.252 

.281746 

.294794 

12 

13 

262i»809 

260.143 

.222 

.326597 

.339645 

271.855 

268.921 

.245 

.330077 

.343447 

13 

14 

283.382 

280.809 

.214 

.372866 

.386236 

292.943  290.090 

.238 

.376881 

.390606 

14 

15 

304.128 

301.634 

.208 

1.417899 

1.431624 

314.171311.376 

.233 

1.422516 

1.436634 

15 

16 

325.011 

322.574 

.203 

.462001 

.476119 

335.499  332.746 

.229 

.467295 

.481844 

16 

17 

345.991 

343.596 

.200 

.505445 

.519994 

356.902  354.181 

.227 

.511489 

.526507 

17 

18 

367.046 

364. 682 

.197 

.548473 

.563491 

378.341  375.6261  .226 

.555356 

.570895 

18 

19 

388.136 

385.778 

.197 

.591314 

.606853 

399.778  397.053'  .227 

i           j 

.599137 

.615246 

19 

20 

409.225 

406.858 

.197 

1.634191 

1.65030o' 

421.171418.414  .230 

1.643062 

1.659800 

20 

21 

430.271 

427.871 

.200 

.677318^  .694056 

442.466  439.6411  .235 

.687354 

.704776 

21 

22 

451.218 

448. 753 

.205 

.7209041  .738326 

463.661,460.806'  .238 

.732240 

.750421 

22 

23 

472.071 

469.575 

.208 

.765165!  .783346 

484.730i481.777 

.246 

.777940 

.796941 

23 

24 

492.795 

490.203 

.810 

.810311-  .829312, 

505.581j502.510 

.256 

.824695 

.844613 

24 

25 

513.308 

510.600 

.226 

1.8565751.876493' 

526.194 

523.0011  .266 

1.872749 

1.893660 

25 

26 

533.586 

530.758  .236 

.904196 

.925107 

546.537 

543.197 

.278 

.922355 

.944362 

26 

27 

553.598 

550.625 

.248 

.953419 

.975426 

566.571 

563.069 

.292 

.973785 

.996989 

27 

28 

573.306 

570.174 

.261 

2.004512 

2.027716 

586.268  582.592 

.306 

2.027320 

2.051833 

28 

29 

592.683 

589.379 

.275 

.057751  .082264  605.584  601.700 

.324 

.083286 

.109250 

29 

30 

611.684 

608.177 

.292 

2.113459  2.139423'!624. 484  620.392 

.341 

2.142017 

2.169554 

30 

31 

630.278 

626.565  .309 

.171965 

.199502  642.958  638.648 

.359 

.203853 

.233109 

31 

32 

348.451 

644.524?  .327 

.233606 

.262862;  660.969:656.414 

.380 

.269207 

.300364 

32 

33 

666.169 

662.0001  .347 

.298793 

.329950! 

678. 4901673. 689 

.400 

.338509 

.371732 

33 

34 

683.404 

678.995  .367 

.367953  .401176 

695.510'690.456 

.421 

.412215 

.447698 

34 

35 

700.148 

695.489 

.388 

2.441538  2.477021' 

712.018 

706.703 

.443 

2.490838 

2.528794 

35 

36 

716.388l711.473l 

.410 

.520060  .558016 

728.012 

722.446 

.464 

.574922 

.615568 

36 

37 

732. 122 

726.959 

.430 

.604061  .644707 

743.491 

737.660 

.486 

.665098 

.708704 

37 

38 

747.349 

741.926 

.452 

.694168 

.737774 

758.478 

752.420 

.505 

.762003 

.808795' 38 

39 

762.093 

756.446 

.471 

.791019 

.837811 

773.009  766.722 

.524 

.866381 

.916692 

39 

40 

776.387 

770.516 

.489 

2.895353 

2.945664 

787.140 

780.682 

.538 

2.979034 

3.033138 

40 

41 

790.289 

784.248 

.503 

3.007972 

3.062076 

801.015 

794.471 

.545 

3.100754 

.158947 

41 

42 

803.937 

797.813 

.510 

.129666 

.187859 

814.766 

808.186 

.548 

.232640 

.295403 

42 

43 

817.466 

811.306 

.513 

.261533 

.324296 

828.710 

822.357 

.529 

.375628 

.443161 

43 

44.   Tr  =  25.8133. 

45.   77  =  26.8757. 

Continued  on  Page  *183. 


TABLE     LXIII 


'173 


GENERAL  VALUATION  OF  ANNUAL  PREMIUM  POLICIES  OF  1,000. 

4  PER  CENT. 


g 

n. 

46. 

47.            1 

••^1 

n. 

V. 

6ra. 

V. 

12m. 

^m.d. 

A(B/). 
6m. 

AB. 

12m. 

V. 

6m. 

V. 

12m. 

^m.d. 

A(B/). 
6m. 

AB. 

12m. 

0 

22.821 

17.640 

.432 

0.011211 

0.022140 

23.778 

18.361 

.451 

0.011332 

0.022376 

0 

1 

40.658 

35.676 

.415 

.323573 

.334617 

42.337 

37.118 

.435 

.323827 

.334997 

1 

2 

58.890 

54.103 

.399 

.511264 

.522434 

61.289 

56.265 

.419 

.511668 

.522976 

2 

3 

77.508 

72.912 

.383 

.648090 

.659398 

80.618 

75.776 

.404 

.648669 

.660130 

3 

4 

96.496 

92.079 

.368 

.757202 

.768663 

100.308 

95.645 

.389 

.757980 

.769609 

4 

5 

115.839 

111.597 

.354 

0.848927 

0.860556 

'l20.346 

115.852 

.374 

0.849929 

0.861742 

5 

6 

135.523 

131.448 

.340 

.928788 

.940601 

1140.714 

136.381 

.361 

.930044 

.942058 

6 

7 

155.532 

151.615 

.326 

1.000098 

1.012112 

161.395 

157.213 

.349 

1.001639 

1.013874 

7 

8 

175.847 

172.079 

.314 

.065008 

.077243 

182.359 

178.310 

.337 

.066875 

.079357 

8 

9 

196.442 

192.804 

.303 

.125005 

.137487 

203.583 

199.661 

.327 

.127241 

.139989 

9 

10 

217.292 

213.778 

.293 

1.181167 

1.193915 

1225.038 

221.220 

.318 

1.183816 

1.196864 

lO' 

11 

238.368 

234.957 

.284  .234303 

.247351 

'246.694 

242.974 

.310 

.237418 

.250788 

11 

12 

259.642 

256.327 

.276 

.285048 

.298418 

;268.532 

264.894 

.303 

.288680 

.302405 

12 

13 

281.095 

277.861 

.2^9 

.333905 

.347630 

'290.512 

286.935 

.298 

.338120 

.352238 

13 

14 

302.687 

299.513 

.265 

.381302 

.395420 

312.597 

309.064 

.294 

.386176 

.400725 

14 

15 

324.383 

321.251 

.261 

1.427604 

1.442153 

334.759 

331.259 

.292 

1.433208 

1.448226 

15 

16 

346.153 

343.055 

.258 

.473124 

.488142 

356.959 

353.465 

.291 

.479546 

.495085 

16 

17 

367.963 

364.869 

.258 

.518148 

.533687i  379.157 

375.653 

.292 

•525487 

.541596 

17 

18 

389.768 

386.666 

.258 

.562943 

.579052!  i401.310 

397.772 

.295 

.571309 

.588047 

18 

19 

411.531 

408.395 

.261 

.607761 

.624499' 423.360 

419.753 

.301 

.617269 

.634691 

19 

20 

433.192 

429.988 

.267 

1.652840 

1.670262' 445.309 

441.670 

.303 

1.663624 

1.681805 

20 

21 

454.753 

451.518 

.270 

.698421 

.716602  467.124 

463.384 

.312 

.710620 

.729621 

21 

22 

476.184 

472.849 

.278 

.744734 

.763735  488.716 

484.853 

.322 

.758517 

.778435 

22 

23 

497.395 

493.940 

.288 

.792031 

.811949  510.060 

506.072 

.332 

.807578 

.828489 

23 

24 

518.363 

514.784 

.298 

.840563 

.861474  531.126 

526.984 

.345 

.858070 

.880077 

24 

25 

539.056 

535.327 

.311 

1.890590 

1.912597  551.870 

547.561 

.359 

1.910278 

1.933482 

25 

26 

559.435 

555.542 

.324 

.942391 

.965595  572.266 

567.777 

.374 

.964494 

.989007 

26 

27 

579.472 

575.401 

.339 

.996250 

2.020763  592.268 

587.564 

.392 

2.021055 

2.047019 

27 

28 

599.120 

594.839 

.357 

2.052499 

.078*63  611.839 

606.919 

.410 

.080302 

.107839 

28 

29 

618.347 

613.853 

.375 

.111476 

.139013  630.969 

625.823 

.429 

.142583 

.171839 

29 

30 

637.138 

632.423 

.393 

2.173525 

2.202781  649.618 

644.219 

.450 

2.208319 

2.239476 

30 

31 

655.4o9'650.494 

.414 

.239061 

.270218  667.761 

662.107 

.471 

.277947 

.311170 

31 

32 

673.281j668.067 

.434 

.308519 

.341742  685.385 

679.469 

.493 

.351928 

.387411 

32 

33 

690.596|685.123 

.456 

.382357 

.417840 

702.479 

696.294 

.515 

.430781 

.468737 

33 

34 

707.387 

701.651 

.478 

.461089 

.499045 

719.042 

712.594 

.537 

.515055 

.555701 

34 

35 

723.'658 

717.664 

.500 

2.545264 

2.585910 

735.069 

728.349 

.560 

2.605386 

2.648992 

35 

36 

739.403 

733.141 

.522 

.635514 

.679120  750.588,743.633 

.580 

.702416 

.749208 

36 

37 

754.649 

748.155 

.541 

.732479 

.779271 

765.636 

758.443 

.599 

.806893 

.857204 

37; 

38 

769.430 

762.704 

.560 

.836904 

.887215 

780.267 

772.897 

.614 

.919623 

.973727 

38 

39 

783.804 

776.903 

.575 

.949594 

3.003698 

794.634 

787.176 

.621 

3.041402 

3.099595 

39 

40 

797.917 

790.930 

.582 

3.071343 

3.129536 

808.875 

801.379 

.625 

3.173332 

3.236095 

40 

41 

811.906 

804.882 

.585 

.203250 

.266013 

823.313 

816.052 

.605 

.316352 

.383885 

41 

42 

826.090 

819.297 

.566 

.346253 

.413786 

1837.140 

829.032 

.676 

.475762 

.551432 

42 

43 

839.673|832.047 

.636 

.505651 

.581321 

849.151 

840.075 

.756 

.656718 

.741317 

43 

46.   7r  =  28.0014. 

47.   7r  =  29.1948. 

Continued  on  Page  *181. 


•*iu 


TABLE    LXIII. 


GENERAL  VALUATION  OF  ANNUAL  PREMIUM  POLICIES  OF  1,000. 

4  PER  CENT. 


Is 

X  =  48. 

49. 

> 

n. 

n. 

V. 

6m. 

V. 

12m. 

|m.d. 

A(B/). 
6m. 

AB. 
12m. 

V. 

6m. 

V. 

12m. 

l^m.d. 

6m. 

aB. 

12m. 

0 

24.784 

19.108 

.473 

0.011464 

0.022634 

25.844 

19.885 

.497 

0.011610 

0.022918 

0 

1 

44.091 

38.614 

.456 

.324105 

.335413 

45.919 

40.149 

.481 

.324412 

.335873 

1 

2 

63.782 

58.490 

.441 

.512114 

.523575 

66.366 

60.781 

.465 

.512607 

.524236 

2 

3 

83.840 

78.730 

.426 

.649307 

.660936 

87.177 

81.769 

.451 

.650009  .661822 

3 

4 

104.253 

99.315 

.412 

.758835 

.770648 

108.331103.090 

.437 

.759776  .771790 

1 

4 

5 

125.001 

120.228 

.398 

0.851031 

0.863045 

129.808124.724 

.424 

0.852241 

0.864476 

5 

6 

146.069 

141.449 

.385 

.931423 

.943658 

151.581146.635 

.412 

.932943 

.945425 

6 

7 

167.425 

162.941 

.374 

1.003337 

1.015819 

173.624168.809 

.401 

1.005208 

1.017956 

7 

8 

189.046 

184.691 

.363 

.068933 

.081681 

195.905191.198 

.392 

.071198 

.084246 

8 

9 

210.902 

206.653 

.354 

.129703 

.142751 

218.396  213.791 

.384 

.132416 

.145786 

9 

10 

232.963 

228.814 

.346 

1.186735 

1.200105 

241.0751236.556 

.377 

1.189945 

1.203670 

10 

11 

255.209 

251.144 

.339 

.240843 

.254568 

263.903:259.447 

.371 

.244617 

.258735 

11 

12 

277.601 

273.598 

.334 

.292679 

.306797 

286.839  282.429 

.368 

.297088 

.31163? 

12 

13 

300.099 

296.140 

.330 

.342768 

.357317 

309.856 

305.480 

.365 

.347885 

.362903 

13 

14 

322.676 

318.751 

.327 

.391542 

.406560 

332.913 

328.542 

.364 

.397454 

.412993 

14 

15 

345.291 

341.372 

.327 

1.439382 

1.454921 

355.965 

351.585 

.365 

1.446188 

1.462297 

15 

16 

367.904 

363.975 

.327 

.486625 

.502734 

378.972 

374.557 

.368 

.494432 

.511170 

16 

17 

390.471 

386.508 

.330 

.533581 

.550319 

401.873 

397.385 

.374 

.542504 

.559926 

17 

18 

412.934 

408.900 

.336 

.580532 

.597954 

424.667 

420.147 

.377 

.590704 

.608885 

18 

19 

435.294 

431.227 

.339 

.627755 

.645936 

447.324 

442.697 

.386 

.639316 

.658317 

19 

20 

457.517 

453.347 

.347 

1.675512 

1.694513 

469.747 

464.995 

.396 

1.688628 

1.708546 

20 

21 

479.512 

475.218 

.358 

.724078 

.743996 

491.915 

487.031 

.407 

.738930 

.759841 

21 

22  501.256 

496.833 

.369 

.773726 

.794637 

513.791 

508.749 

.420 

.790508 

.812515 

22 

23  523.715 

518.137 

.382 

.824732 

.846739 

535.336 

530.120 

.435 

.843667 

.866871 

23 

24 

543.848 

539.099 

.396 

.877391 

.900595 

556.519 

551.115 

.450 

.898710 

.923223 

24 

25 

564.626 

559.693 

.411 

1.932000 

1.956513 

577.292 

571.665 

.469 

1.955992 

1.981956 

25 

26 

585.001 

579.849 

.429 

.988903 

2.014867 

597.617 

591.766 

.488 

2.015862 

2.043399 

26 

27 

604.938 

599.567 

.448 

2.048447 

.075984 

617.484 

611.399 

.507 

.078682 

.107938 

27 

28 

624.425 

618.824 

.467 

.110984 

.140240 

636.853 

630.504 

.529 

.144877 

.176034 

28 

29 

643.424 

637.564 

.488 

.176939 

.208096 

655.694 

649.082 

.551 

.214897 

.248120 

29 

30 

661.906 

655.787 

.510 

2.246754 

2.279977 

673.999 

667.113 

.574 

2.289207  2.324690 

30 

31 

679.860 

673.474 

.532 

.320892 

.356375 

691.751 

684.586 

.597 

.368335  .406291 

31 

32 

697.273 

690.613 

.555 

.399876 

.437832 

708.952 

701.515 

.620 

.452837 

.493483 

32 

33 

714.146 

707.219 

.577 

.484258 

.524904 

725.598 

717.877 

.643 

.543353 

.586959 

33 

34 

730.473 

723.268 

.600 

.574678 

.618284 

741.715 

733.750 

.664 

.640532 

.687324 

34 

35 

746.283 

738.838 

.620 

2.671779 

2.718571' 

757.342 

749.131 

.684 

2.745128  2.795439 

35 

36 

761.612 

753.925 

.641 

.776312 

.826623 

772.538 

764.143 

.700 

.857950'  .912054 

36 

37 

776.517 

768.650 

.656 

.889086 

.943190 

787.459 

778.972 

.707 

.979799  3.037992 

37 

38 

791.153 

783.195 

.663 

3.010899 

3.069092 

802.249 

793.722 

.711 

3.111782,  .174545 

38! 

39 

805.660 

797.664 

.666. 

.142855 

.205618 

817.243 

808.961 

.690 

.2548401  .322373 

39 

40 

820.368 

812.612 

.646 

3.285893 

3.353426 

831.602 

822.441 

.763 

3.414277,3.489947 

40 

41 

834.453 

825.834 

.718 

.445315 

.520985 

844.077 

833.910 

.847 

.595252  .679851 

41 

42 

846.689 

837.084 

.800 

.626281 

.710880J 

855.176 

844.638 

.878 

.797429 

.889806 

42 

43 

857.576 

847.607 

.831 

.828452 

.920829 

865.710 

854.979 

.894 

4.020868|4.121378 

43 

48.   TT  =  30.4602. 

49.   7r  =  31.8029. 

Continued  on  Page  *180. 


♦17^ 


TABLE    LXIII. 


GENERAL  VALUATION  OF  ANNUAL  PREMIUM  POLICIES  OF  1,000. 

4  PER  CENT. 


n. 

50. 

51. 

n. 

V. 

6m. 

V. 

12m. 

-^m.d. 

A(B/). 

6m. 

AB. 
12m. 

V. 

6m. 

V. 

12m. 

4m.d. 

6m. 

-AB. 
12m. 

0 

26.952 

20.675 

.523 

0.011770 

0.023231 

28.120 

21.497 

.552 

0.011951 

0.023580 

0 

1 

47.815 

41.727 

.507 

.324751 

.336380 

49.800 

43.361 

.537 

.325123 

.336936 

1 

2 

69.047 

63.139 

.492 

.513148 

.524961 

71.838 

65.574 

.522 

.513741 

.525755 

2 

3 

90.630 

84.893 

.478 

.650780 

.662794 

94.215 

88.113 

.509 

.651626 

.663861 

3 

4 

112.543 

106.966 

.465 

.760807 

.773042 

116.897 

110.940 

.496 

.761945 

.774427 

4 

5 

134.758 

129.321 

.453 

0.853574 

0.866056 

139.862 

134.042 

.485 

0.855044 

0.867792 

5 

6 

157.247 

151.945 

.442 

.934618 

.947366 

163.076 

157.368 

.476 

.936462 

.949510 

6 

7 

179.981 

174.789 

.433 

1.007268 

1.020316 

186.508 

180.905 

.467 

1.009539 

1.022909 

7 

8 

202.928 

197.840 

.424 

.073696 

.087066 

210.135 

204.623 

.459 

.076441 

.090166 

8 

9 

226.068 

221.067 

.417 

.135399 

.149124 

233.918 

228.471 

.454 

.138685 

.152803 

9 

10 

249.358 

244.422 

.411 

1.193480 

1.207598 

257.813 

252.414 

.450 

1.197378 

1.211927 

10 

11 

272.760 

267.870 

.408 

.248778 

.263327 

281.793 

276.429 

.447 

.253358 

.268376 

11 

12 

296.244 

291.389 

.405 

.301944 

.316962 

305.813 

300.456 

.446 

.307294 

.322833 

12 

13 

319.768 

314.919 

.404 

.353523 

.369062 

329.831 

324.463 

.447 

.359739 

.375848 

13 

14 

:J43.288 

338.430 

.405 

.403973 

.420082 

353.801 

348.396 

.450 

.411161 

.427899 

14 

15 

366.763 

361.867 

.408 

1.453693 

1.470431 

377.659 

372.179 

.457 

1.461968 

1.479390 

15 

16 

390.127 

385.159 

.414 

.503039 

.520461 

401.407 

395.893 

.459 

.512535 

.530716 

16 

17 

413.384 

408.382 

.417 

.552346 

.570527 

425.011 

419.387 

.469 

.563198 

.582199 

17 

18 

436.501 

431.391 

.426 

.601920 

.620921 

448.373 

442.617 

.480 

.614295 

.634213 

18 

19 

459.379 

454.140 

.437 

.652071 

.671989 

471.467 

465.575 

.491 

.666150 

.687061 

19 

20 

481.996 

476.624 

.448 

1.703104 

1.724015 

494.259 

488.201 

.505 

1.719079 

1.741086 

20 

21 

504.318 

498.783 

.461 

.755319 

.777326 

516.704 

510.466 

.520 

.773414 

.796618 

21 

22 

526.299 

520.587 

.476 

.809033 

.832237 

538.774 

532.339 

.536 

.829479 

.853992 

22 

23 

547.911 

542.008 

.492 

.864560 

.889073 

560.414 

553.748 

.556 

.887644 

.913608 

23 

24 

569.105 

562.974 

.511 

'  .922260 

.948224 

581.591 

574.691 

.575 

.948279 

.975816 

24 

25 

589.843 

583.484 

.530 

1.982493 

2.010030 

602.288 

595.144 

.595 

2.011752 

2.041008 

25 

26 

610.114 

603.515 

.550 

2.045624  .0748801 

622.467 

615.048 

.618 

.078508 

.109665 

26 

27 

629.875 

623.007 

.572 

.112085 

.143242 

642.097 

634.403 

.641 

.149002 

.182225 

27 

28 

649.098 

641.962 

.595 

.182329 

.215552 

661.167 

653.189 

.665 

.223712 

.259195 

28 

29 

667.775 

660.359 

.618 

.256830 

.292313 

679.662 

671.393 

.689 

.303173 

.341129 

29 

30 

685.887 

678.187 

.642 

2.336116 

2.374072 

697.582 

689.030 

.713 

2.387949 

2.428595 

30 

31 

703.437 

695.459 

.665 

.420748 

.461394 

714.925 

706.077 

.737 

.478689 

.523295 

31 

32 

720.420 

712.153 

.689 

.511371 

.554977 

731.716 

722.614 

.758 

.576049 

.622841 

32 

33 

736.865 

728.349 

.710 

.608637 

.655429 

747.997 

738.638 

.780 

.680786 

.731097 

33 

34 

752.809 

744.041 

.731 

.713299 

.763610 

763.829 

754.277 

.796 

.793719 

.847823 

34 

35 

768.313 

759.358 

.746 

2.826174 

2.880278 

779.372 

769.726 

.804 

2.915653 

2.973846 

35 

36 

783.537 

774.487 

.754 

.948064 

3.006257 

794.781 

785.094 

.807 

3.047699 

3.110462 

36 

37 

798.626 

789.537 

.757 

3.080077 

.142840 

810.404 

800.971 

.786 

.190804 

.258337 

37 

38 

813.925 

805.086 

.737 

.223157 

.290690 

825.363 

815.014 

.862 

.350273 

.425943 

38 

39 

828.576 

818.838  .811 

.382610 

.458280 

838.360 

826.963 

.950 

.531271 

.615870 

39 

40 

841.304 

830.541  .897 

3.563596 

3.648195 

849.922 

838.140 

.982 

3.733462 

3.825839 

40 

41 

852.627 

841.486  .928 

.765780 

.858157 

860.898 

848.913 

.999 

.956910 

4.057420 

41 

42 

863.376 

852.037 

.945 

.989223 

4.089733 

871.393 

859.132 

1.022 

4.204932 

.314823 

42 

43 

873.655 

862.045 

.968 

4.237242 

.347133 

1 

881.483 

869.091 

1.033 

.481379 

.601459 

43 

50.   TT  =  33.2283. 

51.   7r  =  34.7419. 

Continued  on  Page  *179. 


♦176 


TABLE     LXIII 


GENERAL  VALUATION  OF  ANNUAL  PREMIUM  POLICIES  OF  1,000. 

4  PER   CENT. 


'-a 

1  o  «> 

x=52. 

53. 

V. 

V. 

2ni.d. 

A(B/). 

AB. 

V. 

V. 

-J^m.d. 

^(B/). 

AB. 

n. 

6m. 

12ra. 

6m. 

12in. 

6m. 

12m. 

6m. 

12m. 

n. 
0 

0 

29.347 

22.344 

.584 

0.012143 

0.023956 

30.640 

23.219 

.618 

0.012355 

0.024369 

1 

51.870 

45.045 

.569 

.325528 

.337542 

1  54.029i  46.780 

.604 

.325974 

.338209  1 

2 

74.737 

68.079 

.555 

.514390 

.526625  77.741!  70.642 

.592 

.515109 

.527591 

2 

3 

97.918 

91.408 

.543 

.652558 

.6650401 101. 747i  94.791 

.580 

.653587 

.666335 

3 

4 

131.388 

115.017 

.531 

.763199 

.775947  126.012:119.174 

.570 

.764580 

.777628 

4 

5 

145.111 

138.856 

.521 

0.856661 

0.869709  ;i50.507  143.779 

.561 

0.858445 

0.871815 

5 

6 

169.058 

162.910 

.512 

.938495 

.951865  Il75.205168.571 

.553 

.940729 

1  .954454 

6 

7 

193.205 

187.149 

.505 

1.012034 

1.025759  |200.066:i93.501 

.547:1.014782 

!l.028900 

7 

8 

217.510 

211.521 

.499 

.079464 

.093582  Ij225.045;218.529 

.543 

.082798 

.097347 

8 

9 

241.930 

235.990 

.495 

.142307 

.156856  !250. 110:243.632 

.540 

.146295 

.161313 

9 

10 

266.437 

260.533 

.492 

1.201669 

1.216687  275.220'268.748 

.539 

1.206397 

1.221936 

10 

11 

290.985 

285.087 

.491 

.258404 

.273943 

1300.326 

293.843 

.540 

.263967 

.280076 

11 

12 

315.^29 

309.622 

.492 

.313191 

.329300 

325.382 

318.861 

.543 

.319696 

.336434 

12 

13 

340.026 

334.080 

.496 

.366593 

.383331 

350.321 

343.722 

.550 

.374152 

.391574 

13 

14 

364.408 

358.386 

.502 

.419086 

.436508  375.147 

368.511 

.553 

.427831 

.446012 

14 

15 

388.679 

382.621 

.505 

1.471097 

1.489278  399.820 

393.069 

.563 

1.481162 

1.500163' 15 

16 

412.801 

406.631 

.514 

.523003 

.  542004  i  1424. 240 

417.352 

.574 

.534556 

.554474' 16 

17 

436.676 

430.371 

.525 

.575172 

.595090  |448.382|441. 351 

.586 

.588392 

.609303:17 

18 

460.277 

453.834 

.537 

.627954 

.648865' 

472.207 

465.003 

.600 

.643034 

.665041' 18 

19 

483.571 

476.957 

.551 

.681688 

.703695 

495.670 

488.277 

.616 

.698847 

.722051 

19 

20 

506.509 

499.711 

.567 

1.736718 

1.759922 

518.739  511.142 

.633 

1.756189 

1.780702 

20 

21 

529.063 

522.065 

.583 

.793385 

.817898! 

541.362 

533.521 

.653 

.815454 

.841418 

21 

22 

551.179 

543.944 

.603 

.852069 

.878033 

563.497 

555.413 

.674 

.877034 

.904571 

22 

23 

572.821 

565.347 

.623 

.913151 

.940688 

585.133 

576.794 

.695 

.941318 

.970574 

23 

24 

593.973 

586.250 

.644 

.977007 

2.0062631 

606.227|597.600 

.719 

2.008763 

2.039920 

24 

25 

614.596 

606.591 

.667 

2.044089 

2.075246 

626.746'617.832'  .743 

2.079840 

2.113063 

25 

26 

634.656 

626.371 

.690 

.114858 

.148081! 

646.681637.469  .768 

.155039 

.190522 

26 

27 

654.145 

645.570 

.715 

.189801 

.225284 

666.013|656.498^  ,793 

.234907 

.272863 

27 

28 

673.047 

664.173 

.739 

.269455 

.307411 

684.747674.935:  .818 

.320019 

.360665 

28 

29 

691.360 

682.198 

.764 

.354390 

.395036, 

702.874  692. 754i  .843 

.411032 

.454638 

29 

30 

709.084 

699.619 

.789 

2.445260 

2.488866' 

720.428  710. 04ll  .866 

2.508611 

2.555403 

30 

31 

726.244 

716.520 

.810 

.542723 

.589515' 

737.446  726.791:  .888 

.613522 

.663833 

31 

32 

742.883 

732.896 

.832 

.647543 

.697854 

753.995 

743.140  .905 

.726589 

.780693  32 

33 

759.063 

748.879 

.849 

.760540 

.814644 

770.245 

759.289  .913 

.848626 

.906819 

33 

34 

774.948 

764.667 

.857 

.882523 

.940716 

786.351 

775.353 

.917 

.980750 

3.043513 

34 

35 

790.694  780.372 

.860 

3.014606 

3.077369 

802.681 

791.949 

.894 

3.123910 

3.191443 

35 

36 

806.660 

796.598 

.838 

.157737 

.225270  818.319 

806.629:  .9741  .283420 

.359090 

36 

37 

821.949 

810.950 

.917 

.317225 

.392895  '831.904 

819.120'1.065!  .464444 

.549043 

37 

38 

835.231 

823.162 

1.006 

.498236 

.582835  843.992 

830.803 

1.099!  .666653 

.759030 

38 

39 

847.048 

834.584 

1.039 

.700435 

.792812; 

855.464 

842.065 

1.117  .890112 

.990622 

39 

40 

858.264 

845.594 

1.056 

3.923888 

4.0243981 

866.436 

852.747 

1.141 

4.138140 

4.248031 

40 

41 

868.991 

856.038 

1.079 

4.171913 

.281804' 

876.982 

863.157 

1.152 

.414590 

.534670 

41 

42 

879.301 

866.214 

1.091 

.448362 

.568442 1 1887. 874  874.531! 

1.112 

.722205 

.852747 

42 

43 

889.949 

877.334 

1.051 

.755976 

.8865181 

898.602  884.614 

1.166 

5.077717 

5.225174 

43 

44 

900.438 

887.192 

1.104 

5.111488 

5.2589451 

44 

52.    7r  — 36.3501. 

53.   7r  =  38.0599. 

TABLE    LXIII. 


*177 


GENEIIAL  VALUATION  OF  ANNUAL  PREMIUM  POLICIES  OF  1,000. 

4  PER  CENT. 


54. 

66. 

^S 

V. 

V. 

4m.d. 

A(B/). 

XB. 

V. 

V. 

^m.d. 

X{Bf). 

AB. 

n. 

6m. 

12m. 

6m. 

12m. 

6m. 

12m. 

6m. 

12ra. 

n. 
0 

0 

32.000 

24.121 

.657 

0.012590 

0.024825' 

33.424 

25.033 

.699 

0.012851 

0.025333 

1 

56.275 

48.550 

.644 

.326471 

.338953 

58.608 

50.367 

.687 

.327016 

.339764 

1 

2 

80.851 

73.273 

.632 

.515902 

.528650 

84.064 

75.947 

.676 

.516776 

.529824 

2 

3 

10.5.694 

98.236 

.621 

.654721 

.667769 

109.761 

101.759 

.667 

.655969 

.669339 

3 

4 

130.771 

123.426 

.612 

.766103 

.779473 

135.671 

127.768 

.659 

.767775 

.781500 

4 

5 

156.056 

148.807 

.604  0.860405 

0.874130 

161.752 

153.921 

.653 

0.862562 

0.876680 

5 

6 

181.507174.329 

.598  j  .943189 

.957307 

187.956 

180.177 

.646 

.945901 

.960450 

6 

7 

207.0801199. 952 

.594  1.017813 

1.032362 
.101486 

214.253  206.513 

.645 

1.021148 

1.036166 

7 

8 

232.742|225.652 

.591 

.086468 

240.594|232.861 

.644 

.090511 

.106050 

8 

9 

258.4481251. 365 

.590 

.150690 

.166229 

266.932  259.188 

.645 

.155532 

.171641 

9 

10 

284.150  277.057 

.591 

1.211610 

1.227719 

293.218  285.433 

.649 

1.217360 

1.234098 

10 

11 

309.803 

302.669 

.595 

.270105 

.286843 

319.381311.514 

.656 

.276869 

.294291 

11 

12 

335.334 

328.121 

.601 

.326868 

.344290 

345.425  337.520 

.659 

.334781 

.352962 

12 

13 

360.750 

353.499 

.604 

.382491 

.400672 

371.309  363.284 

.669 

.391685 

.410686 

13 

14 

386.010 

378.642 

.614 

.437472 

.456473 

396.929  388.758 

.681 

.448111 

.468029 

14 

15 

411.011 

403.502 

.626 

1.492270 

1.512188 

422.254  413.935 

.693 

1.504537 

1.525448 

15 

16 

435.726 

428.071 

.638  .547312 

.568223 

447.249  438.748 

.708 

.561391 

.583398 

16 

17 

460.118 

452.286 

.653 

.602984 

.624991 

471.863  463.163 

.725 

. .619102 

.642306 

17 

18 

484.139 

476.112 

.669 

.659685 

.682889 

496.064  487.150 

.743 

.678070 

.702583 

18 

19 

507.756 

499.521 

.686 

.717790 

.742303 

519.796  510.628 

.764 

.738731 

.764695 

19 

20 

530.916 

522.432 

.707 

1.777712 

1.803676 

543.019  533.594 

.785 

1.801501 

1.829038 

20 

21 

553.577 

544.844 

.728 

.839851 

.867388 

565.716i556.024 

.808 

.866797 

.896053 

21 

22 

575.729 

566.734 

.750 

.904610 

.933866 

587.846 

577.852 

.833 

.935103 

.966260 

22 

23 

597.323 

588.034 

.774 

.972462  2.003619 

609.372 

599.077 

.858 

2.006903 

2.040126 

23 

24 

618.331 

608.748 

.799  2.043879 

.077102 

630.284 

619.677 

.884 

.082711 

.118194 

24 

25 

638.739 

628.851 

.824  2.119367 

2.154850 

650.566 

639.640 

.910 

2.163082 

2.201038 

25 

26 

658.531 

648.333 

.850  .199471 

.237427 

670.219 

658.982 

.936 

.248609 

.289255 

26 

27 

677.710 

667.208 

.875 

.284780 

.325426 

689.236 

677.676 

.963 

.339957 

.383563 

27 

281696.269 

685.450 

.902 

.375951 

.419557 

707.651 

695.811 

.987 

.437805 

.484597 

28 

29 

714.238 

703.148 

.924 

.473657 

.520449 

725.505 

713.383 

1.010 

.542930 

.593241 

29 

30 

731.662 

720.296 

.947 

2.578669 

2. 628980 

742.866 

730.534 

1.028 

2.656166 

2.710270 

30 

31 

748.604 

737.034 

.964!  .691818 

.745922 

759.912 

747.476 

1.036 

.778327 

.836520 

31 

32 1765.240 

753.567 

.973 

.813912 

.872105 

776.810 

764.328 

1.040 

.910546 

.973309 

32 

33,781.730 

770.013 

.976 

.946081 

3.008844 

793.941 

781.739 

1.017 

3.053775 

3.121308 

33 

34 

798.448 

787.004 

.954 

3.089275 

.156808 

810.346 

797.139 

1.101 

.213334 

.289004 

34 

35 

814.457 

802.032 

1.035 

3.248807 

3.324477 

824.599 

810.243 

1.196 

3.394392 

3.478991 

35 

36 

828.366 

814.820 

1.129 

.429848 

.514447 

837.279 

822.500 

1.232 

.596622 

.688999 

36 

!37 

840.740 

826.781 

1.163 

.632067 

.724444 

849.314 

834.314 

1.250 

.820094 

.920604 

37 

38 

852.485 

838.310 

1.181 

.855532 

.956042 

860.825 

845.521 

1.275 

4.068129 

4.178020 

38 

39 1863.718 

849.247 

1.206 

4.103563 

4.213454 

871.889 

856.441 

1.287 

.344586 

.464666 

39 

40  874.515 

859.904 

1.218 

4.380017 

4.500097 

883.314 

868.373 

1.245 

4.652202 

4.782744 

40 

41  885.665 

871.548 

1.176 

.687632 

1  .818174 

894.570 

878.951 

1.302 

5.007715 

5.155172 

41 

42 

896.649 

881.871 

1.231 

5.043145 

:5. 190602 

907.380j893.993 

1.116 

.410448 

.570149 

42 

54.   Tr  =  39.8789. 

55.   7T  =  41.8154. 

^178 


TABLE    LXIII 


GENERAL  VALUATION  OF  ANNUAL  PREMIUM  POLICIES  OF  1,000. 

4  PER  CENT. 


;a3 


0 

1 

2 
3 

4 

5 
6 

7 
8 
9 

10 
11 
12 
13 
14 

15 
16 
17 
18 
19 

20 
21 
22 
23 
24 

25 
26 
27 
28 
29 


X  =  56. 


V. 

6m. 


30 
31 
32 


34.930 

61.041 

87.396 

113.973 

140.723 

167.600 
194.572 
221.589 
248.604 
275.564 

302.400 
329.111 
355.661 
381.938 
407.914 

433.550 

458.796 
483.620 
507.961 
531.779 

555.060 
577.757 
599.836 
621.285 
642.088 

662.245 
681.751 
700.638 
718.950 
736.758 


V. 

12m. 


754.241 
771.573 

789.144 
33  805.971 
34i820.589 


35 '833.594 

36  845.939 

37  857.745 

38  869.093 

39  880.812 

I 

40  892.357 


41 
42 


905.496 
926.405 


25.984 

52.221 

78.696 

105.373 

132.197 

159.128 
186.139 
213.164 
240.167 
267.086 

293.837 
320.510 
346.936 
373.064 

398.887 

424.337 
449.380 
473. 983 
498.063 
521.619 

544.625 
567.013 

588.783 
609.912 
630.388 

650.226 
869.400 
688.000 
706.024 
723.615 


^mA. 


740.992 
758.277 
776.135 
791.931 
805.371 

817.942 
830.060 
841.554 
852.755 
864. 994 

875.843 
891.272 
917.662 


.745 
.735 

.725 
.717 
.711 

.706 
.703 
.702 
.703 
.706 

.714 

.717 
.727 
.740 

.752 

.768 
.785 
.803 
.825 
.847 

.870 
.895 
.921 
.948 
.975 

1.002 
1.029 
1.053 
1.077 
1.095 


A(B/). 
6m. 


0.013135 
.327616 
.517736 
.657338 
.769614 

0.864939 
.948885 

1.024822 
.094965 
.160875 

1.223696 
.284333 
.343503 
.401831 
.459862 


AB. 

12m. 


0.025883 
.340664 
.531106 
.671063 
.783732 

0.879488 
.963903 

1.040361 
.111074 
.177613 

1.241118 
,302514 
362504 
421749 
480773 


57. 


V. 

6m. 


1.518076  1.540083 
.576944  .600148 


36.505 

63.564 

90.849 

118.314 

145.907 

173.598 
i  201. 338 
'229.072 
256.752 
284.302 

311.727 
338.985 
365.963 
392.632 
418.952 


.636897 
.698397 
.761881 


.661410 
.724361 

.789418 


1.827783  1.857039 
.896600;  .927757 
.968831  2.002054 

2.0449981  .080481 
.125667  .163623 

2.211438'2.252084 


V. 
12m. 

26.937 

54.118 

81.507 

109.047 

136.695 

164.428 
192.174 
219.897 
247.534 
274.998 

302.383 
329.514 
356.339 

382.851 
408.980 


im.d, 


444. 8721434. 691 


470.357 
495.348 
519.801 


459.950 
484.673 
508.857 


543.704  532.477 


567.006 
589.674 
611.696 
633.053 
653.748 


1.104 
1.108 
1.084 
1.170 
1.268 

1.304 
1.323 
1.349 
1.361 
1.318 


.302984 
.400991 
.506242 
.619575 

2.741811 

.874085 

3.017354 

.176942 

.358020 

3.560262 
.783742 

4.031781 
.308241 
.615858 


1.376  4.971372 
1.185  15.374105 
0.729  I  .847673 


.346590 
.447783 
.556553 
.673679 

2.800004 
.936848 

3.08488 
.252612 
.442619 

3.652639 
884252 

4.141672 
.428321 
.746400 

5.118829 

533806 

6.027960 


56. 


77  =  43.8764. 


555.462 
577.813 
599.506 
620.528 
640.895 


673.774  660.580 
693.165  679.677 


711.966 
730.248 
748.198 


698.181 
716.242 
734.082 


765.992:751.828 


784.032 
801.308 
816.316 
829.668 

842.342 
854.464 
866.114 
878.146 
889.998 


770.163 
786.380 
800.179 
813.085 

825.526 
837.328 
848.827 
861.392 
872.531 


903.488  888.371 
924.955  915.465 


.797 
.787 
.779 
.772 
.751 

.768 
.764 
.765 
.768 

.775 

.779 
.789 
.802 
.815 
.831 

.848 
.867 
.889 
.912 
.936 

.962 

.988 

1.016 

1.044 

1.071 

1.099 
1.124 
1.149 
1.167 
1.176 

1.180 
1.156 
1.244 

1:345 

1.382 

1.401 
1.428 
1.441 
1.396 
1.456 

1.260 
0.791 


6m. 


0.013452 

.328277 
.518790 
.658846 


AB. 
12m. 


0.026500 
.341647 
.532515 
.672964 


.771642  .786191 


0.867556 
.952172 

1.028870 
.099880 
.166762 

1.230688 
.292560 
.353131 
.413038 
.472832 


0.882574 
.967711 

1.044979 
.116618 
.184184 

1.248869 
.311561 
.373049 
.433949 
.494839 


1.533034  1.55G238  15 


.594117 
.656575 

.720871 
.787461 

1.856856  1 
.929573 

2.006144 
.087148 
.173193 


o  a> 


0 

1 

2 
3 

4 

5 
6 

7 
8 
9 

10 
11 
12 
13 
14 


2.264962 
.363147 
.468538 
.581980 
.704299 

2.836635 
.979950 

3.139570 
.320669 
.522925 

3.746413 
994458 

4.270920 
.578540 
.934054 

5.336787 
.810356 


.618630116 
.6825391 17 
.7484081 18 
.816717  19 

.888013  20 
.962796  21 
.041627122 
.125104  23 
.213839  24 

.308568' 25 
.409939  26 
,518849  27 
,636084  28 
,762492129 


2.899398 

3.047483 

.215240 

.405268 

.615302 

3.846923 

4.104349 

391000 

709082 

5.081511 

5.496488 
.990643 


57. 


77  =  46.0730. 


30 
31 
32 
33 
34 

35 
36 
37 
38 
39 

40 
41 


♦179 


TABLE    LXIII 


GENERAL  VALUATION  OF  ANNUAL  PREMIUM  POLICIES  OF  1,000. 

4  PER  CENT. 


o  o 

n. 
0 

58.   77  =  48.4132. 

59.   7T  =  50.9095. 

n. 

V. 

6m. 

V. 
12m. 

|m.d. 

6m. 

AB. 

12m, 

V. 

6m. 

V. 

12m. 

l^m.d. 

6m. 

AB. 

12m. 

38.173 

27.933 

.853 

0.013795 

0.027165 

39.933 

28.956 

.915 

0.014173 

0.027898 

0 

1 

66.213 

56.080 

.844 

.328998 

.342723 

68.969 

58.071 

.908 

.329795 

.343913 

1 

2 

94.438 

84.383 

.838 

.519949 

.534067 

98.141 

87.302 

.903 

.521229 

.535778 

2 

3 

122.797 

112.797 

.833 

.660507 

.675056 

'127.417 

116.621 

.900 

.662336 

.677354 

3 

4 

151.253 

141.297 

.830 

.773873 

.788891 

156.742 

145.954 

.899 

.776330 

.791869 

4 

5 

179.761 

169.811 

.829 

0.870437 

0.885976 

186.064 

175.264 

.900 

0.873613 

0.889722 

5 

6 

208.263 

198.302 

.830 

.955794 

.971903 

215.328 

204.482 

.904 

.959790 

.976528 

6 

7 

236.709 

226.704 

.834 

1.033336 

1.050074 

244.455 

233.518 

.911 

1.038258 

1.055680 

7 

8 

265.023 

254.928 

.841 

.105296 

.122718 

273.449 

262.469 

.915 

.111272 

.129453 

8 

9 

293.206 

283.071 

.845 

.173258 

.191439 

302.265 

291.152 

.926 

.180419 

.199420 

9 

10 

321.218 

310.953 

.855 

1.238395 

1.257396 

330.788 

319.513 

.940 

1.246903 

1.266821^10 

11 

348.944 

338.521 

.869 

.301642 

.321560 

358.982 

347.541 

.953 

.311673 

.332584  11 

12 

376.350 

365.767 

.882 

.363764 

.384675 

i386.808 

375.165 

.970 

.375503 

.397510 

12 

13 

403.400 

392.619 

.898 

.425408 

.447415 

414.211 

402.347 

.989 

.439074 

.462278 

13 

14 

430.037 

419.042 

.916 

.487160 

.510364 

441.154 

429.051 

1.009 

.502984 

.527497 

14 

15 

456.227 

445.000 

.936 

1.549549 

1.574062 

1467.575 

455.189 

1.032 

1.567818 

1.593782 

15 

16 

481.910 

470.407 

.959 

.613109 

.639073 

1493.428 

480.757 

1.056 

.634113 

.661650 

16 

17 

507.041 

495.261 

.982 

.678334 

.705871 

'518.697 

505.728 

1.081 

.702384 

.731640 

17 

18 

531.604 

519.5.35 

1.006 

.745707 

.774963 

543.333 

530.028 

1.109 

.773188 

.804345 

18 

19 

555.552 

543.156 

1.033 

.815760 

.846917 

567.298 

553.658 

1.137 

.847083 

.880306 

19 

20 

578.848 

566.126 

1.060 

1.889028 

1.922251 

590.580 

576.592 

1.166 

1.924631 

1.960114 

20 

21 

601.479 

588.419 

1.088 

.966056 

2.001539 

613.159 

598.816 

1.195 

2.006442  2.044398 

21 

22 

623.427 

610.023 

1.117 

2.047438 

.085394 

635.038 

620.349 

1.224 

.093147]  .133793 

22 

23 

644.695 

630.954 

1.145 

.133793 

.174439 

656.210 

641.161 

1.254 

.1854491  .229055 

23 

24 

665.276 

651.184 

1.174 

.225812 

.269418 

676.710 

661.350 

1.280 

.284061 

.330853 

24 

25 

685.203 

670.810 

1.199 

2.324197 

2.370989 

696.587 

680.913 

1.306 

2.389788 

2.440099 

25 

26 

704.525 

689.826 

1.225 

.429746  .480057 

715.915 

700.007 

1.326 

.503491 

'.557595 

26 

27 

723.313 

708.387 

1.244 

.543311  .597415 

734.892 

718.868 

1.335 

.626008 

.684201 

27 

28 

741.760 

726.721 

1.253 

.665723  .723916 

753.704 

737.629 

1.340 

.758492 

.821255 

28 

29 

760.046 

744.958 

1.257 

2.798128 

.860891 

772.776 

757.013 

1.314 

.901915 

.969448  29 

30 

778.586 

763.800 

1.232 

2.941494 

3.009027 

791.040 

774.158 

1.407 

3.061611 

3.137281  30 

31 

796.339 

780.466 

1.323 

3.101150 

.176820 

806.907 

788.746 

1.513 

.242761 

.327360 

31 

32 

811.763 

794.647 

1.426 

.282273 

.366872 

821.024 

802.391 

1.553 

.445051 

.537428 

32 

33 

825.486 

807.911 

1.465 

.484545 

.576922 

834.422 

815.544 

1.573 

.668560 

.769070 

33 

34 

838.510 

820.696 

1.484 

.708043 

.808553 

847.237 

828.020 

1.601 

.916617 

4.026508 

34 

35 

850.966 

832.824 

1.512 

3.956094 

4.065985 

859.554 

840.178 

1.615 

4.193086 

4.313166 

35 

36 

862.940 

844.642 

1.525 

4.232559 

.352639 

872.275 

853.462 

1.568 

.500710 

.631252 

36 

37 
38 

875.305 
887.485 

857.555 
869.002 

1.480 
1.540 

.540181 
.895695 

.670723 
5.043152 

884.805 

865.238 

1.631 

.856225 

5.003682 

37 

51. 

903.790 

891.899 

50. 

.991 

5.176810  5.324267 

46 

45 

902.165 

889.617 

1.046 

5.144503 

5.291960 

893.739 

882.453 

.941 

4.821300  4.951842 

45 

44 

891.902 

879.971 

.994 

4.788992 

4.919534 

883.535 

871.797 

.978 

.513687|  .633767 

44 

51.   77  =  34.7419. 

50.   TT  =  33.2283. 

Continued  from  Page  *175. 


*180 


TABLE    LXIII. 


GENERAL  VALUATION  OF  ANNUAL  PREMIUM  POLICIES  OF  1,000. 

4  PER  CENT. 


n. 

a;  =  60.  TT  =53.5745. 

61.    77  =  56.4196. 

n. 
0 

V. 

6m. 

V. 

12in. 

Jm.d. 

6m. 

AB. 
12m. 

V. 

6m. 

V. 
12m. 

l^m.d. 

A(B/-). 
6m. 

AB. 

12m. 

0 

41.779 

29.984 

.983' 

0.014592 

0.028710 

43.727 

31.033 

1.058 

0.015054 

0.029603 

1 

71.822 

60.086 

.978 

.330676 

.345225 

74.806 

62.159 

1.054 

.331641 

.346659 

1 

2 

101.970 

90.279 

.974 

.522636 

.537654 

105.940 

93.301 

1.053 

.524183 

.539722 

2 

3 

132.170 

120.487 

.974 

.664348 

.679887 

137.069 

124.418 

1.054 

.666567 

.682676 

3 

4 

162.366 

150.671 

.975 

.779039 

.795148 

168.138 

155.437 

1.058 

.782025 

.798763 

4 

5 

192.502 

180.760 

.979 

0.87711610.893854 

199.060 

186.263 

1.066 

0.880975 

0.898397 

5 

6 

222.498 

210.662 

.986  .964193!  .981615 

229.841 

217.000 

1.070 

.969050 

.987231 

6 

7 

252.357 

240.477 

.990 

1.0436881.061869 

260.436 

247.451 

1.082 

1.049671 

1.068672 

7 

8 

282.033 

270.015 

1.001 

.117859  .136860 

290.715 

277.560 

1.096 

.125128 

.145046 

8 

9 

311.405 

299.221 

1.015 

.188323 

.208241 

320.648 

307.316 

1.111 

.197052 

.217963 

9 

10 

340.440 

328.085 

1.030 

1.256299 

1.277210 

350.190 

336.643 

1.129 

1.266672 

1.288679 

10 

11 

369.096 

356.533 

1.047 

.322746 

.344753 

379.282 

365.501 

1.148 

.334978 

.358182 

11 

12 

397.316 

384.526 

1.066 

.388471 

.411675 

407.886 

593.852 

1.170 

.402793 

.427306 

12 

13 

425.063 

412.026 

1.086 

.454167 

.478680 

435.936 

421.600 

1.195 

.470862 

.496826 

13 

14 

452.272 

438.943 

1.111 

.520487 

.546451 

463.382 

448.744 

1.220 

.539848 

.567385 

14 

15 

478.895 

465.273 

1.135 

1.588023 

1.615560 

490.210 

475.255 

1.246 

1.610360 

1.639616 

15 

16 

504.918 

490.989 

1.161 

.657331 

.686587 

516.364 

501.053 

1.276 

.683027 

.714184 

16 

17 

530.288 

516.014 

1.190 

.728998 

.760155 

541.806 

526.140 

1.305 

.758466 

.791689 

17 

18 

554.968 

540.348 

1.218 

.803611 

.836834 

566.524 

550.48811.336 

.837290 

.872773 

18 

19 

578.944 

563.966 

1.248 

.881753 

.917236 

590.496  574.0831.368 

.920149 

.958105 

19 

20 

602.197 

586.854 

1.279 

1.964052 

2. 002008 

613.723  596.9431.398 

2.007708 

2.048354 

20 

21 

624.729 

609.029 

1.308 

2.051156 

.091802 

636.200  619.0381.430 

.100699 

.144305 

21 

22 

646.531 

630.460 

1.339 

.143780 

.187386 

657.9651640.4721.458 

.199859 

.246651 

22 

23 

667.643 

651.252 

1.366 

.242648 

.289440 

679.067|661.24l!l.486 

.306018 

.356329 

23 

24  688.112 

671.398 

1.393 

.348577 

.398888 

699.586  681.5121.506 

.420055 

.474159 

24 

25  708.017 

691.061 

1.413 

2.462436 

2.516540 

719.734  701.5361.516 

2.542825 

2.601018 

25 

26 1727.560  710.485 

1.423 

.585071 

.643264 

739. 705|721.454 1.521 

.675498 

.738261 

26 

27  [746. 9321729. 806 

1.427 

.717644 

.780407 

759.9531742.032:1.493 

.819059 

.886592 

27 

28  766.574  749.767 

1.401 

.861132 

.928665 

779.343 

760.2341.592 

.978853 

3.054523 

28 

29:785.382  767.423 

1.497 

3.020874 

3. 096544 

796.188 

775.7221.706 

3.160070 

.244669 

29 

30 1801. 722  782. 447 

1.606 

3.202055 

3.286654 

811.175 

790.2081.747 

3.362403 

3.454780 

30 

31i816.260j796.499 

1.647 

.404365 

.496742 

825.400 

804.172ll.769 

.585938 

.686448 

31 

32i830.058!810.043 

1.668 

.627887 

.728397 

839.005i817.417|1.799 

.834011 

.943902 

32 

33  1843. 2541822. 892 

1.697 

.875951 

.985842 

852.081 

830.325 

1.813 

4.110487 

4.230567 

33 

34 

855.939  835.412 

1.711 

4.152423 

4.272503 

865.586 

844.427 

1.763 

.418116 

.548658 

34 

35 
36 

869.039  849.092 
881.943  861.219 

1.662 

1.727 

4.460049 
.815565 

4.590591 
.963022 

878.888|856.929!l.830 

4.773633 

4.921090 

35 

49. 

906.763 
897.099 

896.073 

886.992 

48. 

.891 

.842 

5.239465 
4.883955 

5.386922 
.014497 

48 

47 

47s905.321 

894.049 

.939 

5.208451 

5.355908 

46,895.469 

884.790 

1  .890 

4.852941 

4.983483 

887.290 

876.747 

.879 

.576344 

4.696424 

46 

45i885.469 

874.346 

!  .927 

.545329 

.665409 

877.791 

867.372 

.868 

.299901 

.409792 

45 

44 

875.785 

864.788 

J  .916 

.268885 

.378776 

867.908 

857.750 

.847 

.051887 

.152397 

44 

49.    77  =  31.8029. 

48.   77=30.4602. 

Continued  from  Page  *174. 


TABLE     LXIII. 


♦181 


GENERAL  VALUATION  OP  ANNUAL  PREMIUM  POLICIES  OP  1,000. 

4  PER  CENT. 


11 

62.   7r=  59.4582. 

63.,   77  =  62.7079. 

V. 

V. 

^m.d. 

^(B/). 

AB. 

V. 

V. 

|m.d. 

MB/). 

AB. 

n. 

6m. 

12m. 

6m. 

12m. 

6m. 

12m. 

6m. 

12m. 

n. 
0 

0 

45.791 

32.123 

1.139 

0.015557 

0.030575 

47.957 

33.206 

1.229 

0.016117 

0.031656 

1 

77.922 

64.263 

1.138 

.332703 

.348242 

81.150 

66.385 

1.230 

.333876 

.349985 

1 

2 

110.048 

96.375 

1.139 

,525890 

.541999 

114.276 

99.460 

1.235 

.527773 

.544511 

2 

3 

142.110 

128.388 

1.144 

.669013 

.685751 

147.249 

132.  .329 

1.243 

.671708 

.689130 

3 

4 

174.024 

160.202 

1.152 

.785315 

.802737 

180.070 

165.103 

1.247 

.788943 

.807124 

4 

5 

205.791 

191.922 

1.156 

0.885232 

0.903413 

212.691 

197.572 

1.260 

0.889920 

0.908921 

5 

6 

237.365 

223.349 

1.168 

.974401 

.993402 

244.979 

229.677 

1.275 

.980304 

1.000222 

6 

7 

268.614 

254.422 

1.183 

1.056274 

1.076192 

276.895 

261.406 

1.291 

1.063566 

.084477 

7 

8 

299.506 

285.132 

1.198 

.133156 

.154067 

308.396 

292.677 

1.310 

.142016 

.164023 

8 

9 

329.994 

315.398 

1.216 

.206687 

.228694 

339.416 

323.447 

1.331 

.217330 

.240534 

9 

10 

360.018 

345.180 

1.236 

1.278129 

1.301333 

369.915 

353.676 

1.353 

1.290782 

1.315295 

10 

11 

389.538 

374.438 

1.258 

.348487 

.373000 

399.824 

383.264 

1.380 

.363433 

.389^97 

11 

12 

418.486 

403.076 

1.284 

.418636 

.444600 

429.090 

412.208 

1.407 

.436163 

.463700 

12 

13 

446.812 

431.089 

1.310 

.489331 

.516868 

457.696 

440.476 

1.435 

.509753 

.539009 

13 

14 

474.498 

458.449 

1.337 

.561254 

.590510 

485.584 

467.984 

1.467 

.584950 

.616107 

14 

15 

501.490 

485.074 

1.368 

1.635084 

1.666241 

512.713 

494.733 

1.498 

1.662469 

1.695692 

15 

16 

527.748 

510.964 

1.399 

.711483 

.744706 

539.068 

520.695 

1.531 

.742997 

.778480 

16 

;i7 

553.257 

536.092 

1.430 

.791095 

.826578 

564.628 

545.853 

1.565 

.827247 

.865203 

17 

18 

577.996 

560.442 

1.463 

.874598 

.912554 

589.395 

570.229 

1.597 

.915934 

.956580 

18 

19 

601.968 

584.03511.494 

.962681 

2.003327 

613.362 

593.788 

1.631 

2.009829 

2.053435 

19 

20 

625.165 

606.837 

1.527 

2.056091 

2.099697 

636.569 

616.642 

1.661 

2.109709 

2.156501  20 

21 

647.626 

628.957 

1.556 

.155586 

.202378 

659.069 

638.788 

1.690 

.216433 

.266744 

21 

22 

669.403 

650.391 

1.584 

.262008 

.312319 

680.950 

660,403 

1;712 

.330904 

.385008 

22 

23 

690.580 

671.312 

1.606 

.376247 

.430351 

702.432 

681.754 

1.723 

.454006 

.512199 

23 

24 

711.374 

691.977 

1.616 

.499172 

.557365 

723.727 

702.992 

1.728 

.586925 

.649688 

24 

25 

731.984 

712.533 

1.621 

2.631959 

2.694722 

745.318 

724.935 

1.699 

2.730665 

2.798198 

25 

26 

752.881 

733.771 

1.593 

.775604 

.843137 

765.993 

744.343 

1.804 

.890586 

.966256 

26 

27 

772.892 

752.555 

1.695 

.935457 

3.011127 

783.954 

760.857 

1.925 

.3.071889 

3.156488 

27 

28 

790.276 

768.539 

1.811 

3.116714 

.201313 

799.934 

776.304 

1.969 

.274279 

.366656 

28 

29 

805.743 

783.489 

1.854 

.319074 

.411451 

815.103 

791.193 

1.993 

.497847 

.598357 

29 

30 

820.423 

797.900 

1.877 

3.542624 

3.643134 

829.608 

805.316 

2.024 

3.745941 

3.855832 

30 

31 

834.464 

811.570 

1.908 

.790707 

.900598 

843.552 

819.079 

2.039 

4.022428 

4.142508 

31 

32 

847.959 

824.890 

1.922 

4.067188 

4. 187268 

857.951 

834.116 

1.986 

.330062 

.460604 

32 

33 
34 

861.897 

875.625 

839.445 
852.347 

1.871 
1.940 

.374819 
.730338 

.505361 

.877795 

872.136 

847.447 

2.057 

.685583 

.833040 

33 

49 

47. 

909.402 
900.085 

899.781 
891.023 

46. 

.802 

.755 

5.29975815.447215 
4.944248  5.074790 

50 
49 

908.121 

897.981 

.845 

5.269889 

5.417346 

48 

898.636 

889.067 

.797 

4.914379 

.044921 

890.624 

881.145 

.790 

.636639  4.756719 

48 

47 

889.006 

879.010 

.833 

.606769 

4.726849 

881.465 

872.103 

.780 

.360198  .470089 

47 1 

46 

879.682 

869.807 

.823 

.330327 

.440218 

871.935 

862.825 

.759 

.112187i  .212697 

46 1 

45 

869.981 

860.362 

.802 

.082315 

.182825 

861.970 

853.044 

.744 

3.888759  3.981136 

45 1 

44 

859.838 

850.405 

.786 

3.858883 

3.951260 

851.472 

842.896 

.715 

3.686599  3.771198 

44 

47.   7r=  29.1948. 

46.    77  =  28.0014. 

Continued  from  Page  *173. 


*183 


TABLE    LXIII, 


GEKERAL  VALUATION  OP  ANNUAL  PREMIUM  POLICIES  OF  1,000. 

4  PER  CENT. 


•^3 


0 

1 

2 
3 

4 

5 
6 

7 
8 
9 

10 
11 
12 
13 
14 

15 
16 
17 
18 
19 

20 
21 
22 
23 
24 

25 
26 
27 
28 
29 

30 
31 
32 


51 
50 

49 
48 
47 
46 
45 

44 


a;  =  64.  7T  =  66.1832. 


V. 

6m. 


50.251 

84.515 

118.621 

152.569 

186.311 

219.707 
252.720 
285.302 
317.387 
348.935 

379.872 
410.142 
439.730 
468.576 
496.636 

523.898 
550.335 
575.953 
600.744 
624.747 

648.020 
670.652 
692.872 
714.899 
737.230 

758.616 
777.195 
793.723 
809.412 
824.417 

838.838 
853.734 
868.404 


V. 

12m. 


34.318 

68.530 

102.528 

136.427 

170.012 

203.219 
236.038 
268.383 
300:209 
331.478 

362.082 
392.019 
421.258 
449.711 
477.379 

504.233 
530.255 
555.468 
579.836 
603.475 

626.382 
648.739 
670.823 
692.791 
715.487 

735.562 

752.644 
768.620 
784.021 
798.629 

812.865 
828.419 

842.207 


^m.d 


1.328 
1.332 
1.341 
1.345 
1.358 

1.374 
1.390 
1.410 
1.432 
1.455 

1.482 
1.510 
1.539 
1.572 
1.605 

1.639 
1.673 
1.707 
1.742 
1.773 

1.803 
1.826 
L837 
1.842 
1.812 

1.921 
2.046 
2.092 
2.116 
2.149 

2.164 
2.110 
2.183 


6m. 


0.016730 
.335169 
.529844 
.674678 
.792937 

0.895089 
.986824 

1.071612 
.151802 
.229081 

1.304781 
.379966 
.455545 
.532361 
.611199 

1.692801 

.777922 

.867311 

'.961768 

2.062093 

2.169165 
283905 
407210 
540281 
684131 

2.844130 

3.025486 

227910 

451500 

699606 

3.976100 

4.283737 

639260 


AB. 

12m. 


0.032839 
.351907 
.547266 
.692859 
.811938 

0.915007 

1.007735 

.093619 

.175006 

.253594 

1.330745 
.407503 
.484801 
.563518 
.644422 

1.728284 
.815878 
.907957 

2.005374 
.108885 

2.219476 
338009 
465403 
603044 
751664 

2.919800 

3.110085 

320287 

552010 

809497 

4.096180 
414279 

786717 


45. 


910.611 
901.451 

892.151 
883.147 


901.478 
892.869 

883.157 
874.269 


873.778l865.148 


863.983 
853.663 

842.062 


855.533 
845.557 

834.892 


.761 
.715 

.750 
.740 
.719 
.704 
.675 

.598 


5.329103 
4.973594 

4.665985 
.389545 
.141536 

3.918111 
.715956 

3.535015 


5.476560 
.104136 

4.786065 
.499436 
.242046 
.010488 

3.800555 

3.610685 


45.       TT  =  26.8757. 


65. 


V. 

6m. 


V. 

12m. 


35. 

70. 


52.665 

87.981 
123.137105. 
158.077140. 
192.661174. 

226.8461208. 
260.586  242. 
293.8121275. 
326.481307. 
358.517  339. 


427 
634 
737 
516 


|m.d. 


1.437 
1.446 
1.450 
1.463 


77  =  69.9017.  |>.g 
laa 

o« 


A(B/). 
6m. 


903  1.480 


382 
340 
720 
411 


389.863!370.413 
420.503  400.691 
450. 3741430. 155 
479.431|458.806 
507.661486.614 

535.0391513.562 
561.567(539.670 
587.238'564.904 
612.095:589.384 
636. 1951613. 104 


659.631 
682. 642 
705.450 

728.575 
750.721 

769.960 
787.076 
803.323 
818.860 
833. 794 

849.219 
864.411 


636.256 
659.125 
681.873 
705.376 
726.164 

743.853 
760.398 
776.345 
791.473 
806.214 

822.321 
836.600 


1.496 
1.517 
1.539 
1.563 
1.592 

1.621 
1.651 
1.685 
1.719 
1.754 

1.790 
1.825 
1.861 
1.893 
1.924 


0.017409 
.336590 
.532128 
.677946 
.797339 

0.900800 
.994016 

1.080498 
.162604 
.242082 

1.320266 
.398248 
.477002 
.557408 

.640277 

1.726422 
.816633 
.911746 

2.012589 
.120066 


1.948  12.235117 
1.960  .358659 


1.965 
1.933 
2.046 

2.176 
2.223 

2.248 
2.282 
2.298 

2.242 
2.318 


.491905 
.635882 
.795971 

2.977388 

3.179852 

.403466 

.651587 

.928088 

4.235729 
.591254 


AB. 

12m. 


0.034147 
.354012 
.550309 
.696947 
.817257 

0.921711 

1.016023 

.103702 

.187117 

.268046 


n. 


1.347803  10 
.427504J 11 
.5081591 12 


.590631 
.675760 

1.764378 
.857279 
.955352 

2.059381 
.170377 

2.289221 
.416852 
.554668 
.703415 
.871641 

3.061987 
.272229 
.503976 
.761478 

4.048168 

4.366271 

.738711 


44. 


911. 
902. 
893. 

884. 
875. 
865. 
855. 
844. 


752 
740 
592 

734 
518 
882 
729 
318 


831.182 


903.080 
894.611 
885.057 

876.314 
867.341 

857.882 
848.068 

837.577 

825.246 


.723 

.677 
.711 

.702 
.681 
.667 
.638 
.562 

.495 


5.357955 

.002446 

4.694837 


5.505412 

.132988 
4.814917 


4.418398:4.528289 
.170391  .270901 

3.946968!  .039345 
.744818  3.829417 


563883 
3.404507 


.639553 
3.472040 


44.   TT  =  25.8133. 


13 
14 

15 
16 
17 
18 
19 

20 
21 
22 
23 
24 

25 
26 
27 
28 
29 

30 
31 


Continued  from  Page  *172. 


*183 


TABLE    LXIII, 


GENERAL  VALUATION  OF  ANNUAL  PREMIUM  POLICIES  OP  1,000. 

4  PER  CENT. 


O  V 

n. 


0 
1 
2 
3 

4 

5 
6 

7 
8 
9 

10 
11 
12 
13 
14 

15 
16 
17 
18 
19 

20 
21 
22 
23 
24 

25 
26 
27 
28 
29 

30 


66. 


TT  =  73.8817. 


V. 

6ni. 


V. 

12m. 


36.499 

72.893 
108.948 
144.598ll.593 
179.8321.610 


55.191 

91.637 
127.861 
163.714 
199.156 

234.135 

268.582 
302.450 
335.662 
368.160 

399.925 
430.893 
461.018 
490.284 
518.668 

546.170 
572.784 
598.555 
623.539 
647.836 

671.692 
695.338 
719.313 

742.272 
762.217 

779.962  751.597 
796.805  768.131 
812.913l783.814 


im.d, 


1.558 
1.562 
1.576 


214.556 
248.725 
282.293 
315.149 
347.289 

378.679 
409.225 
438.929 
467.758 
495.695 

522.763 
548.924 
574.303 

598.894 
622.896 

646.605 
670.189 
694.555 
716.107 


1.632 
1.655 
1.680 
1.709 
1.739 

1.771 
1.806 
1.841 
1.877 
1.914 

1.951 
1.988 
2.021 
2.054 

2.078 

2.091 
2.096 
2.063 
2.180 


828.397 
844.387 


860.137i830.598 


734.445  2.314 


2.364 
2.389 
2.425 
2.442 
2.383 

2.462 


799.097 
815.795 


A(B/). 
6m. 


0.018151 
.338158 
.534636 
.681545 
.802203 

0.907098 

1.001958 

.090304 

.174556 

.256464 

1.337388 
.418490 
.500777 
.585157 
.672514 

1.763695 
.859579 
.961029 

2.068979 
.184394 

2.308211 
.441661 

.585786 
.745980 
.927468 

3.129977 
.353620 
.601757 
.878267 

4.185913 

4.541440 


AB. 

12m. 


0.035573 
.356339 
.553637 
.701463 
.823114 

0.929105 

1.025162 

.114817 

.200520 

.284001 

1.366644 
.449647 
.534000 
.620640 
.710470 

1.804341 
903185 

2.007821 
.119290 
.238498 

2.366404 
.504424 
.653319 
.821650 

3.012067 

3.222354 
.454130 
.711648 
.998347 

4.316455 

4.688897 


43. 


53  912.830 
52  903.959 
51  894.953 
50  886.234 


49 
48 
47 
46 
45 

44 


877.161 
867.676 
857.681 
846.448 
833.518 

820.015 


904.593 
896.256 
886.852 
878.245 

869.412 
860.101 
850.440 
840.112 

827.974 

814.252 


.686  5.386341 
.642  I  .030832 
.675  14.723224 
.666  .446786 


.646 
.631 
.603 

.528 
.462 


4.198780 

3.975360 

.773214 

.592286 

.432918 


480  3.289958  3.352721 


5.533798 
.161374 

4.843304 
.556677 

4.299290 
.067737 

3.857813 
.667956 
.500451 


43. 


-n  =  24.8099. 


67. 


7T  =  78.1464. 


V. 

6m. 


57.956 

95.553 

132.763 

169.548 

205.852 

241.604 
276.755 
311.225 
344.955 
377.922 

410.064 
441.329 
471.705 
501.164 
529.707 

557.330 

584.076 
610.008 
635.225 
659.984 


V. 

12m. 


37.772 

75.193 

112.194 

148.762 

184.802 

220.265 
255.105 
289.206 
322.563 
355.142 

386.845 
417.674 
447.596 
476.591 
504.684 

531.836 
558.176 
583.699 
608.611 
633.218 


684.527  657.695 
709.409  682.984 
733.238  705.352 


753.939 
772.356 

789.837 
806.556 
822.625 
839.222 
855.569 


724.385 

742.187 

759.347 
775.625 
791.486 
808.817 
824.181 


im.d. 


1.682 
1.697 
1.714 
1.732 
1.754 

1.778 
1.804 
1.835 
1.866 
1.898 

1.935 
1.971 
2.009 
2.048 
2.085 

2.125 
2.158 
2.192 
2.218 
2.230 

2.236 
2.202 
2.324 
2.463 
2.514 

2.541 

2.578 
2.595 
2.534 
2.616 


6m. 


0.018977 
.339877 
.537400 
.685527 
.807566 

0.914052 

1.010719 

.101154 

.187778 
.272364 

1.356348 
.440919 
.527119 
.615927 
.708260 

1.805057 
.907224 

2.015731 
.131572 
.255712 

2.389400 
.533699 
.694016 

.875587 
3.078149 

3.301825 
.549982 
.826502 

4.134153 
.489683 


AB. 

12m. 


0.037168 
.358878 
.557318 
.706438 
.829573 

0.937256 

1.035232 

.127118 

.215315 

.301620 

1.387505 
.474142 
.562602 
.653883 
.748906 

1.848663 
.954016 

2.066042 
.185676 
.313905 


o  « 


n. 


0 
1 
2 
3 
4 

5 
6 
7 
8 
9 

10 
11 
12 
13 
14 

15 
16 
17 
18 
19 


2.452163 

.601232 

.769686 

.960186  23 
3.170526  24 


20 
21 
22 


3.402335 
.659873 
.946582 

4.264695 
.637140 


42. 


913.846 
905.109 
896.237 
887.648 
878.712 

869.368 
859.523 
848.459 
835.722 
822.421 


906.021 
897.809 
888.545 
880.067 
871.366 

862.194 
852.679 
842.505 
830.549 
817.032 


809.303  803.948 


.652 
.608 
.641 
.632 
.612 

.598 
.570 
.496 
.431 
,449 


5.414289 
.058780 

4.751172 
.474735 
.226730 

4.003313 

3.801170 

.620248 

.460889 

.317940 


446  3.186108 


5.561746 
.189322 

4.871252 
.584626 
.327240 

4.095690 

3.885769 

.695918 

.528422 

.380703 

3.244301 


42. 


n  =  23.8627. 


25 
26 
27 
28 
29 


54 
53 
52 
51 
50 

49 
48 
47 
46 
45 

44 


Continued  from  Page  *171, 


*184 


TABLE     LXIII 


GENERAL  VALUATION  OF  ANNUAL  PREMIUM   POLICIES    OF  1,000. 

4  PER  CENT. 


5*8 
e  o 

n. 


0 
1 
2 
3 

4 

5 
6 

7 
8 
8 

10 
11 
12 
13 
14 

15 
16 
17 
18 
19 

20 
21 
22 
23 
24 

25 
26 
27 

28 


55 

54 
53 
52 
51 
50 

49 
48 
47 
46 
45 

44 


a;  =  68. 


TT  =  82.7146. 


V. 

6in. 


60.803 

99.474 

137.703 

175.432 

212.587 

249.118 
284.942 
819.994 
354.257 
387.659 

420.153 
451.721 
482.335 
512.001 
540.707 

568.503 
595.453 
621.660 
647.391 
672.896 

698.757 
723.520 
745.034 
764.174 
782.341 

799.716 
816.416 
833.664 
850.653 


V. 

12m. 


Jm.d. 


38.890 

77.344 

115.347 

152.802 

189.657 

225.864 
261.304 
295.970 
329.828 
362.776 

394.815 
425.911 
456.045 
485.241 
513.458 

540.883 
567.358 
593.247 
618.820 
644.258 

670.540 
693.786 
713.566 
732.067 
749.900 

766.817 
783.301 
801.312 
817.279 


A(B/). 
6m. 


1.826  0.019871 


1.844 
1.863 
1.886 
1.911 


1.938 
1.970 
2.002 
2.036 
2.074 

2.112 
2.151 
2.191 
2.230 
2.271 

2.306 
2.341 
2.868 
2.381 
2.386 


.341777 
.540461 
.689912 
.813485 

0.921718 

1.020413 

.113155 

.202390 

.289970 

1.377356 
.465773 
.556332 
.650050 
.747937 


AB. 

12m. 


69. 


7r=  87.6177. 


V. 

6m. 


0.038872  63.814 
361695  103.588 


.561372 
.711919 
.836689 

0.946231 

1.046877 

.140692 

.281646 

.321127 

1.410579 
.501256 
.594288 
.690696 
.791543 


1.850956  1.897748 
.960123  2.010434 


2.076469 
.200989 
.334959 


3512. 

478 
622 
676 
703 

742 
760 
696 
781 


479462 
.639923 
.821592 
.024217 
.247932 

.496111 
.7726441  , 
.0803024 
.435835  . 


.130573 
.259182 
.397722 

J.  546995 
.715593 
.906191 

}.  116594 
.348442 

J.  606002 

.892724 

210844 

583292 


41. 


914.809  907.373 


906.197 
897.453 
888.988 
880.179 
870.970 

861.267 
850.362 
837.807 
824.698 
811.769 


899.278 
890.148 
881.792 
873.216 
864.176 

854.797 
844.770 
832.986 
819.662 
806.767 


798.724  793.803 


620  5.4418215.589278 


.577 
.609 
.600 
.580 
.566 

.539 
.466 
.402 
.420 
.417 

.410 


5.086313 

4.778705 

.502269 

.254265 

.030850 

3.828711 
.647794 
.488443 
.345505 
.213688 

3.092060 


5.216855 

4.898785 
.612160 
.354775 
.123227 

3.913310 
.723464 

.555976 
.408268 
.271881 

3.146164 


142.845 
181.503 
219.512 

256.786 
293.256 
328.906 
363.660 
397.469 

430.313 
462.166 
493.082 
522.901 
551.821 


V. 

12m. 


40.009 

79.550 

118.521 

156.867 

194.540 

281.413 

267.482 
302.711 
336.992 
370.327 

402.681 
434.034 
464.412 
493.771 
522.253 


579.861549.851 
607.1281576.788 
633.901603.396 
660.439|629.863 
687.3441657.208 


713. 
735. 
755. 

774. 
792. 

809. 
827. 
845. 


111681. 
494  701. 
410721. 
312739. 

390  757. 


765 
712 
388 


774. 
793. 
809. 


395 

976 
226 
780 
381 

532 
273 

886 


^m.d. 


1.984 
2.003 
2.027 
2.053 
2.081 

2.114 
2.148 
2.183 
2.222 
2.262 

2.303 
2.344 
2.385 

2.427 
2.464 

2.501 
2.528 
2.542 
2.548 
2.511 

2.643 
2.793 
2.849 
2.878 
2.917 

2.936 

2.870 
2.960 


6m. 


AB. 

12m. 


0.020877 
.343875 
.543830 
.694753 
.820009 

0.930202 

1.031134 

.126416 

.218572 

.309480 

1.400636 
.493338 

.588735 
.687936 

.791977 

1.901933 

2.018880 
.143853 
.278157 
.422901 

2.583533 
.765318 
.968018 

3.191778 
.489984 

3.716532 

4.024198 

379735 


0.040795 
.364786 
.565887 
.717957 
.844522 

0.956166 

1.058671 

.155672 

.249729 

.342703 


O  4> 


1.43611P 
.531294 
.629381 
.731542  13 
.838769  14 


1.952244 

2.072984 
.202046 
.340920 


.4904341 19 

2.659203  20 
.849917  21 

8.060395:22 
.292288  23 
.549875  24 


3.836612 

4.154740 

527192 


40. 


41. 


7r  =  22.9667. 


915.718 
907.224 

898.601 
890.252 
881.565 
872.483 
862.913 

852.157 

839.777 
826.849 
814.096 
801.232 

788.130 


908.649 
900.666 

891.661 
883.420 
874.963 
866.047 

856.797 

846.908 
885.286 
822.147 
809.429 
796.648 

783.700 


.589 
.546 

.578 
.569 
.550 
.536 
.510 

.437 
.374 
.392 
.389 
.382 

.369 


5.468963 
.118454 

4.805847 
.529411 
.281409 
.057995 

3.855859 

3.674947 
.515604 
.372677 
.240874 
.119264 

3.006757 


56 
55 

54 
53 
52 
51 
50 

.750617  49 
.583137  48 
.435440  47 
.299067  46 
.173368  45 

.057068  44 


5.616420 
.243996 

4.925927 
.689302 
.381919 
.150372 

3.940458 


40. 


7r  =  22.1206. 


Continued  from  Page  *170. 


TABLE     LXIIT. 


*186 


GENERAL  VALUATION  OF  ANNUAL  PREMIUM  POLICIES  OF  1,000. 

4  PER  CENT. 


^1 


n. 


70. 


TT  =  92.8725. 


V. 

6m. 


67.031 
107.923 
148.193 
187.786 
226.612 

264.604 
301.739 
337.941 
373.158 
407.372 


V. 

12m. 


10  440.553 

11  472.705 

121503.818 
13|533.944 
14j563.153 

15  1591.557 

16  619.445 
17i647.089 
18|675.116 
19 '701.956 


20 
21 
22 
23 

24 

25 
26 


725.272 
746.018 
765.707 
784.539 
802.640 

821.333 

839.746 


41.189 

81.784 

121.728 

160.971 

199.381 

236.954 
273.650 
309.359 
344.084 

377.787 

410.447 
442.090 
472.673 
502.342 
531.091 

559.150 
586.867 
614.437 
642.922 
668.117 

689.555 
709.607 
728.935 
747.270 
765.136 

784.657 
801.962 


im.d. 


MB/). 

6m. 


AB. 
12m. 


2.154  0.021969 
2.178  .346181 
.547542 
.700080 
.827224 


2.205 
2.235 

2.269 


2.304 
2.341 
2.382 
2.423 

2.465 

2.509 
2.551 
2.595 
2.633 
2.672 

2.701 
2.715 
2.721 
2.683 
2.820 

2.976 
3.034 
3.064 
3.106 
3.125 


0.939579 

1.042974 

.141097 

.236500 

.331096 

1.426454 
.523913 
.624715 
.729994 
.840901 

1.958570 

2.084085 

.218790 

.363822 

.524658 


0.042880 
.368188 
.570746 
.724593 
.853188 

0.967116 

1.072230 

.172254 

.269723 

.366579 

1.464410 
.564559 
.668321 

.776786 
.891212 

2.012674 
. 142278 
.281553 
.431355 
.600328 


2.706581:2.791180 


.909369 

3.133184 

.381422 

.657988 


3.056  3.965663 
3.149  4.321204 


3.001746 
.233694 
.491313 
.778068 

4.096205 
.468661 


39. 


57  916.577 
56  908.196 
55  899.687 

1541891.447 
53  882.876 
52  873.914 

|51j864.470 
'50 '853.857 


49 
48 
47 
46 

45 

44 


841.640 
828.882 
816.299 
803.605 

790.675 

777.379 


909.856 
901.979 
893.093 

884.960 

876.615 
867.817 
858.690 
848.931 

837.463 
824.497 
811.947 
799.331 
786.558 

773.472 


.560 
.518 
.550 

.541 
.522 
.508 
.482 
.410 

.348 
.374 
.363 
.356 
.343 

.325 


5.495734 

.140226 

4.832619 

4.556183 
.308182 
.084770 

3.882638 
.701730 

3.542394 
.399476 
.267686 
.146094 
.033609 

2.929447 


5.643191 

.270768 
4.952699 

4.666074 
.408692 

.177147 

3.967237 

.777400 

3.609927 
.462239 
.325879 
.200198 
.083920 

2.976239 


71. 


7r  =  98.5145. 


V. 

6m. 


V. 

12m. 


^m.d. 


A(B/). 
6m. 


70.427  42.339  2.3410.023182  0.045189  0 

112.426  83.999  2.369  .348727  .371931  1 

153.720124.928  2.399  .551629  .576142  2 

194.215164.987  2.436  .705977  .731941  3 

233.837  204.174  2.472  .835200  .862737  4 

272.568  242.447  2.510  0.949934  0.979190  5 

310.326  279.691  2.553  1.056082  1.087239  6 

347.056  315.907  2.596  .157363  .190586  7. 

382.739  351.058  2.640  .256364  .291847  8 

417.346  385.120  2.686  .355071  .393027  9 

450.879  418.123  2.730  1.455096  1.495742  10 
483.328  450.020  2.776  .557872  .601478  11 
514.749  480.964  2.815  .664667  .711459  12 
545.213  510.947  2.855  .776732  .827043  13 
574.836  540.212  2.885  .895277  .94938114 

603.923  569.119  2.900  2.021447  2.079640  15 
632.753  597.874  2.907  .156634  .219397  16 
661.986  627.583  2.867  .302013  .369546  17 
689.978  653.860  3.010  .463094  .538764  18 
714.297  676.219  3.173  .645183  .729782  19 

735.932  697.132  3.233  2.848077  2.940454  20 
756.469  717.2913.265  3.071958  3.172468:21 
776.100  736.413  3.308  .320234  .430125|22 
794.986  755.046  3.328  .596822  .716902 
814.483  775.406  3.256  .904507  4.035049 

833. 688  793. 455  3.353  4. 260054  4. 407511 


AB. 
12m. 


n. 


38. 


39. 


7r  =  21.3199. 


917.390 
909.116 
900.714 
892.579 

884.116 
875.267 
865.944 
855.465 
843.402 

830.807 
818.383 
805.849 
793.084  789.263 
779.957  776.343 

766.418|763.009 


910.998 
903.221 
894.448 
886.418 

878.178 
869.492 
860.480 
850.846 
839.522 

826.721 
814.330 
801.874 


.533 
.491 
.522 
.513 

.495 
.481 
.455 
.385 
.323 

.341 
.338 
.331 
.318 
.301 

.284 


5.522155 

.166647 

4.859041 

.582606 

4.334606 
.111196 

3.909066 
.728163 
.568832 

3.425923 
.294145 
.172570 
.060106 

2.955971 

2.859371 


5.669612 
.297189 

4.979121 
.692497 

4.435116 
.203573 

3.993665 
.803833 
.636365 

3.488686 
.352338 
.226674 
.110417 
.002763 

2.902977 


23 

24 

25 


38. 


77  =  20.5624. 


58 
57 
56 
55, 

54 
53 
52 
51 
50 

49 
48 
47 
46 
45 

44 


Continued  from  Page  *169. 


*186 


TABLE    LXIII 


GENERAL  VALUATION  OP  ANNUAL  PREMIUM  POLICIES  OP  1,000. 

4  PER  CENT. 


&2 

n. 

a;  =  72.  TT  =  104.570. 

73.   TT  =  111.075. 

•■si 

n. 

V. 

6m. 

V. 

12in. 

^m.d. 

A(B/). 
6m. 

aB. 
12m. 

V. 

6m. 

V. 

12m. 

^m.d. 

6m. 

AB. 

12m. 

0 

74.036 

43.502 

2.545 

0.024515 

0.047719 

77.879 

44.682 

2.766 

0.025979 

0.050492 

0 

1 

117.156 

86.240 

2.576 

.351524 

.376037 

122.086 

88.415 

2.806 

.354626 

.380590 

1 

2 

159.441 

128.071 

2.614 

.556152 

.582116 

165.343 

131.196 

2.846 

.561148 

.588685 

2 

3 

200.815 

168.990 

2.652 

.712491 

.740028 

207.624 

172.978 

2.887 

.719674 

.748930 

3 

4 

241.258 

208. 955 

2.692 

.844001 

.873257 

248.845 

213.637 

2.934 

.853740 

.884897 

4 

5 

280.685 

247.846 

2.737 

0.961393 

0.992550 

288.944 

253.175 

2.981 

0.974085 

1.007308 

5 

6 

319.040 

285.663 

2.781 

1.070602 

1.103825 

327.900 

291.549 

3.029 

1.086682 

.122165 

6 

7 

356.300 

322.368 

2.828 

.175381 

.210864 

365.679 

328.735 

3.079 

.195360 

.233316 

7 

8 

392.437 

357.936 

2.875 

.278392 

.316348 

402.287 

364.764 

3.127 

.302827 

.343473 

8 

9 

427.452 

392.398 

2.921 

.381666 

.422312 

437. 71^ 

399.586 

3.177 

.411211 

.454817 

9 

10 

461.337 

425.705 

2.969 

1.486911 

1.530517 

472.014 

433.367 

3.221 

1.522247 

1.569039 

10 

11 

494.146 

458.017 

3.011 

.595585 

.642377 

505.271 

466.100 

3.264 

.637511 

.687822 

11 

12 

525.956 

489.326 

3.053 

.709074 

.759385 

537.611 

498.048 

3.297 

.758458 

.812562 

12 

13 

556.890 

519.884 

3.084 

.828692 

.882796 

569.365 

529.607 

3.313 

.886412 

.944605 

13 

14 

587.262 

550.070 

3.099 

.955661 

2.013854 

600.840 

560.998 

3.320 

2.022905 

2.085668 

14 

15 

617.368 

580.096 

3.106 

2.091434 

2.154197 

632.752 

593.431 

3.277 

2.169222 

2.236755 

15 

16 

647.892 

611.118 

3.064 

.237235 

.304768 

663.312 

622.118 

3.433 

.330963 

.406633 

16 

17 

677.123 

638.557 

3.214 

.398613 

.474283 

689.861 

646.528 

3.611 

.513497 

.598096 

17 

18 

702.516 

661.905 

3.384 

.580902 

.665501 

713.481 

669.359 

3.677 

.716678 

.809055 

18 

19 

725.108 

683.742 

3.447 

.783926 

.876303 

735.900 

691.366 

3.711 

.940734 

3.041244 

19 

20 

746.552 

704.792 

3.480 

3.007885 

3.108395 

757.341 

712.242 

3.758 

3.189113 

3.299004 

20 

21 

767.061 

724.760 

3.525 

.256208 

.366099 

777.951 

732.584 

3.781 

.465757 

.585837 

21 

22 

786.774 

744.217 

3.546 

.532821 

.652901 

799.235 

754.811 

3.702 

.773472 

.904014 

22 

23 
24 

59 

807.132  765.477 

827.185|784.323 

3.471 
3.572 

.840520 
1 1 Qfin7^ 

.971062 

820.200 

774.514 

3.807 

4.129033 

4.276490 

23 

Ht,l.V\)\J  t  0  rr**j-i:tj*j^\j\ 

36. 

60 
59 

37. 

918.890 
910.810 

913.103 
905.510 

.482 
.442 

5.574024 
5.218516 

5.721481 
5.349058 

918.161 

912.080 

.507 

5.548246 

5.695703 

58 

909.986 

904.397 

.466 

.192738 

.323280 

902.607 

896.944 

.472 

4.910910 

.030990 

58 

57 

901.687 

895.730 

.496 

4.885132 

.005212 

894.666 

889.105 

.463 

.634476 

4.744367 

57 

56 

893.651 

887.799 

.488 

.608697 

4.718588 

886.402 

88L060 

.445 

.386478 

.486988 

56 

55 

885.291 

879.659 

.469 

.360698 

.461208 

877.763 

872.579 

.432 

.163071 

.255448 

55 

54 

876.550 

871.078 

.456 

4.137290 

4.229667 

868.659 

863.780 

.407 

3.960945 

4.045544 

54 

53 

867.339 

862.176 

.430- 

3.935162 

.019761 

858.429 

854.373 

.338 

.780050 

3.855720 

53 

52 

856.988 

852.658 

.361 

.754263 

3.829933 

846.651 

843.318 

.278 

.620731 

.688264 

52 

51 

845.073 

841.473 

.300 

.594939 

.662472 

834.354 

830.819 

.295 

.477838 

.540601 

51 

50 

832.629 

828.827 

.317 

.452038 

.514801 

822.224 

818.722 

.292 

.346082 

.404275 

50 

49 

820.357 

816.587 

.314 

3.320271 

3.378464 

809.986 

806.560 

.286 

3.224535 

3.278639 

49 

48 

807.975 

804.281 

.308 

.198711 

.252815 

797.523 

794.247 

.273 

.112109 

.162420 

48 

47 

795.365 

791.824 

.295 

.086267 

.136578 

784.707 

781.633 

.256 

.008023 

.054815 

47 

46 

782.397  779.061 

.280 

2.982156 

.028948 

771.488 

768.615 

.239 

2.911484 

2.955090 

46 

45 

769.023  765.889 

.261 

.885589 

2.929195 

757.836 

755.195 

.220 

.821765 

.862411 

45 

44 

755.211752.312 

.242 

2.805832 

2.836478 

743.728 

741.310 

.201 

2.738237 

2.776193 

44 

37.   TT  =  19.8452. 

36.   TT  =  19.1663. 

Continued  from  Page  *168. 


♦187 


TABLE    LXIII. 


GENERAL  VALUATION  OF  ANNUAL  PREMIUM  POLICIES  OF  1,000. 

4  PER  CENT. 


11 

n. 
0 

74.   TT  =  118.069. 

75.    7r=  135.579. 

n. 
0 

V. 

6m. 

V. 

13in. 

-^m.d. 

A(B/). 
6m. 

AB. 

13m.- 

V. 

6m. 

V. 

13m. 

^m.d. 

A(B/). 
6m. 

AB. 

13m. 

81.924 

45. 779 

3.013 

0.037616 

0.053580 

86.355 

46.930 

3.277 

0.029403 

0.056940 

1 

137.304 

90.560 

3.054 

.358048 

.385585 

133.637 

93.765 

3.323 

.361802 

.391058 

1 

2 

171.463 

134.397 

3.097 

.566649 

.595905 

177.855 

137.367 

3.374 

.573730 

.603887 

2 

3 

314.613 

176.858 

3.146 

.737630 

.758777 

331.843 

180.740 

3.425 

.736408 

.769631 

3 

4 

356.586 

318.344 

3.195 

.864531 

.897744 

264.577 

333.835 

3.479 

.876447 

.911930 

4 

5 

397.363 

358.413 

3.346 

0.988135 

1.033618 

306.031 

363.638 

3.533 

1.003701 

1.041657 

5 

6 

336.910 

397.339 

3.398 

1.104508 

.143464 

346.180 

303.153 

3.586 

.134370 

.164916 

6 

7 

375.331 

335.053 

3.348 

.317518 

.358164 

385.041 

341.351 

3.641 

.342130 

.285736 

7 

8 

413.313 

371.503 

3.401 

.339973 

.373579 

433.669 

378.409 

3.688 

.360118 

.406910 

8 

9 

448.318 

406.864 

3.446 

.444037 

.490819 

459.153 

414.316 

3.736 

.480513 

.530824 

9 

10 

483.031 

441.138 

3.493 

1.561535 

1.611846 

494.639 

449.363 

3.772 

1.605247 

1.659351 

10 

11 

516.884 

474.571 

3.536 

.684149 

.738253 

539.463 

483.983 

3.790 

.735978 

.794171 

11 

12 

550.133 

507.606 

3.543 

.813330 

.871533 

563.990 

518.419 

3.798 

.874485 

.937248 

12 

13 

583.070 

540.466 

3.550 

.950716 

2.013479 

598.998 

553.998 

3.750 

2.022241 

2.089774 

13 

14 

616.475 

574.415 

3.505  13.097673 

.165306 

633.533  585.467 

3.921 

.184988 

.260658 

14 

15 

648.464 

604.444 

3.668  3.359861 

3.335531 

661.645i612.244 

4.117 

2.368201 

2.453800 

15 

16 

676.354 

639.995 

3.855  .443697 

.537396 

687.557  637.290 

4.189 

.571816 

.664193 

16 

17 

700.9791653.894 

3.934  .646073 

.738449 

712.150  661.431 

4.227 

.796138 

.896648 

17 

18 

734.447 

676.931 

3.960 

.870347 

.970757 

735.671 

684.333 

4.278 

3.044672 

3.154563 

18 

19 

746.893 

698.783 

4.009 

3.118695 

3.338586 

758.279 

706.647 

4.303 

.321403 

.441483 

19 

20 

768.464 

730.076 

4.033 

3.395377 

3.515457 

781.627 

731.039 

4.216 

3.639161 

3.759703 

20 

21 
22 

790.743 
813.690 

743.343 

763.968 

3.950 
4.060 

.703111 
4.058683 

.833653 
4.306139 

804.626 

753.644  4.333 

.984743 

4.133300 

21 

34. 

62 

35. 

920.234 

914.990 

.437 

5.634707 

5.773164 

61 

919.579 

914.071 

.459 

5.599505 

5.746963 

912.330 

907.563 

.397 

.369199 

.399741 

61 

60 

911.590 

906.563 

.419 

.343997 

.374539 

904.305 

899.183 

.427 

4.961593 

.081673 

60 

59 

903.478 

898.093 

.449 

4.936393 

5.056473 

896.535 

891.513 

.419 

4.685161 

4.795053 

59 

58 

895  635 

890.341 

.440 

.659958 

4.769849 

888.453 

883.643 

.401 

.437164 

.537674 

58 

57 

887.454 

883.385 

.433 

.411961 

.513471 

880.000 

875.346 

.388 

.313759 

.306136 

57 

56 

878.911 

873.999 

.409 

.188555 

.280932 

871.094 

866.738 

.363 

.011639 

.096338 

56 

55 

869.909 

865.398 

.384 

3.986433 

.071031 

861.085 

857.536 

.296 

3.830750 

3.906430 

55 

54 

859.793 

855.996 

.316 

3.805540 

3.881210 

849.564 

846.730 

.237 

3.671441 

3.738974 

54 

53 

848.146 

845.064 

.357 

.646336 

.713759 

837.533 

834.493 

.253 

.538561 

.591334 

53 

52 

835.986 

833.705 

.373 

.503341 

.566104 

835.666 

833.658 

.251 

.396834 

.455017 

52 

51 

833.990 

830.743 

.371 

.371594 

.429787 

813.695 

810.760 

.245 

.375303 

.339407 

51 

50 

811.890 

808.715 

.365 

.350061 

.304165 

801.503 

798.716 

.233 

.163910 

.313331 

50 

49 

799.565 

796.540 

.353 

3.137653 

3.187963 

788.965 

786.375 

.316 

3.058866 

3.105658 

49 

48 

786.891 

784.066 

.335 

.033587 

.080379 

776.033 

773.639 

.199 

3.962380 

.005986 

48 

47 

773.830 

771.193 

.319 

3.937076 

2.980682^ 

763.677 

760.511 

.180 

.873736 

3.913373 

47 

46 

760.330 

757.933 

.300 

.847391 

.8880371 

748.876 

746.938 

.162 

.789380 

.837336 

46 

45 

746.370 

744.193 

.181 

.763905 

.8018611 

734.633 

733.908 

.144 

.711436 

.746909 

45 

44 

731.973 

730.033 

.163 

3.686005 

3.731488 

719.945 

718.441 

.125 

3.638638 

3.671861 

44 

35.   TT  =  18.5341. 

34.   TT  =  17.9149. 

Continued  fio-u  Page  *167. 


♦188 


TABLE     LXIII. 


GENERAL  VALUATION  OF  ANNUAL  PREMIUM  POLICIES  OP  1,000, 

4  PER  CENT. 


n. 
0 

.r  =  76.  77  =  133.656. 

77.    77=142.352. 

"3  3 

n. 

V. 

6m. 

V. 

12m. 

im.d. 

A(B/). 
6m. 

AB. 
12m. 

V. 

6m. 

V. 

12m. 

im.d. 

A(B/). 
6m. 

AB. 

12m. 

90.874 

48.092 

3.565 

0.031370 

0.060626 

95.758 

49.163 

3.883 

0.033566 

0.064723 

0 

1 

138.320 

94.891 

3.619 

.365966 

.397123 

144.242 

96.970 

3.939 

.370572 

.403795 

1 

2 

184.473 

140.399 

3.673 

.579461 

.612684 

191.347 

143.371 

3.998 

.586900 

.622383 

2 

3 

239.311 

184.568 

3.729 

.746131 

.781614 

237.029 

188.335 

4.058 

.756894 

.794850 

3 

4 

272.797 

227.369 

3.786 

.889659 

.927615 

281.293 

231.900 

4.116 

.904298 

.944944 

4 

5 

314.932 

268.839 

3.841 

1.020957 

1.061603 

324.128 

274.004 

4.177 

1.040118 

1.083724 

5 

6 

355.707 

308.919 

3.899 

.146221 

.18982V 

365.604 

314.851 

4.229 

.170591 

.217383 

6 

7 

395.188 

347.801 

3.949 

.269462 

.316254 

405.817 

354.431 

4.282 

.299854 

.350165 

7 

8 

433.467 

385.477 

3.999 

.393642 

.443953 

444.922 

393.061 

4.322 

.430952 

.485056 

8 

9 

470.691 

422.250 

4.037 

.521119 

.575223 

483.316 

431.220 

4.341 

.566257 

.624450 

9 

10 

507.240 

458.574 

4.055 

1.653836 

1.712029 

521.375 

469.178 

4.350 

1.708034 

1.770797 

10 

11 

543.468 

494. 706 

4.064 

.793770 

.856533 

559.962 

508.394 

4.297 

.85810* 

.925634 

11 

12 

580.199 

532.036 

4.014 

.942538 

2.010071 

596.914 

543.081 

4.486 

2.022455 

2.098125 

12 

13 

615.374 

565.055 

4.193 

2.105990 

.181660 

629.015 

572.597 

4.702 

.206741 

.291340 

13 

14 

645.931 

593.151 

4.398 

.289675 

.374274 

657.576 

600.203 

4.781 

.411044 

.503421 

14 

15 

673.118 

619.430 

4.474 

2.493593 

2.585970 

684.684 

626.813 

4.823 

2.635785 

2.736295 

15 

16 

698.923 

644. 760 

4.514 

.718100 

.818610 

710.610 

652.055 

4.880 

.884565 

.994456116 

17 

723.602 

668.788 

4.568 

.966743 

3.076634 

735.529 

676.651 

4.906 

3.161431 

3.281511' 17 

18 

747.323 

692.202 

4.593 

3.243532 

.363612 

761.265 

703.527 

4.812 

.469260 

.599802 

18 

jl9 
20 

771.822 
795.952 

717.785 
740.464 

4.503 
4.624 

.551322 
3.906919 

.681864 
4.054376 

786.615 

727.352 

4.939 

.824875 

.972332 

19 

32. 

33. 

921.441 

916.686 

.396 

5.674326 

K  Q01  lyQQ 

OA 

O.o-ci  too  v± 

63 

920.854 

915.861 

.416 

5.649642 

5.797099 

913.694 

909.406 

.357 

.318819 

.449361  63 

62 

913.030 

908.508 

.377 

.294135 

.424677 

905.830 

901.193 

.386 

.011214 

.131294  62 

61 

905.088 

900.214 

.406 

4.986529 

.106609 

898.216 

893.677 

.378 

4.734781 

4.844672  61 

60 

897.398 

892.624 

.398 

.710097 

4.819988 

890.293 

885.964 

.361 

.486786 

.587296  60 

59 

889.397 

884.834 

.380 

4.462101 

4.562611 

882.010 

877.833 

.348 

4.263384 

4.355761!  59 

58 

881.031 

876.622 

.367 

.238698 

.331075 

873.283 

869.397 

.324 

.061267 

.145866  58 

57 

872.218 

868.103 

.343 

.036579 

.121178 

863.473 

860.378 

.258 

3.880384 

3.956054  57 

56 

862.311 

858.994 

.276 

3.855693 

3.931363 

852.181 

849.778 

.200 

.721083 

.788616  56 

55 

850.908 

848.290 

.218 

.696388 

.763921 

840.391 

837.795 

.216 

.578216 

.640979|56 

54 

839.000 

836.188 

.234 

3.553515 

3.616278 

828.761 

826.196 

.214 

3.446495 

3.504688 

54 

53 

827.255 

824.474 

.232 

.421786 

.479979 

817.028 

814.536 

.208 

.324996 

.379100 

53 

62 

815.406 

812.698 

.226 

.300276 

.354380 

805.079 

802.731 

.196 

.212632 

.262943 

52 

51 

803.339 

800.777 

.214 

.187898 

.238209 

792.791 

790.637 

.180 

.108624 

.155416 

61 

50 

790.929 

788.563 

.197 

.083873 

.130665 

780.117 

778.155 

.163 

.012186 

.055792 

50 

49 

778.130 

775.957 

.181 

2.987412 

3.031018 

767.028 

765.289 

.145 

2.922589 

2.963235 

49 

48 

764.910 

762.964 

.162 

.897788 

2.938434 

753.502 

751.977 

.127 

.839212 

.877168 

48 

47 

751.250 

749.519 

.144 

.814377 

.852333 

739.543 

738.237 

.109 

.761444 

.796927 

47 

46 

737.153 

735.643 

.126 

.736568 

.772051 

725.149 

724.058 

.091 

.688756 

.721979 

46 

45 

722.616 

721.324 

.108 

.663831 

.697054 

710.333 

709.450 

.074 

.620655 

.651812 

45 

44 

707.654 

706.571 

.090 

2.595674 

2.626831 

695.103 

694.427 

.056 

2.556708 

2.585964 

44 

33.   77  =  17.3376. 

32.   77  =  16.7902. 

Coutinaed  from  Page  *166. 


TABLE     LXIII 


189 


GENERAL  VALUATION  OF  ANNUAL  PREMIUM  POLICIES  OF  1,000. 

4  PER  CENT. 


n. 

78.   :r  =  151.701. 

79.   u  ==  161.769. 

li 

n. 

V. 

6m. 

V. 
13m. 

l^m.d. 

MB/). 

6m. 

AB. 

13m. 

V. 

6m. 

V. 

13m. 

^m.d. 

6m. 

AB. 

13m. 

0 

100.990 

50.379 

4.336 

0.035976 

0.069199 

106.576 

51.383 

4.599 

0.038642 

0.074135 

0 

1 

150.539 

99.078 

4.388 

.375648 

.411131 

157.164 

101.175 

4.666!  .381365 

.419331 

1 

2 

198.573 

146.367 

4.351 

.595130 

.633076 

306.181 

149.418 

4.730  .604319 

.644865 

2 

3 

345.137 

193.185 

4.413 

.768806 

.809453 

353.615 

196.044 

4.798  .783033 

.835639 

3 

4 

390.176 

336.467 

4.476 

.930540 

.964146 

399.545 

341.377 

4.856  .938656 

.985348 

4 

5 

333.797 

379.435 

4.531 

1.061377 

1.108169 

344.077 

385.107 

4.914  1.085004 

1.135315 

5 

6 

376.088 

331.051 

4.586 

.197679 

.347990 

387.381 

337.886 

4.958 

.337833 

.381937 

6 

7 

417.316 

361.679 

4.638 

.333673 

.387777 

439.899 

370.143 

4.980 

.371359 

.439453 

7 

8 

457.596 

401.813 

4.649 

.473430 

.530613 

473.044 

413.176 

4.989 

.518708 

.581471 

8 

9 

497.633 

441.733 

4.657 

.616630 

.679383 

514.774 

455.604 

4.931  .673714 

.740347 

9 

10 

538.305 

483.978 

4.603 

1.768380 

1.835913 

555.695 

494.016 

5.140  1.839770 

1.915440 

10 

11 

577.066 

519.456 

4.801 

.933901 

3.009571! 

591.343 

536.701 

5.379  3.035850 

3.110449 

11 

12 

610.838 

550.498 

5.038 

3.118963 

.3035631 

633.870 

557.371 

5.467;  .331394 

.333671 

12 

13 

640.865 

579.531 

5.111 

.333761 

.416138 

653.889 

586.738 

5.5131  .456730 

.557340 

13 

14 

669.374 

607.517 

5.155 

.548804 

.649314; 

681.599,614.691 

5.576!  .705916 

1 

.815807 

14 

15 

696.641 

634.064 

5.315 

3.797761 

3.907653 

709.195  641.939 

5.605  3.983005 

3.103085 

15 

16 

733.849 

659.933 

5.343 

3.074734 

3.194804; 

737.694  671.691 

5.500  3.390950 

.431493 

16 

17 
18 

749.916 

776.577 

688.198 
713.355 

5.143 

5.377 

.383603 

fV  O  O  ."i  A  G\ 

.513145 

.885699 

765.767  698.074 

5.641  .646630 

.794077 

17 

.738343 

66 

30. 

31. 

933.537 
914.933 

918.311 

.360 

5  733991 

5  870448 

65 

931.998 

917.469 

.377 

5.698773 

5.846339 

91l!064 

!333 

.367484 

.498036 

65 

64 

914.335 

910.357 

.339 

5.343364 

5.473806 

907.303 

903.003 

.350 

5.059879 

5.179959 

64 

63 

906.534 

903.131 

.368 

.035659 

.155739! 

899.737 

895.633 

.343 

4.783447 

4.893338 

63 

62 

898.991 

894.676 

.360 

4.759337 

4.869118 

891. 949 

888.051 

.335 

.535453 

.635963 

62 

61 

891.143 

887.035 

.343 

.511333 

.6117431 

883.817 

880.068 

.313 

.313053 

.404430 

61 

60 

883.937 

878.980 

.330 

.387833 

.380309 

875. 349 

871.787 

.388 

.109939 

.194538 

60 

59 

874.393 

870.634 

.306 

4.085716 

4.170315 

865. 630 

863.933 

.334 

3.939063 

4.004733 

59 

58 

864.575 

861.689 

.341 

3.904836 

3.980506 

854,535 

853.538 

.167 

.769768 

3.837301 

58 

57 

853.389 

851.189 

.183 

.745539 

.813073 

843.960 

840.763 

.183 

.636913 

.689675 

57 

56 

841.709 

839.318 

.199 

.603677 

.665440 

831.543 

839.377 

.181 

.495305 

.553398 

56 

55 

830.189 

837.839 

.197 

.470964 

.539157 

830.035 

817.930 

.175 

.373735 

.437839 

55 

54 

818.566 

816.378 

.191 

3.349475 

3.403579 

808.394 

806.341 

.163 

3.361386 

3.311697 

54 

53 

806.739 

804.584 

.179 

.337134 

.387435 

796.331 

794.468 

.147 

.157411 

.304303 

53 

52 

794.557 

793.603 

.163 

.133133 

.179935 

783.789 

783.315 

.131 

.061013 

.104619 

52 

51 

783.001 

780.339 

.147 

.036715 

.080331 

770.9391769.584 

.113 

3.971467 

.013113 

51 

50 

769.035 

767.493 

.138 

3.947144 

3.987790 

757.661j756.516 

.095 

.888151 

3.936107 

50 

49 

755.636 

754.306 

.111 

3.863799 

3.901755 

743.957 

743.037 

.077 

3.810456 

3.845939 

49 

48 

741.808 

740.695 

.093 

.786069 

.831553 

739.837 

739.108 

.060 

.737856 

.771079 

48 

47  737.550 

736.650 

.075 

.713436 

.746649 

715.383  714.767 

.043 

.669860 

.701017 

47 

46  713.874 

713.179 

.058 

.645379 

.676536 

700.330|700.0],9 

.036 

.606033 

.635389 

46 

45 

697.786 

697.397 

.041 

.581495 

.610751 

684.994 

684.863 

.011 

.545968 

.573505 

45 

44 

683.310 

683.004 

.036 

3.531363 

3.548899 

669.304 

669.346 

.004 

3.489377 

3.515341 

44 

31.   7r  =  16.3713. 

30.   77  =  15.7791. 

Continued  from  Page  *165. 


'190 


TABLE    LXIII 


GENERAL  VALUATION  OF  ANNUAL  PREMIUM  POLICIES  OF  1,000. 

4  PER  CENT. 


i 

n. 
0 

a;  =  80.  TT  =  172.614. 

81.   7r  =  184.307. 

1 
n. 

V. 

6in. 

V. 

12m. 

^m.d. 

A(B/). 
6m. 

12m. 

V. 

6m. 

V. 

12m. 

|m.d. 

A(B/). 
6m. 

AB. 

12m. 

112.553 

52.490 

5.005 

0.041593 

0.079549 

118.990 

53.673 

5.443 

0.044845 

0.085491 

0 

1 

164.225103.346 

5.073 

.387468 

.428114 

171.764 

105.548 

5.518 

.394354 

.4379601  1 

2 

214.229:152.497 

5.144 

.614311 

.657917 

222.864 

155.873 

5.583 

.625476 

.672268  2 

3 

262.645  200.180 

5.205 

.796670 

.843462 

272.408 

204.636 

5.648 

.812927 

.863238  3 

4 

309.589 

246.384 

5.267 

.958568 

1.008879 

320.587 

252.230 

5.696 

.980820 

1.034924 

4 

5 

355.239 

291.480 

5.313 

1.111288 

1.165392 

367.890'299.244 

5.721 

1.140469 

1.198662 

5 

6 

400.060 

336.026 

5.336 

.261311 

.319504 

414.780 

346.009 

5.731 

.298706 

.361469 

6 

7 

444.488 

380.336 

5.346 

.413224 

.475987 

462.320 

394.324 

5.666 

.459969 

.527502 

7 

8 

489.533 

426.116 

5.285 

.570269 

.637802 

507.846 

437.060 

5.899 

.631901 

.7075711  8 

9 

532.670 

466.609 

5.505 

.739384 

.815054 

547.395 

473.424 

6.164 

.821168 

.905767  9 

10 

570.143 

501.064 

5.757 

1.926817 

2.011416 

582.584 

507.436 

6.262 

2.028623 

2.121000  10 

11 

603.484 

533.290 

5.850 

2.133118 

.225495 

615.981 

540.220 

6.313 

.255275 

.355785  11 

12 

635.129 

564.354 

5.898 

.359073 

.459583 

647.923 

571.319 

6.384 

.505169 

.615060  12 

13 

665.394 

593.820 

5.964 

.608561 

.718452 

678.625 

601.623 

6.417 

.782647 

.902727, 13 

14 

694.484 

622.534 

5.996 

.885817 

3.005897 

710.332 

634.735 

6.300 

3.090792 

3.221334 

14 

15 
16 

724.528 
754.121 

653.908 
681.720 

5.885 
6.033 

3.193848 
.549559 

3.324390 
.697016 

741.565 

664.088 

6.456 

3.446559 

3.594016 

15 

29. 

923.504 

919.583 

28. 

.327 

5  770798'-'^  ?»i  ^'>^^ 

68 
67 

67 

923.028 

918.915 

.343 

5.746996 

5.894453 

916.027 

912.556 

!289 

.415291 

.545833 

66 

915.488 

911.829 

.305 

.391489 

.522031 

908.436 

904.629 

.317 

.107686 

.227766 

66 

65 

907.835 

903.836 

.333 

.083884 

.203964 

901.087 

897.375 

.309 

4.831255 

4.941146 

65 

64 

900.423 

896.521 

.325 

4.807453 

4.917344 

893.439 

889.929 

.293 

4.583262 

4.683772 

64 

63 

892.713 

889.014 

.308 

.559460 

.659970 

1885.445 

882.081 

.280 

.359864 

.452241 

63 

62 

884.651 

881.100 

.296 

.336060 

.428437 

1877.020 

873.939 

.257 

.157753 

.242352 

62 

61 

876.157 

872.890 

.272 

.133948 

.218547 

867.552 

865.233 

.193 

3.976880 

.052550 

61 

60 

866.610 

864.112 

.208 

3.953072 

.028742 

856.654 

855.002 

.  .138 

.817593 

3.885126 

60 

59 

855.621 

853.796 

.152 

3.793783 

3.861316 

845.272 

843.436 

.153 

3.674746 

3.737509 

59 

58 

844.145 

842.133 

.168 

.650931 

.713694 

'834.047 

832.240 

.151 

.543052 

.601245 

58 

57 

832.826 

830.845 

.165 

.519231 

.577424 

|822.723 

820.985 

.145 

.421588 

.475692 

57 

56 

821.408 

819.496 

.159 

.397759 

.451863 

811.188 

809.591 

.133 

.309272 

.359583 

56 

55 

809.779 

808.008 

.148 

.285432 

.335743 

1799.328 

797.917 

.118 

.205325 

.252117 

55 

54 

797.819 

796.237 

.132 

3.181471 

3.228263 

1787.095 

785.870 

.102 

3.108962 

3.152568 

54 

53 

785.484 

784.089 

.116 

.085091 

.128697 

1774.461 

773.451 

.084 

.019460 

.060106 

53 

52 

772.745 

771.567 

.098 

2.995568 

.036214 

761.406 

760.602 

.067 

2.936199 

2.974155 

52 

51 

759.580 

758.611 

.081 

.912280 

2.950236 

747.981 

747.340 

.049 

.858569 

.894052 

61 

50 

745.995 

745.238 

.063 

.834619 

.870102 

734.038 

733.654 

.032 

.786046 

.819269 

50 

49 

731.986 

731.439 

.046 

2.762059 

2.795282 

719.738 

719.553 

.015 

2.718140 

2.749297 

49 

48 

717.566 

717.221 

.029 

.694109 

.725266 

705.037 

705.053 

.001 

.654419 

.683675 

48 

47 

702.744 

702.600 

.012 

.630337 

.659593 

689.958 

690.152 

.016 

.594476 

.622013 

47 

46 

687.539 

687.575 

.003 

.570335 

.597872 

674.531 

674.895 

.030 

.537926 

.563890 

46 

45 

671.983 

672.191 

.017 

.513717 

.539681 

658.764 

659.298 

.044 

.484453 

.508966 

45 

44 

i 

656.086 

656.464 

.032 

2.460167 

2.484680 

642.687 

643.362 

.056 

2.433756 

2.456960 

44 

— 

29.   TT  =  15.3125. 

28.   TT  =  14.8689. 

Continued  from  Page  *164. 


U91 


TABLE    LXIII. 


GENERAL  VALUATION  OF  ANNUAL  PREMIUM  POLICIES  OF  1,000. 

4  PER  CENT. 


li 

n. 

82.   77  =  196.942. 

83.    :t  =  210.594. 

li 

11. 

V. 

6in. 

v. 

12in. 

Jm.d. 

A(B/). 
6m. 

AB. 

12m. 

V. 

6m. 

V. 

12m. 

\mA. 

6m. 

AB. 

12m. 

0 

125.880 

54.817 

5.922 

0.048478 

0.092084 

133.429 

56.263 

6.431 

0.052451 

0.099243 

0 

1 

179.877 

107.996 

5.990 

.401959 

.448751 

188.818 

110.780 

6.503 

.410393 

.460704 

1 

2 

232.232 

159.525 

6.059 

.637870 

.688181 

242.683 

163.991 

6.558 

.651621 

.705725 

2 

3 

283.142 

209.818 

6.110 

.830995 

.885099 

295.568 

216.552 

6.585 

.851002 

.909195 

3 

4 

333.129 

259.498 

6.136 

1.005502 

1.063695 

347.991 

268.836 

6.596 

1.033065 

1.095828 

4 

5 

382.678 

308.916 

6.147 

1.173060 

1.235823 

401.142 

322.853 

6.524 

1.209337 

1.276870 

5 

6 

432.915 

359.972 

6.079 

.340355 

.407888 

452.039 

370.631 

6.784 

.390937 

.466607 

6 

7 

481.023 

405.131 

6.324 

.516239 

.591909 

496.256|411.287 

7.081 

.586356 

.670955 

7 

8 

522.815 

443.558 

6.605 

.708048 

.792647 

535.596 

449.312 

7.190 

.797620 

.889^97 

8 

9 

560.000 

479.499 

6.708 

.917087 

2.009464 

572.936 

485.965 

7.248 

2.026552j2.127062 

9 

10 

595.291 

514.142 

6.762 

2.144692 

2.245202 

608.646 

520.734 

7.326 

2.277765 

2.387656 

10 

11 

629.045 

547.005 

6.837 

.395138 

.505029 

642.971 

554.614 

7.363 

.555967 

.676047 

11 

12 

661.487 

579.028 

6.872 

.672919 

.792999 

678.421 

591.633 

7.232 

.864483 

.995025 

12 

13 
14 

694.994 
727.998 

614.018 
645.036 

6.748 
6.914 

.981220 
3.337062 

3.111762 
.484519 

713.338 

624.450 

7.407 

3.220429J3.367886 

13 

26. 

70 

27. 

924.385 

920.820 

.297 

5.817832 

5.965289 

69 

923.956 

920.218 

.312 

5.794407 

5.941864 

917.023 

913.901 

.260 

5.462325 

5.592867 

69 

68 

916.538 

913.246 

.274 

.438899 

.569441 

909.549 

906.096 

.288 

.154720 

.274800 

68 

67 

909.007 

905.382 

.302 

.131295 

.251375 

902.313 

898.953 

.280 

4.878290 

4.988181 

67 

66 

901.715 

898.184 

.294 

4.854864 

4.^64755 

894.783 

891.623 

.263 

.630298 

.730808 

66 

65 

894.129 

890.798 

.278 

.606872 

.707382 

886.911 

883.895 

.251 

.406901 

.499278 

65 

64 

886.196 

883.012 

.265 

4.383474 

4.475851 

'878.617 

875.878 

.228 

4.204793 

4.289392 

64 

63 

877.839 

874.933 

.242 

.181365 

.265964 

869.294 

867.306 

.166 

.023923 

.099593 

63 

62 

868.446 

866.297 

.179 

.000493 

.076163 

858.563 

857.233 

.111 

3.864643 

3.932176 

62 

61 

857.633 

856.147 

.124 

3.841210 

3.908743 

847.357 

845.844 

.126 

.721803 

.784566 

61 

60 

846.342 

844.671 

.139 

.  .698366 

.761129 

836.304 

834.821 

.124 

.590121 

.648314 

60 

59 

835.205 

833.564 

.137 

3.566678 

3.624871 

825.154 

823.739 

.118 

3.468672 

3.522776 

59 

58 

823.970 

822.398 

.131 

.445223 

.499327 

813.798 

812.520 

.106 

.356375 

.406686 

58 

57 

812.527 

811.094 

.119 

.332916 

.383227 

802.119 

801.026 

.091 

.252453 

.299245 

57 

56 

800.760 

799.512 

.104 

.22JJ982 

.275774 

790.075 

789.164 

.076 

.156122 

.199728 

56 

55 

788.623 

787.560 

.089 

.132636 

.176242 

777.635 

776.936 

.058 

.066659 

.107305 

55 

54 

776.089 

775.239 

.071 

3.043154 

3.083800 

764.780  764.285 

.041 

2.983445 

3.021401 

54 

53 

763.137 

762.491 

.054 

2.959917 

2.997873 

751.514  751.227 

.024 

.905872 

2.941355 

53 

52 

749.769 

749.334 

.036 

.882316 

.917799 

737.8341737.751 

.007 

.833417 

.866640 

52 

51 

735.985 

735.756 

.019 

.809828 

.843051 

723.753:723.868 

.010 

.765591 

.796748 

51 

50 

721.798 

721.767 

.003 

.741964 

.773121 

709.279  709.590 

.026 

.701964 

.731220 

50 

49 

707.213 

707.381 

.014 

2.678291 

2.707547 

694.431694.918 

.041 

2.642128 

2.669665 

49 

48 

692.253 

692.597 

.029 

.618404 

.645941 

679.242 

679.896 

.055 

.585701 

.611665 

48 

47 

676.947 

677.460 

.043 

.561916 

.58^880 

663.719 

664.539 

.068 

.532368 

.556881 

47 

46 

661.305 

661.986 

.057 

.508516 

.533029 

647.888 

648.849 

.080 

.481830 

.505034 

46 

45 

645.355 

646.177 

.068 

.457901 

.481105 

631.787 

632.878 

.091 

.433790 

.455797 

45 

44 

629.132 

630.085 

.079 

2.409775 

2.431782 

615.439 

616.648 

.101 

2.388007 

2.408918 

44 

27.   TT  =  14.4479. 

26.    rr  =  14.0485. 

Continued  from  Page  *163. 


*193 


TABLE     LXIII 


GENERAL  VALUATION   OF  ANNUAL  PREMIUM  POLICIES   OF  1,000. 

4  PER  CENT. 


a;  =84.  77  =  225.442. 

85.   Tr  =  241.622. 

li 

n. 

V. 

6m. 

V. 

12in. 

^m.d. 

6m. 

AB. 
12ra. 

V. 

6m. 

V. 
12m. 

im.d. 

6m. 

AB. 

12m„ 

0 

141.605 

57.768 

6.986 

0.056912 

0.107223 

150.731 

59.840 

7.574 

0.061816 

0.115920 

0 

1 

198.680!ll4.150 

7.044 

.419758 

.473862 

210.206 

118.949 

7.605 

.430060 

.488253 

1 

2 

254.719 

169.845 

7.073 

.666832 

.725025 

269.158 

177.746 

7.618 

.683828 

.746591 

2 

3 

310.266 

225.246 

7.085 

.873363 

.936126 

328.931 

238.493 

7.537 

.898194 

.965727 

3 

4 

366.586 

282.483 

7.009 

1.063734 

1.131267 

386.169 

292.224 

7.829 

1.102046 

1.177716 

4 

5 

420.517 

333.110 

7.284 

1.253934 

1.329604 

435.895 

337.944 

8.163 

1.310810 

1.395409 

5 

6 

467.371 

376.189 

7.599 

.454640 

.539239 

480.136 

380.706 

8.286 

.530046 

.622423 

6 

7 

509.056 

416.481 

7.715!  .669110 

.761487 

522.127 

421.925 

8.350 

.763647 

.864157 

7 

8 

548:621 

455.319 

7.775 

.899935 

2.000445 

562.286 

461.026 

8.438 

2.017529 

2.127420 

8 

9 

586.461 

492.161 

7.858 

2.152236 

.262127 

600.888 

499.127 

8.480 

.297183 

.417263 

9 

10 

622.832  528.061 

7.898 

2.431031 

2.551111 

640.753 

540.758 

8.333 

2.606442 

2.736984 

10 

11 
12 

660.395  567.287 
697  395  602  061 

7.759 
7  944 

.739852 
3  095944 

.870394 
3  243401 

680.022 

577.663 

8.530 

.962744 

3.110201 

11 

\J  tJ   1  •t/Ct/'Jw-^*  VJJ. 

1  •  «/^^ 

t/«  \J  tJfJ  %J    JL  J. 

t7»  /v^t/^v/X 

24. 

72 

71 

25. 

925.180 

921.937 

.270 

5.864170 

6.011627 

71 

924.793 

921.393 

.283 

5.841083  5.988540 

917.922 

915.115 

.234 

.508663 

5.639205 

70 

917.484 

914.524 

.247 

.485576  .616118 

910.553 

907.420 

.261 

.201059 

.321139 

70 

69 

910.064 

906.775 

.274 

5.177972 

5.298052 

903.418 

900.378 

.253 

4.924629 

5.034520 

69 

68 

902.879 

899.684 

.266 

4.901542 

.011433' 

895.996 

893.151 

.237 

.676637 

4.777147 

68 

67 

895.405 

892.406 

.250 

.653550 

4.754060; 

888.234 

885.532 

.225 

.453242 

.545619 

67 

66 

887.590 

884.735 

.238 

.430154 

.522531!  1880.056 

877.628 

.202 

.251136 

.335735 

66 

65 

879.355 

876.775 

.215 

.228047 

.312646 

870.866 

869.177 

.141 

.070270 

.145940 

65 

64 

870.100 

868.266 

.153 

4.047179 

4.122849 

860.285 

859.246 

.087 

3.910994 

3.978527 

64 

63 

859.446 

858.265 

.098 

3.887901 

3.955434 

849.238 

848.017 

.102 

.768162 

.830925 

63 

62 

848.322 

846.959 

.114 

.745066 

.807829 

838.341 

837.150 

.099 

.636489  .694682 

62 

61 

837.349 

836.015 

.111 

.613388 

.671581 

827.347 

826.224 

.094 

.5150541  .569158 

61 

60 

826.279 

825.014 

.105 

.491947 

.546051 

816.151 

815.163 

.082 

.402774  .453085 

60 

59 

815.005 

813.876 

.094 

3.379658 

3.429969 

804.638 

803.831 

.067 

3.298874  3.345666 

59 

58 

803.412 

802.465 

.079 

.275748 

.322540 

792.762 

792.136 

.052 

.202571 

.246177 

58 

57 

791.453 

790.689 

.064 

.179431 

.223037 

780.498 

780.081 

.035 

.113142 

.153788 

57 

56 

779.104 

778.549 

.046 

.089986 

.130632 

767.825 

767.607 

.018 

.029970 

.067926 

56 

55 

766.342 

765.989 

.029 

.006793 

.044749 

754.745 

754.734 

.001 

2.952448 

2.987931 

55 

54 

753.171 

753.026 

.012 

2.929246  2.964729 

741.259 

741.449 

.016 

2.880053 

2.913276 

54 

53 

739.591 

739.648 

.005 

.856822;  .890045 

727.377 

727.761 

.032 

.812297 

.843454 

53 

52 

725.612 

725.865 

.021 

.7890331  .820190 

713.105 

713.684 

.048 

.748752 

.778008 

52 

51 

711.242 

711.690 

.037 

.725447 

.754703 

698.468 

699.219 

.063 

.689012 

.716549 

51 

50 

696.503 

697.125 

.052 

.665661 

.693198 

683.493 

684.409 

.076 

.632693 

.658657 

50 

49 

681.422 

682.211 

.066 

2.609289 

2.635253 

668.187 

669.268 

.090 

2.579484 

2.603997 

49 

48 

666.011 

666.965 

.079 

.556021 

.580534 

652.581 

653.799 

.102 

.529085 

.552289 

48 

47 

650.295 

651.388 

.091 

.505554 

.528758 

636.707 

638.054 

.112 

.481202 

.503209 

47 

46 

634.311 

635.533 

.102 

.457595 

.479002 

620.588 

622.052 

.122 

.435594 

.456505 

46 

45 

618.080 

619.420 

.112 

.411902 

.432813 

604.256 

605.816 

.130 

.392028 

.411946 

45 

44 

601.634 

603.071 

.120 

2.368242 

2.388160 

587.734 

589.388 

.138 

2.350298 

2.369299 

44 

25.   Tr  =  13.6687. 

24.   TT  =  13.3082. 

Continued  from  Page  *163. 


♦193 


TABLE     LXIII. 


GENERAL  VALUATION  OF  ANNUAL  PREMIUM  POLICIES  OF  1,000. 

4  PER  CENT. 


li 

n. 
0 

86.   77  =  259.448. 

87.   77  =  279.436. 

p4tH 

n. 
0 

V. 

6m. 

V. 

12m. 

Jm.d. 

A(B/). 
6m. 

AB. 
12m. 

V. 

6m. 

V. 
12m. 

^m.d. 

A(B/). 
6m. 

AB. 

12m. 

161.160 

62.872 

8.191 

0.067214 

0.125407 

173.086 

66.735 

8.863 

0.073392 

0.136155 

1 

223.866 

125.411 

8.205 

.441636 

.504399 

240.927 

135.683 

8.770 

.454427 

.521960 

1 

2 

287.441 

190.024 

8.118 

.702683 

.770216 

305.893 

196.668 

9.102 

.727812 

.803482 

2 

3 

348.324 

247.175 

8.429 

.930001 

1.005671 

362.333 

248.561 

9.481 

.972065 

1.056664 

3 

4 

401.214 

295.805 

8.784 

1.151718 

.236317 

412.546 

297.096 

9.621 

1.210687 

.303064 

4 

5 

448.271 

341.289 

8.915 

1.378303 

1.470680 

460.206 

343.880 

9.694 

1.455162 

1.555672 

5 

6 

492.934 

385.132 

8.984 

.616135 

.716645 

505.788 

388.^60 

9.794 

.715063 

.824954 

6 

7 

535.651 

426.721 

9.077 

.872380 

.982271 

549.600 

431.504 

9.841 

.997939 

2.118019 

7 

8 

576.708 

467.247 

9.122 

2.153307 

2.273387 

594.848 

478.756 

9.674 

2.308839 

.439381 

8 

9 
10 

619.111 
660.879 

511.528 

550.782 

8.965 
9.175 

.463217 
2.819828 

.593759 
2.967285 

639.418 

520.644 

9.898 

.665921 

.813378 

9 
74 

22. 

23. 

925.897'922.944 

.246 

5.909879 

6.057336 

73 

925.548 

922.453 

.258 

5.887099 

6.034556 

918.733  916.211 

.210 

.554372 

5.684914 

73 

72 

918.338 

915.677 

.222 

.531592 

5.662134 

911.460  908.615 

.237 

.24676* 

.366848 

72 

71 

911.018 

908.033 

.249 

.223988 

.344068 

904.417  901.664 

.229 

4.970339 

.080230 

71 

70 

903.930 

901.037 

.241 

4.947558 

.057449 

897.089  894.530 

.213 

.722348 

4.822858 

70 

69 

896.557 

893.858 

.225 

4.699567 

4.800077 

889.428  887.009 

.202 

4.498954 

4.591331 

69 

68 

888.846 

886.289 

.213 

.476173 

.568550 

881.357879.207 

.179 

.296850 

.381449 

68 

67 

880.724 

878.438 

.191 

.274068 

.358667 

872.284  870.866 

.118 

.115987 

.191657 

67 

66 

871.593 

870.043 

.129 

.  .093203 

.168873 

861.841861.063 

.065 

3.956716 

.024249 

66 

65 

861.083 

860.177 

.075 

3.933930 

.001463 

850. 9361849. 979 

1 

.080 

.813890 

3.876653 

65 

64 

850.108 

849.023 

.090 

3.791101 

3.853864 

840.179 

839.252 

.077 

3.682227 

3.740420 

64 

63 

839.283 

838.227 

.088 

.659433 

.717626 

829.328 

828.467 

.072 

.560803 

.614907 

63 

62 

828.364 

827.374 

.083 

.538004 

.592108 

818.277 

817.549 

.061 

.448538 

.498849 

62 

61 

817.241 

816.387 

.071 

.425732 

.476043 

806.911 

806.364 

.046 

.344658 

.391450 

61 

60 

805.804  805.130 

.056 

.321842 

.368634 

795.190 

794.819 

.031 

.248379 

.291985 

60 

59 

794.007i793.512 

.041 

3.225551 

3.269157 

783.084 

782.920 

.014 

3.158981 

3.199627 

59 

58 

781.824  781.536 

.024 

.136138 

.176784 

770.574 

770.608 

.003 

.075846 

.113802158 

57 

769.235 

769.146 

.007 

.052985 

.090941 

757. 663 

757.900 

.020 

2.998369 

.033852  57 

56 

756.241 

756.357 

.010 

2.975486 

.010969 

744.350 

744.786 

.036 

.926027 

2.959250  56 

55 

742.844 

743.160 

.026 

.903118 

2.936341 

730.648 

731.275 

.052 

.858334 

.889491155 

54 

729.054 

729.562 

.042 

2.835395 

2.866552 

716.562 

717.381 

.068 

2.794862 

2.824118' 54 

53 

714.877 

715.579 

.058 

.771887 

.801143 

702.112 

703.102 

.083 

.735205 

.762742  53 

52 

700.337 

701.210 

.073 

.712190 

.739727 

687.331 

688.483 

.096 

.678982 

.704946  52 

51 

685.460 

686.497 

.086 

.655921 

.681885 

672.223 

673.538 

.110 

.625883 

.650396' 51 

50 

670.257 

671.457 

.100 

.602768 

.627281 

656.817 

658.268 

.121 

.575607 

.598811  50 

49 

654.753 

656.091 

.112 

2.552433 

2.575637 

641.148 

642.726 

.131 

2.527863 

2.549870  49 

48 

638.984 

640.449 

.122 

.504621 

.526628 

625.238 

626.931 

.141 

.482409 

.503320 

48 

47 

622.972 

624.553 

.132 

.459093 

.480004 

609.117 

610.905 

.149 

.439015 

.458933 

47 

46 

606.748 

608.425 

.140 

.415615 

.435533 

592.808 

594.688 

.157 

.397476 

.416477 

46 

45 

590.335 

592.105 

.147 

.373984 

.392985 

576.331 

578.288 

.163 

.357599 

.375780 

45 

44 

573.754 

575.600 

.154 

2.334006 

2.352187 

559.752 

561.734 

.165 

2.319204 

2.336626 

44 

23.    77=12.9656. 

22.   77  =  12.6399. 

Continued  from  Page  *161 


nu 


TABLE    LXIII 


GENERAL  VALUATION  OF  ANNUAL  PREMIUM  POLICIES  OF  1,000. 

4  PER  CENT. 


li 

88.   Tr  =  302.168. 

89.    n  =  329.342. 

&»2 

V. 

V. 

^m.d. 

^(B/). 

AB. 

V. 

V. 

^m.d. 

^(B/). 

AB. 

n. 

6m. 

12m. 

6m. 

12m. 

6m. 

12m. 

6m. 

12m. 

n. 
0 

0 

188.023 

73.878 

9.51 

0.080005 

0.147538 

199.951 

70.559 

10.78 

0.091697 

0.167367 

1 

257.635 

139.224 

9.87 

.472731 

.548401 

265.249 

130.597 

11.22 

.497892 

.582491 

1 

2 

318.110 

194.827 

10.27 

.761752 

.846351 

323.345 

186.752 

11.38 

.800873 

.893250 

2 

3 

371.914 

246.833 

10.42 

1.021673 

1.114050 

378.488 

240.881 

11.47 

1.076513 

1.177023 

3 

4 

422.982 

296.963 

10.50 

.277234 

.377744 

431.225 

292.227 

11.58 

.352468 

.462359 

4 

5 

471.823 

344.516 

10.61 

1.543045 

1.652936 

481.914 

342.260 

11.64 

1.643617 

1.763697 

5 

6 

518.769 

390.853 

10.66 

.829022 

.949102 

534.266 

396.930 

11.45 

.958640 

2.089182 

6 

7 

567.252 

441.483 

10.48 

2.141481 

2.272023 

585.833 

445.393 

11.70 

2.317667 

.465124 

7 

8 

615.009 

486.367 

10.72 

.499301 

.646758 

75 

21. 

926.546 
919.466 

923.855 
917.201 

20. 

.224 

.189 

5.955022 
.599515 

6.102479 
5.730057 

76 
75 

926.229 

923.411 

.235 

5.932518  6.079975 

74 

919.109 

916.718 

.199 

5.577011*5.707553 

912.279 

909.695 

.215 

5.291911 

5.411991 

74 

73 

911.879 

909.169 

.226 

.2694071  .389487 

905.319 

902.826 

.208 

.015482 

.125373 

73 

72 

904.879 

902.259 

.218 

4.992978  .102869 

898.078 

895.776 

.192 

4.767492 

4.868002 

72 

71 

897.596 

890.169 

.202 

.744988  4.845498 

890.507 

888.344 

.180 

.544099 

.636476 

71 

70 

889.982 

887.694 

.191 

.521594  .613971 

882.532 

880.635 

.158 

.341997 

.426596 

70 

69 

881.958 

879.939 

.168 

4.319491|4.404090 

873.566 

872.392 

.098 

4.161137 

4.236807 

69 

68 

872.941 

871.648 

.108 

.138629  .214299 

863.246 

862.704 

.045 

.001870 

.069403 

68 

67 

862.561 

861.904 

.055 

3.979360  .046893 

852.469 

851.752 

.060 

3.859050 

3.921813 

67 

66 

851.722 

850.888 

.069 

.836538  3.899301 

841.841 

841.151 

.058 

.727394 

.785587 

66 

65 

841.030 

840.225 

.067 

.704878  .763071 

831.117 

830.494 

.052 

.605980 

.660084 

65 

64 

830.245 

829.506 

.062 

3.583460  3.637564 

820.196 

819.705 

.041 

3.493730 

3.544041 

64 

63 

819.260 

818.654 

.051 

.471202 

.521513 

808.966 

808.651 

.026 

.389867 

.436659 

63 

62 

807.964 

807.536 

.036 

.367331 

.414123 

797.382 

797.244 

.011 

.293610 

.337216 

62 

61 

796.313 

796.062 

.021 

.271063 

.314669 

785.420 

785.485 

.005 

.204239 

.244885 

61 

60 

784.281 

784.234 

.004 

.181679 

.222325 

773.057 

773.318 

.022 

.121137 

.159093 

60 

59 

771.846 

771.997 

.013 

3.098561 

3.136517 

760.299 

760.760 

.038 

3.043699 

3.079182 

59 

58 

759.014 

759.366 

.029 

.021104 

.056587 

747. 144 

747.802 

.055 

2.971405 

.004628 

58 

57  745.782 

746.332 

.046 

2.948786  2.982009 

733. 603 

734.450 

.071 

.903767 

2.934924 

57 

56  733.162 

732.902 

.062 

.881122  .912279 

719.683 

720.720 

.086 

.840359 

.869615 

56 

55  718.161 

719.092 

.078 

.817683  .846939 

705.405 

706.610 

.100 

.780778 

.808315 

55 

54  703.800 

704.900 

.092 

2.758065  2.785602 

690.797 

692.164 

.114 

2.724640 

2.750604 

54 

53 

689.107 

690.369 

.105 

.701886 

.727850 

675.869 

677.395 

.127 

.671638 

.696151 

53 

52 

674.091 

675.515 

.119 

.648837 

.673350 

660.645 

662.306 

.138 

.621472 

.644676 

52 

51 

658.779 

660.338 

.130 

.598617 

.621821 

645.161 

646.948 

.149 

.573850 

.595857 

51 

50 

643.205 

644.890 

.140 

.550936 

.572943 

629.439 

631.339 

.158 

.528533 

.549444 

50 

49 

627.391 

629.190 

.150 

2.505553 

2.526464 

613.507 

615.502 

.166 

2.485291 

2.505209 

49 

48 

611.367 

613.261 

.158 

.462237 

.482155 

597.392 

599.477 

.174 

.443920 

.462921 

48 

47 

595.157 

597.143 

.165 

.420784 

.439785 

581.110 

583.271 

.180 

.404229 

.422410 

47 

46 

578.780 

580.842 

.172 

.381004 

.399185 

564.727 

566.912 

.182 

.366037 

.383459 

46 

45 

562.302 

564.388 

.174 

.342714 

.360136 

548.269 

550.506 

.186 

.329195 

.345933 

45 

44 

545.749  547.886 

.178 

2.305763 

2.322501 

531.735 

533.997 

.188 

2.293553 

2.309662 

44 

21.   TT  =  12.3304. 

20.    TT  =  12.0361. 

Continued  from  Page  *160. 


TABLE     LXIII. 


♦195 


GENERAL  VALUATION  OF  ANNUAL  PREMIUM  POLICIES  OF  1,000. 

4  PER  CENT. 


o® 


90. 


n  =  357.261. 


V. 

6m. 


310.938 
373.435 
333.764 
389.504 
444.043 


5  500.3^8 

6  555.849 


V. 

13m. 


64.595 
135.014 
183.353 
338.496 
393.338 


|m.d. 


13.19 
13.37 
13.46 
13.58 
13.64 


351.14713.44 
403.39013.71 


MB/). 

6m. 


0.105165 
.533683 
.841311 

1.136333 
.436615 

1.756106 
3.117313 


AB. 
12m. 


0.189764 
.616059 
.941731 

1.346113 
.556695 

1.886648 
3.264670 


19. 


77  936.847 


919.806 
913.658 


934.377 
917.660 
910.196 


74  905.7381903.365 
73  898.537i896.354 
72  1891.008  888.964 
71 1883.076  881.397 
70l874.16l|873.099 


)863. 8981863.466 
i853.18l!853.574 
i  843. 611:843.033 
i831. 947  831.434 

1831.087  830.705 


64  1809.919  809. 713 
63  798.399i798.368 


786.503 
774.309 
761.533 


59  748.439 
581734.974 
571731.131 
56^706.932 
55:693.406 


54^677. 
53  1663. 
52  647. 
51  631. 
50,615. 

49  599. 
48  583. 


47 
46 
45 

44 


567.034:569.314 

550. 

534 


559 
431 

032 
387 
544 

518 
326 


786.674 
774.575 
762.087 

749.200 
735.923 

722.269 
708.237 
693.871 

679.184 
664.179 
648.906 
633.383 
617.634 

601.698 

585.582 


.667 
.225 


517.748 


552.998 
536.581 


520.112 


.214 

.179 
.305 

.198 
.183 
.170 
.148 
.089 

.036 
.051 
.048 
.043 
.033 

.017 
.003 
.014 
.030 
.047 

.063 
.079 
.095 
.109 
.132 

.135 
.147 
.157 
.166 
.174 

.182 
.188 
.190 
.194 
.196 

.197 


5. 977398'6. 124855 
.62189115.752433 
.314287  .434367 


5.037858 

4.789869 

.566476 

.364375 

.183516 


5.147749 

4.890379 

.658853 

.448974 

.259186 


4.0243514.091784 
3.881433  3.944196 


.749781 
.638373 
.516138 

3.413373 

316036 
336667 
143581 
066161 

3.993888 
.936376 
.863898 
.803350 

.747353 

3. 694394 
.644178 
.596613 
.551358 
.508185 

3.466891 
.437385 
.389186 
.353445 
.316914 

2.283464 


.807974 
.682476 
.566439 

3.459065 
.359632 
.267313 
.181537 
.101644 

3.037111 
3.957433 

.893154 
.830887 
.773316 

3.718807 
.667382 
.618619 
.572269 
.528103 

2.485892 
.445466 
.406608 
.369183 
.333023 

2.298003 


19. 


7r  =  11.7560. 


91. 


T  =  384.586. 


V. 

6m. 


224.588 
288.013 
348.673 


V. 
12m. 


64.590 
126.850 
185.909 


406.976l243.458 


^m.d. 


13.33 
13.43 
13.56 
13.63 


467.193  306.339  13.40 


536.504  363.083  13.70  1.896111  3.043568 


A(B/). 
6m. 


0.117487 
.549533 
.885337 

1.303501 
.531344 


AB. 

13m. 


•^3 
o  a> 


0.309864  0 
.650033  1 


.995138 

1.333581 

.661786 


18. 


937.133 
930.130 
913.019 
906.136 

898.973 
891.484 
883.594 
874.736 
864.518 

853.858 
843.344 
833.737 
831.934 
810.824 

799.366 
787.533 
775.304 
763.685 
749.671 

736.277 
733.508 
708.384 
693.934 
679.168 

664.108 
648.793 
633.340 


924.679:  .205 

918.097|  .169 

910.672  .196 

903.8771  .188 


896.904 
889.552 
881.936 

873.772i 
864.190 

853.3561 

842.870| 
832.328' 
821.656| 
810.722 

799.437 
787.805 
775.770 
763.349 
750.530 

737.323 
723.741 

709.784 
695.494 
680.885 

665.960 
650.767 
635.328 


.173 

.161 
.139 
.079 

.037 

.042 
.040 
.034 
.023 
.008 


5.999652.6.147109 
.64414515.774687 


.336541 
.060113 

4.812123 
.588731 
.386631 
.205773 
.046509 


.456621 
.170004 

4.912633 

.681108 
.471330 
.281443 
.114042 


3.903695  3.966458 
.773045  .830338 


.650643 
.538403 
.434555 


.006  3.338318 
.033  .248971 


617.481:619.662 
601.539  6D3. 810 

585.433  587.779 
569.338  571.597 
553.949  555.369 
536.593  539.038 
530.303j533.656 

503.813  506.361 


.039 
.055 
.073 

.087 
.103' 
.117 
.130 
.143 

.154 
.165 
.174 
.183 
.189 

.195 

.197 
.303 
.304 
.304 


.165899 
.088496 
.016344 

3.948656 
.885306 
.835791 
.769739 
.716813 

3.666744 
.619331 
.574036 
.530939 

.489707 

3.450180 
.413169 
.375534 
.340097 
.305761 


.304  3.2733913.387409 


.704746 
.588714' 66 
.481347  65 


3.381934 
.389617 
.303855 
.133979 
.049467 

3.979813 
.914563 
.853328 
.795693 
.741326 


2.689948  64 
.641238  53 


.594947 
.550847 

.508708 

2.468361 
.429591 
.392262 
.356206 
.321300 


18. 


rr  =  11.4897. 


52 
51 
50 

49 
48 
47 
46 
45 

44 


Continued  from  Page  *159. 


U96 


TABLE    LXIII, 


GENERAL  VALUATION  OF  ANNUAL  PREMIUM  POLICIES  OP  1,000. 

4  PER  CENT. 


n. 

x  =  92.     7r  =  413.801. 

93.   n  =  446.049. 

0  0 

n. 

V. 

6m. 

V. 

12m. 

|m.d. 

6m. 

AB. 

12m. 

V. 

6m. 

V. 

12m. 

^m.d. 

MB/). 

6m. 

AB. 

12m. 

0 

240.180 

66.559 

14.47 

0.131006 

0.231516 

256.844 

67.639 

15.77 

0.147474 

0.257365 

0 

1 

305.028 

129.696 

14.61 

.5795-10 

.689401 

323.619 

133.549 

15.84 

.61£040 

.735120 

1 

2 

367.358 

191.219 

14.68 

.936727 

1.056807 

392.582 

205.566 

15.59 

.996003 

1.126545 

2 

3 

4 

431.731 

AQK   1  on 

258.442 

o-t  o  noK 

14.44 
14.76 

1.280853 
.652883 

.411395 
.800340 

460.511 

269.408 

15.93 

1.382805 

.530262 

3 

^vO.  Loo'^oi-o.yjoo 

16. 

80 

17. 

927.663 

925.424 

.187 

6.043818  6.191275 

79 

927.405 

925.061 

.195 

6.021790 

6.169247 

920.729 

918.907 

.152 

5.688311 

5.818853 

79 

78 

920.436 

918.512 

.160 

5.666283 

5.796825 

913.690 

911.556 

.178 

.380708 

.500788 

78 

77 

913.363 

911.125 

.187 

.358680 

.478760 

906.874i904.829 

.170 

.104280 

.214171 

77 

76 

906.514 

904.365 

.179 

.082251 

.192142 

899.783 

897.924 

.155 

4.856291 

4.956801 

76 

75 

899.388 

897.427 

.163 

4.834262 

4.934772 

892.368 

890.646 

.144 

.632899 

.725276 

75 

74 

891.937 

890.113 

.152 

4.610871 

4.703248 

884.555 

883.095 

.122 

4.430800 

4.515399 

74 

73 

884.087 

882.525 

.130 

.408771 

.493370 

875.775 

875.021 

.063 

.249945 

.325615 

73 

72 

875.264 

874.413 

.071 

.227914 

.303584 

865.668 

865.534 

.011 

.090685 

.158218 

72 

71 

865.108 

864.879 

.019 

.068652 

.136185 

855.114 

854.807 

.026 

3.947874 

.010637 

71 

70 

854.501 

854.100 

.033 

3.925840 

3.988603 

844.703 

844.425 

.023 

.816231  3.874424 

1 

70 

69 

844.041 

843.667 

.031 

3.794194 

3.852387 

834.202  833.987 

.018 

3.694836  3.748940 

69 

68 

833.487 

833.178 

.026 

.672794 

.726898 

823.505 

823.421 

.007 

.582608 

.632919 

68 

67 

822.740 

822.561 

.015 

.560561 

.610872 

812.506 

812.595 

.007 

.478774 

.525566 

67 

66 

811.686 

811.682 

.000 

.456721 

.503513 

801.162 

801.422 

.022 

.382554 

.426160 

66 

65 

800.287 

800.455 

.014 

.360493 

.404099 

789.4451 789. 906 

.038 

.293229 

.333875 

65 

64 

788.513 

788.882 

.031 

3.271157 

3.311803 

777.338 

777.990 

.054 

3.210183 

3.248139 

64 

63 

776.346 

776.908 

.047 

.188098 

.226054 

764.843 

765.691 

.071 

.132812 

.168295 

63 

62 

763:791 

764.549 

.063 

.110712 

.146195 

751.958 

752.999 

.087 

.060597 

.093820 

62 

61 

750.844 

751.796 

.079 

.038479 

.071702 

738.697 

739.923 

.102 

2.993054 

.024211 

61 

60 

737.517 

738.656 

.095 

2.970914 

.002071 

725.064 

726.476 

.118 

.929755 

2.959011 

60 

59 

723.818 

725.143 

.110 

2.907590 

2.936846 

711.080 

712.657 

.131 

2.870299 

2.897836 

59 

58  709.766 

711.257 

.124 

.848105 

.875642 

696.774 

698.508 

.145 

.814305 

.840269 

58 

57 

695.390 

697.039 

.137 

.792078 

.818042 

682.152  684.044 

.158 

.761465 

.785978 

57 

56 

680.697 

682.504 

.151 

.739201 

.763714 

667.243  669.266 

.169 

.711483 

.734687 

56 

55 

665.714 

667.654 

.162 

.689177 

.712381 

652.078  654.224 

.179 

.664068 

.686075 

55 

54 

650.477 

652.539 

.172 

2.641714 

2.663721 

636.679 

638.937 

.188 

2.618980 

2.639891 

54 

53 

635.002 

637.178 

.181 

.596574 

.617485 

621.076 

623.426 

.196 

.575994 

.595912 

53 

62 

619.324|621.591 

.189 

.553529 

.573447 

605.293 

607.732 

.203 

.534904 

.553905 

52 

51 

603.464  605.821 

.196 

.512375 

.531376 

589.346 

591.859 

.209 

.495523 

.513704 

51 

50 

587.438|589.870 

.203 

.472924 

.491105 

573.302 

575.838 

.211 

.457672 

.475094 

50 

49 

571.316 

573.771 

.205 

2.434995 

2.452417 

557.183 

559.770 

.216 

2.421202 

2.437940 

49 

48 

555.119 

557.625 

.209 

.398440 

.415178 

540.988 

543.601 

.218 

.385967 

.402076 

48 

47 

538.846 

541.377 

.211 

.363112 

.379221 

524.762 

527.381 

.218 

.351838 

.367377 

47 

46 

522.540 

525.078 

.211 

.328882 

.344421 

508.534 

511.148 

.218 

.318694 

.333712 

46 

45 

506.232 

508.766 

.211 

.295629 

.310647 

492.333 

494.924 

.216 

.286421 

.300970 

45 

44 

489.954 

492.463 

.209 

2.263238 

2.277787 

476.189 

478.748 

.213 

2.254918 

2.269036 

44 

17.   TT  =  11.2364. 

16,   n  =  10.9953. 

Continued  from  Page  *158 


*197 


TABLE    LXIII. 


GENERAL  VALUATION  OF  ANNUAL  PREMIUM  POLICIES  OF  1,000. 

4  PER  CENT. 


II 

n. 

94.   n  =  481.198. 

95.   77  =  520.729. 

•■si 

n. 

V. 

6m. 

Y. 
12m. 

Jm.d. 

A(B/). 
6m. 

AB. 

12m. 

V. 

6m. 

V. 

12m. 

^m.d. 

6m. 

AB. 

12m. 

0 

275.945 

70.691 

17.11 

0.166535 

0.286615 

301.923 

83.117 

18.23 

0.187522 

0.318064 

0 

1 
2 

349.910 
422.768 

147.932 
216.406 

16.83 
17.20 

.655087 
1 076479 

.785629 
1  223936 

380.323 

156.799 

18.63 

.713515 

.860972 

1 

^•\j  i  \j^  1  t/ 

J-^/V/Vv  tJtJXJ 

14. 

82 

15. 

928.144 

926.099 

.170 

6.087566 

6.235023 

81 

927.909 

925.770 

.178 

6.065742 

6.213199 

921.272 

919.641 

.136 

5.732059 

5.862601 

81 

80 

921.008 

919.283 

.144 

5.710235 

5.840777 

914.297 

912.356 

.162 

.424456 

.544536 

80 

79 

914.001 

911.966 

.170 

5.402632 

5.522712 

907.542 

905.689 

.154 

5.148028 

5.257919 

79 

78 

907.216 

905.270 

.162 

.126203 

.236094 

900.516 

898.848 

.139 

4.900040 

.000550 

78 

77 

900.158 

898.397 

.147 

4.878215 

4.978725 

893.167 

891.635 

.128 

.676650 

4.769027 

77 

76 

892.778 

891.153 

.135 

.654825 

.747202 

885.426 

884.152 

.106 

.474551 

.559150 

76 

75 

885.002 

883.637 

.114 

.452725 

.537324 

876.725 

876.152 

.048 

.293698 

.369368 

75 

74 

876.262 

875.601 

.055 

4.271871 

4.347541 

866.710 

866.750 

.003 

4.134440 

4.201973 

74 

73 

866.202 

866.157 

.004 

.112612 

.180145 

856.250 

856.121 

.011 

3.991634 

.054397 

73  i 

72 

855.696 

855.480 

.018 

3.969804 

.032567 

845.935 

845.832 

.009 

.859997 

3.918190 

72 

71 

845.334 

845.146 

.016 

.838164 

3.896357 

835.528 

835.489 

.003 

.738609 

.792713 

71 

70 

834.882 

834.757 

.010 

.716772 

.770876 

824.929 

825.019 

.008 

.626391 

.676702 

70 

69 

824.235 

824.240 

.000 

3.604549 

3.654860 

814.029 

814.291 

.022 

3.522569 

3.569361 

69 

68 

813.286 

813.464 

.015 

.500722 

.547514 

802.786 

803.219 

.036 

.426365 

.469971 

68 

67 

801.995 

802.343 

.029 

.404510 

.448116 

791.176 

791.806 

.052' 

.337059 

.377705 

67 

66 

790.332 

790.880 

.040 

.315195 

.355841 

779.179 

779.998 

.068 

.254037 

.291993 

66 

65 

778.281 

779.019 

.062 

.232161 

.270117 

766.796 

767.811 

.085 

.176694 

.212177 

65 

64 

765.844 

766.777 

.078 

3.154805 

3.190288 

754.029 

755.234 

.100 

3.104513 

3.137736 

64 

63 

753.019 

754.144 

.094 

.082607 

.115830 

740.887 

742.276 

.116 

.037009 

.068166 

63 

62 

739.820 

741.129 

.109 

.015084 

.046241 

727.377 

728.950 

.131 

2.973756 

.003012 

62 

61 

726.249 

727.744 

.125 

2.951809 

2.981065 

713.520 

715.256 

.145 

.914353 

2.941890 

61 

60 

712.330 

713.989 

.138 

.892380 

.919917 

699.342 

701.235 

.158 

.858419 

.884383 

60 

59 

698.090 

699.905 

.151 

2.836417 

2.862381 

684.854 

686.902 

.171 

2.805649 

2.830162 

59 

58 

683.536 

685.508 

.164 

.783613 

.808126 

670.079 

672.258 

.182 

.755744 

.778948 

58 

57 

668.696 

670.799 

.175 

.733670 

.756874 

655.052 

657.352 

.192 

.708415 

.730422 

57 

56 

653.602 

655.827 

.185 

.686299 

.708306 

639.793 

642.204 

.201 

.663424 

.684335 

56 

55 

638.275 

640.611 

.195 

.641262 

.662173 

624.331 

626.833 

.209 

.620545 

.640463 

55 

54 

622.744 

625.172 

.202 

2.598329 

2.618247 

608.690 

611.281 

.216 

2.579573 

2.598574 

54 

53 

607.033 

609.550 

.210 

.557301 

.576302 

592.888 

595.552 

.222 

.540322 

.558503 

53 

52 

591.161 

593.751 

.216 

.517987 

.536168 

576.987 

579.675 

.224 

.502614 

.520036 

52 

51 

575.190 

577.804 

.218 

.480209 

.497631 

561.015 

563.752 

.228 

.466299 

.483037 

51 

50 

559.146 

561.810 

,  .222 

.443819 

.460557 

544.968 

547.730 

.230 

.431233 

.447342 

50 

49 

543.027 

545.716 

.224 

2.408671 

2.424780 

528.888 

531.657 

.231 

2.397289 

2.412828 

49 

48 

526.876 

529.572 

.225 

.374637 

.390176 

512.806 

515.571 

.230 

.364345 

.379363 

48 

47 

510.723 

513.415 

.224 

.341595 

.356613 

496.752 

499.493 

.228 

.332289 

.346838 

47 

46 

494.598 

497.265 

.222 

.309435 

.323984 

480. 754 

483.463 

.226 

.301020 

.315138 

46 

45|478.528 

481.164 

.220 

.278052 

.292170 

464.831 

467.497 

.222 

.270452 

.284177 

45 

44 

462.535 

465.127 

.216 

2.247362 

2.261087 

449.013 

451.618 

.217 

2.240494 

2.253864 

44 

15.   7r=  10.7660. 

14.    7:  =  10.5480. 

Continued  from  Page  *157. 


♦198 


TABLE    LXIII, 


GENERAL  VALUATION  OF  ANNUAL  PREMIUM  POLICIES  OF  1,000. 

4  PER  CENT. 


n. 
0 

83 

a:  =  96.  tt  =  571.434. 

li 

n. 

V. 

6m. 

V. 

12m. 

^m.d. 

A(B/). 
6m. 

AB. 
12m. 

V. 

6m. 

V. 

12m. 

im.d. 

6m. 

AB. 

12m. 

325.898 

80.362 

20.46 

0  924964 

n  Q  79/1 91 

M 

V.yC'/C'^i/Urr  v/.t^  1  /v^/vjl 

12. 

13. 

928.580 
921.766 

926.711 
920.307 

.156 
.122 

6.130933 

5.775427 

6.278390 

928.367 

926.412 

.163 

6.109295|6.256752 

5.905969  83 

82 

921.525 

919.982 

.129 

5.75378815.884330 

914.848 

913.083 

.147 

.467823 

.587903  82 

81 

914.579 

912.728 

.154 

.4461851  .566265 

908.150 

906.471 

.140 

.191395 

.301286  81 

80 

907.854 

906.090 

.147 

169757  .279648 

901.180 

899.686 

.125 

4.943407 

.043917  80 

791900.856 

899.277 

.132 

4.921768i5.022278 

893.894 

892.533 

.113 

4.720017 

4.812394  79 

78 

893.539 

892.095 

.120 

.698378 

4.790755 

886.216 

885.112 

.092 

.517921 

.602520i  78 

77 

885.831 

884.644 

.099 

.496281 

.580880 

877.587 

877.178 

.034 

.337069 

.412739!  77 

76 

877.167 

876.678 

.041 

.315428 

.391098 

867.654 

867.854 

.017 

.177814 

.245347  76 

75 

867.194 

867.316 

.010 

.156172 

.223705 

857.283 

857.313 

.002 

.035011 

.097774 

75 

74 

856.779 

856.731 

.004 

4.013368  4.076131 

847.052 

847.110 

.005 

3.903379 

3.961572 

74 

73 

846.507 

846.487 

.002 

3.881733 

3.939926 

836.731 

836.852 

.010 

.781997 

.836101 

73 

72 

836.144 

836.187 

.004 

.760348 

.814452 

826.220 

826.468 

.021 

.669788 

.720099 

72 

71 

825.590 

825.761 

.014 

.648135 

.698446 

815.410 

815.829 

.035 

.565978 

.612770 

71 

70 

814.736 

815.079 

.029 

.544319 

.591111 

804.261 

804.849 

.049 

.469788 

.513394 

70 

69 

803.542 

804.054 

.043 

3.448122 

3.491728 

792.747 

793.531 

.065 

3.380499 

3.421145  69 

68 

791,981 

792.690 

.059 

.358825 

.399471 

780.849 

781.821 

.081 

.297498 

.335454  68 

67 

780.034 

780.932 

.075 

.275813 

.313769 

768.569 

769.734 

.097 

.220181 

.255664167 

66 

767.705 

768.796 

.091 

.198484 

.233967 

755. 907 

757.262 

.113 

.148029 

.181252 

66 

65 

754.991 

756.273 

.107 

.126318 

.159541 

742.875 

744.411 

.128 

.080561 

.111718 

65 

64 

741.906 

743.370 

.122 

3.058832 

3.089989 

729.476 

731.196 

.143 

3.017349 

3.046605 

64 

63 

728.453 

730.101 

.137 

2.995601 

.024857 

715.734 

717.615 

.157 

2.957993 

2.985530 

63 

62 

714.654 

716.465 

.151 

.936222 

2.963759 

701. 674 

703.711 

.170 

.902114 

.928078^  62  j 

61 

700.537 

702.503 

.164 

.880317 

.906281 

687.306 

689.496 

.183 

.849405 

.873918!  61 

60 

686.110 

688.231 

.177 

.827578 

.852091 

672.  653 

674.973 

.193 

.799569 

.822773  60 

59 

671.397 

673.649 

.188 

2.777708 

2.800912 

657.  750 

660.191 

.203 

2.752318 

2.774325 

59 

58 

656.434 

658.806 

.198 

.730419 

.752426 

642. 618 

645.168 

.212 

.707414 

.728325 

58 

57 

641.240 

643.722 

.207 

.685473 

.706384 

627.  284 

629.925 

.220 

.664630 

.684548 

57 

56 

625.843 

628.417 

.214 

.642643 

.662561 

611.772 

614.501 

.227 

.623764 

.642765 

56 

55 

610.269 

612.930 

.222 

.601725 

.620726 

596. 101 

598.902 

.233 

.584630 

.602811 

55 

54 

594.534 

597.268 

.228 

2.562534 

2.580715 

580.  333 

583.157 

.235 

2.547049 

2.564471 

54 

53 

578.701 

581.459 

.230 

.524891 

.542313 

564.  493 

567.367 

.240 

.510872 

.527610 

53 

52 

562.797 

565.604 

.234 

.488648 

.505386 

548.  578 

551.477 

.242 

.475958 

.492067 

52 

51 

546.817 

549.649 

.236 

.453660 

.469769 

532.  631 

535.537 

.242 

.442178 

.457717 

51 

50 

530.806 

533.645 

.237 

.419800 

.435339 

516.  683* 

519.584 

.242 

.409412 

.424430  50 

49 

514.792 

517.627 

.336 

2.386947 

2.401965 

500.  763 

503.640 

.240 

2.377548 

2.392097  49 

48 

498.806 

501.617 

.234 

.354991 

.369540 

484.897 

487.743 

.237 

.346487 

.360605  48 

47 

482.877 

485.656 

.232 

.323828 

.337946 

469.106 

471.909 

.234 

.316143 

.329868  47 

46 

467.021 

469.757 

.228 

.293376 

.307101 

453.418 

456.161 

.229 

.286428 

.299798  46 

45 

451.269 

453.945 

.223 

.263543 

.276913 

437.861 

440.534 

.223 

.257261 

.270309^45 

44 

435.648 

438.254 

.217 

2.234250 

2.247298 

422.448 

425.046 

.216 

2.228576 

2.241324 

44 

13.    7r=  10.3400. 

12.   TT  =  10.1419. 

Continued  from  Page  *156. 


♦199 


TABLE    LXIII. 


GENERAL  VALUATION  OP  ANNUAL  PREMIUM  POLICIES  OF  1,000. 

4  PER  CENT. 


n. 

11. 

10. 

ti 

n. 
86 

V. 

6m. 

V. 

12m. 

^m.d. 

A(B/). 
6m. 

AB. 

12m. 

V. 

6m. 

V. 

12m. 

|m.d. 

MB/). 

6m. 

AB. 

12m. 

928.975 

927.266 

.142 

6.173956 

6.321413 

85 

928.783 

926.995 

.149 

6.152485 

6.299942 

922.212 

920.910 

.109 

5.818449 

5.948991 

85 

84 

921.994 

920.616 

.115 

5.796979 

5.927521 

915.346 

913.740 

.134 

5.510846 

5.630926 

84 

83 

915.103 

913.419 

.140 

.489376 

.609456 

908.699 

907.179 

.127 

.234418 

.344309 

83 

82 

908.431 

906.833 

.133 

.212948 

.322839 

901.783 

900.445 

.111 

4.986431 

.086941  82 

81 

901.488 

900.074 

.118 

4.9649591  .065469 

894.551 

893.346 

.100 

.763042 

4.855419  81 

80 

894.230 

892.949 

.107 

.741571 

4.833948 

886.932 

885.982 

.079 

.560946 

.645545  80 

79  886.583 

885.557 

.086 

4.539474 

4.624073 

878.368 

878.108 

.022 

4.380096 

4.455766  79 

78 

877.987 

877.654 

.028 

.358623 

.434293 

868.51] 

868.855 

.029 

.220843 

.288376  78 

77 

868.093 

868.366 

.023 

.199370 

.266903 

858.217 

858.393 

.015 

.078044 

.140807 

77 

76 

857.761 

857.866 

.009 

.056569 

.119332 

848.064 

848.267 

.017 

3.946416 

.004609 

76 

75 

847.570 

847.702 

.011 

3.924939 

3.983132 

837.822 

838.087 

.022 

.825041 

3.879145  75 

74 

837.289 

837.484 

.016 

3.803560 

3.857664 

827.389 

827.782 

.033 

3.712840 

3.763151 

74 

73 

826.819 

827.141 

.027 

.691355 

.741666 

816.662 

817.223 

.047 

.609040 

.655832 

73 

72 

816.051 

816.543 

.041 

.587550 

.634342 

805.598 

806.327 

.061 

.512862 

.556468 

72 

71 

804.945 

805.605 

.055 

.491366 

.534972 

794.170 

795.094 

.077 

.423588 

.464234 

71 

70 

793.476 

794.331 

.071 

.402085 

.442731 

782.362 

783.472 

.093 

.340606 

.378562 

70 

69 

781.623 

782.666 

.087 

3.319093 

3.357049 

770.175 

771.478 

.109 

3.263312 

3.298795 

69 

68 

769.392 

770.627 

.103 

.241788 

.277271 

757.610 

759.099 

.124 

.191188 

.224411 

68 

67 

756.778 

758.202 

.119 

.169651 

.202874 

744.675 

746.346 

.139 

.123751 

.1549081 67 1 

66 

743.796 

745.401 

.134 

.102199 

.133356 

731.379 

733,231 

.154 

.060576 

.089832 

66 

65 

730.450 

732.237 

.149 

.039006 

.068262 

717.740 

719.753 

.168 

.001263 

.028800 

65 

64 

716.761 

718.709 

.162 

3.979672 

3.007209 

703.787 

705.953 

.180 

2.945431 

2.971395 

64 

63 

702.756 

704.859 

.175 

.923818 

2.949782 

689.527 

691.846 

.193 

.892777 

.917290 

63 

62 

688.443 

690.699 

.188 

.871137 

.895650 

674.985 

677.434 

.204 

.843004 

.866208 

62 

61 

673.848 

676.233 

.199 

.621333 

.844537 

660.196 

662.763 

.214 

.795822 

.817829 

61 

60 

659.002 

661.508 

.209 

.774117 

.796124 

645.177 

647.854 

.223 

.750995 

.771906 

60 

59 

643.928 

646.543 

.218 

2.729253 

2.750164 

629.959 

632.726 

.231 

2.708297 

2.728215 

59 

58 

628.654 

631.359 

.225 

.686513 

.706431 

614.566 

617.419 

.238 

.667526 

.686527 

58 

57 

613.203 

615.995 

.233 

.645696 

.664697 

599.013 

601.939 

.244 

.628495 

.646676 

57 

56 

597.591 

600.456 

.239 

.606615 

.624790 

583.365 

586.313 

.246 

.591028 

.608450 

56 

55 

581.885 

584.773 

.241 

.569092 

.586514 

567.644 

570.642 

.250 

.554976 

.571714 

55 

54 

566.106 

569.043 

.245 

3.532980 

2.549718 

551.849 

554.872 

.252 

2.520197 

2.536306 

54 

53 

550.252 

553.214 

.247 

.498136 

.514245 

536.024 

539.053 

.252 

.486563 

.502102 

53 

52 

5  54.369 

537.337 

.247 

.464430 

.479969 

520.196 

523.221 

.252 

.453956 

.468974 

52 

51 

518.481 

521.446 

.247 

.431745 

.446763 

504.396 

507.397 

.250 

.422264 

.436813 

51 

50 

502.623 

505.563 

.245 

.399970 

.414519 

488. 650 

491.620 

.248 

.391388 

.405506 

50 

49 

486.818 

489.728 

.243 

2.369004 

2.383122 

472.979 

475.906 

.244 

2.361244 

2.374969 

49 

48 

471.089 

473.955 

.239 

.338763 

.352488 

457.410 

460.278 

.239 

.331743 

.345113 

48 

47 

455.462 

458.269 

.234 

.309158 

.322528 

441.971 

444.769 

.233 

.302806 

.315854 

47 

46 

439.965 

442.701 

.228 

.280110 

.293158 

426.674 

429.398 

.227 

.274370 

.287118 

46 

45 

424.611 

427.274 

.222 

.251553 

.264301 

411.542 

414.176 

.219 

.246367 

.258849 

45 

44 

409.424 

411.995 

.214 

2.223421 

2.235903 

396.596 

399.135 

.212  2.218737 

2.230972 

44 

11.    77  =  9.9535. 

10.    TT  =  9.7739. 

Continued  from  Page  *155. 


*300 


TABLE     LXIY. 


VALUE  OP  /'  AND  LOG  /  FOR  EVERY  YEAR  AND  MONTH  OF  AGE, 

4  PER  CENT. 


Tear 

of 

Age. 

x-\-n. 

h  =  Om. 

im. 

l4m. 

2im. 

3jm. 

4im. 

5|m. 

Tear 

of 
Age. 

X  +  n. 

*Dec. 

Nov. 

Oct. 

Sept. 

Aug. 

July. 

/' =.961538 

.963141 

.966346 

.969551 

.972756 

.975962 

.979167 

Log/. 

* 

10 

1.980143 

T.  980989 

T.  982675 

1.984355 

T.  986029 

T.987696 

1.989357 

10 

11 

.980134 

.980980 

.982668 

.984348 

.986022 

.987691 

.989352 

11 

12 

.980128 

.980974 

.982662 

.984344 

.986019 

.987687 

.989349 

12 

13 

.980118 

.980965 

.982654 

.984336 

.986011 

.987681 

.989344 

13 

14 

.980105 

.980953 

.982642 

.984326 

.986002 

.987673 

.989337 

14 

15 

1.980094 

T.  980942 

1.982633 

1.984317 

T.  985994 

T.987666 

T.989331 

15 

16 

.980084 

.980932 

.982624 

.984309 

.985988 

.987660 

.989325 

16 

17 

.980070 

.980919 

.982612 

.984298 

.985978 

.987651 

.989318 

17 

18 

.980055 

.980904 

.982599 

.984286 

.985968 

.987642 

.989310 

18 

19 

.980639 

.980889 

.982585 

.984274 

.985956 

.987633 

.989302 

19 

20 

T.  980020 

T.  980871 

T.  982568 

1.984259 

1.985943 

T.987621 

T.989292 

20 

21 

.980000 

.980852 

.982551 

.984244 

.985929 

.987608 

.989281 

21 

22 

.979978 

.980831 

.982532 

.984226 

.985914 

.987595 

.989269 

22 

23 

.979955 

.980809 

.982512 

.984208 

.985898 

.987580 

.989257 

23 

24 

.979928 

.980783 

.982488 

.984187 

.985879 

.987564 

.989243 

24 

25 

T.  979901 

1.980758 

T.  982465 

T.  984166 

1.985860 

T.987548 

1.989229 

25 

26 

.979866 

.980724 

.982434 

.984138 

.985835 

.987526 

.989210 

26 

27 

.979833 

.980692 

.982406 

.984112 

.985813 

.987505 

.989193 

27 

28 

.979795 

.980656 

.982373 

.984083 

.985786 

.987483 

989173 

28 

29 

.979748 

.980611 

.982332 

.984045 

.985753 

.987454 

.989148 

29 

30 

T.  979704 

1.980569 

T.  982294 

1.984011 

T.  985722 

T.987426 

T.989124 

30 

31 

.979652 

.980519 

.982249 

.983970 

.985686 

.987395 

.989097 

31 

32 

.979598 

.980468 

.982201 

.983928 

.985648 

.987361 

.989068 

32 

33 

.979535 

.980407 

.982147 

.983879 

.985604 

.987323 

.989035 

33 

34 

.979466 

.980341 

.982087 

.983825 

.985556 

.987280 

.988998 

34 

35 

T.  979386 

T.  980265 

T.  98201 7 

T.  983  762 

1.985500 

1.987232 

T.988956 

35 

36 

.979307 

.980189 

.981948 

.983700 

.985445 

.987182 

.988914 

36 

37 

.979220 

.980106 

.981873 

.983632 

.985384 

.987130 

.988868 

37 

38 

.979117 

.980008 

.981783 

.983551 

.985312 

.987066 

.988813 

38 

39 

.979006 

.979901 

.981686 

.983464 

.985235 

.986998 

.988754 

39 

40 

1.978883 

1.979784 

T.  981580 

T.  983368 

T.  985149 

T.986923 

1.988689 

40 

41 

.978757 

.979663 

.981470 

.983269 

.985061 

.986845 

.988622 

41 

42 

.978602 

.979515 

.981335 

.983148 

.984953 

.986750 

.988540 

42 

43 

.978448 

.979368 

.981201 

.983027 

.984845 

.986656 

.988459 

43 

44 

.978268 

.979196 

.981045 

.982886 

.984720 

.986545 

.988364 

44 

45 

1.978073 

T.  979009 

T.  980876 

1.982733 

1.984583 

T.986426 

T.988260 

45 

46 

.977861 

.978807 

.980691 

.982567 

.984435 

.986296 

.988149 

46 

47 

.977624 

.978580 

.980485 

.982382 

.984271 

.986151 

.988023 

47 

48 

.977365 

.978332 

.980260 

.982179 

.984090 

.985992 

.987886 

48 

49 

.977082 

.978062 

.980013 

.981957 

.983892 

.985819 

.987736 

49 

50 

T.  976767 

T.  977760 

1.979740 

T.981711 

T.  983673 

T.985626 

1.987570 

50 

51 

.976422 

.977430 

.979440 

.981441  ; 

.983432 

.985414 ' 

.987388 

51 

52 

.976044 

.977069 

.979112 

.981145  ' 

.983169 

.985183 

.987188 

52 

53  1 

.975630 

.976673 

.978752' 

1 

.980821 

.982881 

.984930  . 

.986970 

53 

*  Months  of  Entry  for  Annual  Valuation  Dec.  31. 
X-\-tl  +  h=  Present  Age  in  Years  and  Fraction  ;    f'=h  +  {l—h)vj  f=  h-\-(l—h)  vpx + n-L 


TABLE     LXIY. 


♦201 


VALUE  OF  /  AND  LOG  /  FOR  EVERY  YEAR  AND  MONTH  OF  AGE. 


4  PER  CENT. 


Year 

of 
Age. 

x-\-n. 

6m. 

6|-m. 

7im. 

8jm. 

9iin. 

10|m. 

llim. 

1  Year 

June. 

May. 

April. 

March. 

Feb. 

Jan. 

of 
Age. 

X  +  71. 

/'=.  980769 

.982372 

.985577 

.988782 

.991987 

.995192 

.998397 

Log/. 

1 

10 

1.990185 

T.  991011 

T.  992660 

1.994302 

T.  995937 

1.997667 

1.999190 

10 

11 

.990180 

.991007 

.992656 

.994300 

.995936 

.997566 

.999190 

11 

12 

.990178 

.991004 

.992654 

.994298 

.995934 

.997565 

.999190 

12 

13 

.990173 

.991000 

.992651 

.994294 

.995932 

.997564 

.999189 

13 

14 

.990167 

.990995 

.992646 

.994291 

.995930 

.997562 

.999189 

14 

15 

T.990161 

1.990990 

T.  992642 

T.  994288 

T.  995928 

T.997561 

1.999188 

15 

16 

.990156 

.990985 

.992638 

.994285 

.995926 

.997560 

.999188 

16 

17 

.990149 

.990979 

.992633 

.994281 

.995923 

.997558 

.999187 

17 

18 

.990142 

.990972 

.992628 

.994277 

.995919 

.997556 

.999187 

18 

19 

.990135 

.990965 

.992622 

.994272 

.995917 

.997555 

.999186 

19 

20 

T.990125 

T.  990957 

1.992614 

T.  994267 

T.  995912 

T.  997552 

T.  999185 

20 

21 

.990115 

.990948 

.992608 

.994261 

.995908 

.997550 

.999185 

21 

22 

.990104 

.990938 

.992600 

.994255 

.995904 

.997547 

.999184 

22 

23 

.990093 

.990928 

.992591 

.994249 

.995900 

.997545 

.999183 

23 

24 

.990080  • 

.990916 

.992581 

.994241 

.995894 

.997541 

.999182 

24 

25 

T.990067 

T.  990903 

T.  992571 

T.  994234 

L995889 

T.  997538 

1.999181 

25 

26 

.9900,50 

.990888 

.992559 

.994224 

.995882 

.997534 

.999179 

26 

27 

.990033 

.990873 

.992547 

.994214 

.995875 

.997530 

.999178 

27 

28 

.990015 

.990856 

.992533 

.994204 

.995868 

.997525 

.999176 

28 

29 

.989992 

.990835 

.992516 

.994191 

.995858 

.997519 

.999175 

29 

30 

T.989971 

1.990815 

T.  992499 

1.994178 

T.  995849 

T.  997514 

T.  999173 

30 

31 

.989945 

.990792 

.992481 

.994163 

.995839 

.997508 

.999171 

31 

32 

.989919 

.990768 

.992461 

.994148 

.995828 

.997501 

.999169 

32 

33 

.989888 

.990740 

.992439 

.994130 

.995815 

.997494 

.999166 

33 

34 

.989855 

.990709 

.992413 

.994110 

.995802 

.997486 

.999163 

34 

35 

1.989816 

T.  990673 

1.992384 

T.  994088 

T.  995785 

T.  997476 

T.  999160 

35 

36 

.989777 

.990638 

.992355 

.994065 

.995769 

.997466 

.999157 

36 

37 

.989735 

.990599 

.992324 

.994041 

.995752 

.997456 

.999154 

37 

38 

.989684 

.990553 

.992286 

.994012 

.995732 

.997444 

.999150 

38 

39 

.989630 

.990504 

.992246 

.993981 

.995709 

.997431 

.999146 

39 

40 

1.989570 

1.990449 

T.  992201 

T.  993946 

1.995684 

1.997416* 

T.  999140 

40 

41 

.989509 

.990392 

.992155 

.993911 

.995660 

.997401 

.999135 

41 

42 

.989433 

.990323 

.992099 

.993867 

.995628 

.997382 

.999129 

42 

43 

•989358 

.990254 

.992043 

.993824 

.995597 

.997364 

.999123 

43 

44 

.989270 

.990175 

.991977 

.993773 

.995562 

.997343 

.999116 

44 

1  45 

T.989175 

1.990088 

T.  991907 

T.  993718 

T.  995522 

T.997319 

1.999108 

45 

46 

.989071 

.989993 

.991829 

.993659 

.995480 

.997293 

.999099 

46 

47 

.988956 

.989887 

.991743 

.993592 

.995432 

.997265 

.999090 

47 

48 

.988830 

.989772 

.991649 

.993519 

.995381 

.997234 

.999080 

48 

49 

.988692 

.989646 

.991547 

.993440 

.995324 

.997200 

.999069 

49 

50 

T.988539 

T.  989506 

T.  991433 

1.993351 

1.995261 

1.997164 

1.999057 

50 

51 

.988371 

.989352 

.991308 

.993254 

.995192 

.997122 

.999042 

51 

52 

.988187 

.989184 

.991170 

.993149 

.995117 

.997077 

.999028 

52 

53 

.987986 

.989000 

.991021 

.993032 

.995035 

.  9970^8. 

999012 

53 

*20Z 


TABLE     LXIY. 


VALUE  OF  /'  AND  LOG  /  FOR  EVERY  YEAR  AND  MONTH  OP  AGE. 

4  PER  CENT. 


Year 

of 

Age. 

h  =  Om. 

im. 

l4m. 

24m. 

34m. 

44m. 

54ni. 

Year 

of 
Age. 

x-\-n. 

*  Dec. 

Nov. 

Oct. 

Sept. 

Aug. 

July. 

/' =.961538 

.963141 

.966346 

.969551 

.972756 

.975962 

.979167 

, 

Log/. 

54 

T.  975175 

1.976238 

T.  978357 

T.  980465 

T.  982563 

T.984651 

1.986729 

54 

55 

1.974667 

1.975752 

T.  977916 

1.980068 

1.982210 

1.984341 

1.986462 

55 

56 

.974117 

.975227 

.977438 

.979638 

.981827 

.984005 

.986172 

56 

57 

.973500 

.974637 

.976903 

.979156 

.981397 

.983628 

.985847 

57 

58 

.972835 

.974001 

.976325 

.978636 

.980935 

.983222 

.985497 

58 

59 

.972102 

.973301 

.975689 

.978064 

.980426 

.982775 

.985111 

59 

60 

1.971290 

T.  972525 

T.  974984 

T.  977430 

1.979861 

T.982280 

1.984685 

60 

61 

.970397 

.971672 

.974210 

.976733 

.979242 

.981736 

.984216 

61 

62 

.969425 

.970743 

.973367 

.975975 

.978568 

.981144 

.983706 

62 

63 

.968344 

.969710 

.972430 

.975132 

.977818 

.980487 

.983140 

63 

64 

.967161 

.968580 

.971404 

.974210 

.976998 

.979768 

.982521 

64 

65 

T.  965853 

1.967331 

T.  970271 

1.973192  1.976093 

T.978974 

T.981838 

65 

66 

.964427 

.965969 

.969036 

.972082 

.975107 

.978110 

.981093 

66 

67 

.962842 

.964456 

.967664 

.970850 

.974012 

.977152 

.980268 

67 

68 

.961128 

.962819 

.966181 

.969518 

.972829 

.976116 

.979377 

68 

69 

.959205 

.960983 

.964519 

.968026 

.971504 

.974956 

.978379 

69 

70 

1.957120 

T.  958994 

1.962718 

1.966409 

T.  970070 

1.973700 

T.977300 

70 

71 

.954811 

.956791 

.960724 

.964621 

.968484 

.972312 

.976108 

71 

72 

.952281 

.954378 

.958541 

.962664 

.966749 

.970796 

.974805 

72 

73 

.949508 

.951734 

.956150 

.960522 

.964851 

.969137 

973381 

73 

74 

.946420 

.948789 

.953490 

.958140 

.962742 

.967295 

.971800 

74 

75 

T.  943060 

T.  945588 

T.  950599 

1.955554 

1.960453 

T.965297 

T.970086 

75 

76 

.939374 

.942077 

.947432 

.952722 

.957947 

.963111 

.968215 

76 

77 

.935277 

.938175 

.943915 

.949579 

.955171 

.960692 

.966143 

77 

78 

.930801 

.933915 

.940078 

.946154 

.952148 

.958059 

.963891 

78 

79 

.925875 

.929230 

.935863 

.942396 

.948832 

.955174 

.961425 

79 

80 

T.  920451 

T.  924073 

L 931229 

T.  938268 

1.945195 

T.952013 

T.958726 

80 

81 

.914509 

.918428 

.926162 

.933761 

.941228 

.948569 

.955790 

81 

82 

.907916 

.912169 

.920552 

.928777 

.936848 

.944773 

.952554 

82 

83 

.900757 

.905378 

.914475 

.923386 

.932117 

.940677 

.949070 

83 

84 

.892777 

.897815 

.907720 

.917403 

.926875 

.936145 

.945221 

84 

85 

T.  884080 

T.  889581 

T.  900378 

T.  910913 

1.921200 

T.931247 

T.941068 

85 

86 

.874593 

.880609 

.892397 

.903873 

.915054 

.925954 

.936587 

86 

87 

.863845 

.870458 

.883388 

.895945 

.908148 

.920018 

.931573 

87 

88 

.852462 

.859722 

.873887 

.887604 

.900902 

.913804 

.926334 

88 

89 

.832633 

.841059 

.857435 

.873216 

.888444 

.903156 

.917386 

89 

90 

1.810236 

1.820041 

1.839009 

1.857185 

1.874629 

1.891400 

T.  907548 

90 

91 

.790136 

.801236 

.822619 

.842998 

.862464 

.881095 

.898959 

91 

92 

.768484 

.781043 

.805122 

.827936 

.849610 

.870255 

.889961 

92 

93 

.742635 

.757028 

.784456 

.810256 

.834607 

.857666 

.879562 

93 

94 

.713385 

.729978 

.761375 

.790655 

.818085 

.843885 

.868237 

94 

95 

T.  681936 

T.  701052 

T.  736932 

1.770072 

1.800862 

1.829612 

T.856578 

95 

96 

.627579 

.651472 

.695641 

.735731 

.772430 

.806268 

.837660 

96 

97 

.585026 

.613055 

.664207 

.709965 

.751358 

.789146 

.823908 

97 

98 

.505846 

.542608 

.607936 

.664711 

.714914 

.759910 

.800679 

98 

*  Months  of  Entry  for  Annual  Valuation  Dec.  31. 


TABLE  LXIY. 


*203 


VALUE  OF  /'  AND  LOG  /  FOR  EVERY  YEAR  AND  MONTH  OF  AGE. 


4  PER  CENT. 

Year 

of 
Age. 

x+n. 

6m. 

64m. 

7im. 

84m. 

94m. 

lO^m. 

Il4m. 
Jan. 

Year 

of 
Age. 

x+n. 

June. 

May. 

April. 

March. 

Feb. 

/'=.  980769 

.982372 

.985577 

.988782 

.991987 

.995192 

.998397 

Log/. 

54 

T.987765 

T.  988798 

L 990856 

T.  992905 

T.  994944 

1.996973 

T.  998994 

54 

55 

T.987518 

T.  988572 

1.990673 

1.992763 

1.994843 

T.  996913 

1.998974 

55 

56 

.987252 

.988328 

.990474 

.992609 

.994734 

.996848 

.998952 

56 

57 

.986952 

.988055 

.990251 

.992437 

.994611 

.996774 

.998928 

57 

58 

.986630 

.987760 

.990011 

.992251 

.994479 

.996696 

.998901 

58 

59 

.986275  - 

.987435 

.989747 

.992047 

.994334 

.996609 

.998873 

59 

60 

1.985882 

T.  987076 

T.  989455 

T.  991821 

1.994173 

1.996514 

1.998841 

60 

61 

.985451 

.986682 

.989134 

.991573 

.993997 

.996408 

.998806 

61 

62 

.984982 

.986253 

.988785 

.991302 

.993805 

.996294 

.998768 

62 

63 

.984461 

.985777 

.988397 

.991003 

.993593 

.996167 

.998726 

63 

64 

.983891 

.985256 

.987974 

.990676 

.993360 

.996028 

.998680 

64 

65 

T.983262 

T.  984682 

1.987507 

T.  990315 

T.  993104 

T.  995875 

T.  998630 

65 

66 

.982578 

.984057 

.986999 

.989922 

.992825 

.995710 

.998574 

66 

67 

.981819 

.983363 

.986436 

.989486 

.992517 

.995526 

.998514 

67 

68 

.980999 

.982614 

.985827 

.989017 

.992184 

.995327 

.998448 

68 

69 

.980082 

.981777 

.985147 

.988492 

.991812 

.995105 

.998375 

69 

70 

T.979089 

T.  980871 

T.  984412 

T.  987924 

T.  991409 

T.  994866 

T.  998295 

70 

71 

.977993 

.979870 

.983600 

.987299 

.990966 

.994602 

.998208 

71 

72 

.976796 

.978777 

.982714 

.986615 

.990482 

.994314 

.998113 

72 

73 

.975487 

.977584 

.981746 

.985870 

.989954 

.994000 

.998009 

73 

74 

.974036 

.976260 

.980674 

.985044 

.989370 

.993653 

.997894 

74 

75 

T.972463 

T.  974825 

1.979512 

1.984149 

1.988737 

1.993277 

1.997771 

75 

76 

.970744 

.973259 

.978245 

.983174 

.988048 

.992869 

.997636 

76 

77 

.968843 

.971526 

.976844 

.982098 

.987288 

.992418 

.997487 

77 

78 

.966777 

.969645 

.975324 

.980930 

.986465 

.991929 

.997326 

78 

79 

.964517 

.967587 

.973663 

.979656 

.985566 

.991397 

.997151 

79 

80 

T.  962044 

T.  965337 

T.  971849 

T.  978264 

T.  984586 

T.  990817 

1.996961 

80 

81 

.959354 

.962891 

.969878 

.976755 

.983524 

.990190 

.996754 

81 

82 

.956394 

.960200 

.967713 

.975098 

.982360 

.989502 

.996529 

82 

83 

.953208 

.957305 

.965386 

.973320 

.981112 

.988766 

.996287 

83 

84 

.949689 

.954111 

.962824 

.971365 

.979741 

.987958 

.996023 

84 

85 

T.945896 

T.  950671 

T.  960067 

T.  969264 

1.978270 

1.987093 

T.  995740 

85 

86 

.941807 

.946966 

.957103 

.967008 

.976693 

.986167 

.995438 

86 

87 

.937237 

.942827 

.953798 

.964498 

.974941 

.985139 

.995103 

87 

88 

•932467 

.938513 

.950360 

.961892 

.973125 

.984076 

.994757 

88 

89 

.024330 

.931164 

.944518 

.957475 

.970056 

.982282 

.994174 

89 

90 

1.915401 

T.923115 

T.  938145 

T.  952672 

T.  966729 

T.  980344 

T.  993546 

90 

91 

.907623 

.916118 

.932624 

.948525 

.963865 

.978682 

.993009 

91 

92 

.899490 

.908813 

.926880 

.944226 

.960905 

.976968 

.9924571 

92 

93 

.890109 

.900407 

.920297 

.939316 

.957536 

.975023 

.991833 

93 

94 

.879920 

.891297 

.913193 

.934038 

.953929 

.972948 

.991168 

94 

95 

T.869458 

T.  881965 

T.  905951 

T.  928681 

T.  950280 

1.970856 

1.990501 

95 

96 

.852543 

.866934  ^ 

.894359 

.920155 

.944504 

.967560 

.989454 

96 

97 

.840299 

.856093  ! 

.886056 

.914085 

.940414 

.965238 

.988719 

97 

98 

.819713 

.837947  ! 

1 

.872269 

.904075 

1 

.933710 

.961452 

1 

.987527' 

98 

*204 


TABLE    LXY. 


JOINT  LIVES  MALE.     CORRECTION  TO  BE  ADDED  TO  THE  YOUNGEST  AGE  FOR  REDUCING 
TWO  LIVES  .C,  y,  AND  ALSO  THREE  LIVES  x,  y,  z  TO  THE  CASE  OF  TWO  EQUAL  AGES. 

Y.  M.  denote  Years  and  Months.  For  Two  Lives,  the  Correction  is  given  in  the  Second  Column  only. 
For  Three  Lives,  if  a"  be  the  Youngest  Age,  enter  the  Table  jointly  with  y—x,  z—x  to  find  the  Correc- 
tion of  the  Age  x,  to  give  u,  that  is,  one  of  the  two  Equal  Ages.  With  u,  which  increases  uniformly 
with  the  age,  proceed  as  before  explained  on  Pages  358,  259. 


'si 

Two 

Difference  of  Years  or  Ages  z  —  X. 

!bI 

i«^ 

Lives. 

P<! 

,                             , 

,                       , 

, 

y-x 
Yr. 

0 

1 

2 

3 

4 

5 

6 

7 

Y.     M. 

8 

Y.     M. 

9 

y-x 
Yr. 

Y.    M. 

Y.     M. 

Y.    M. 

Y.     M. 

Y.    M. 

Y.    M. 

Y.    M. 

Y.     M. 

Y. 

M. 

0 

0    0.0 

4    3.2 

4    7.2 

4  11.7 

5    4.3 

5    9.2 

6    2.4!  6    7.9 

7    1.8'  7 

7.8 

8 

2.2 

0 

1 

0    6.1 

4    7.2 

4  11.3 

5    3.6 

5    8.0 

6    0.8 

6    5.91  6  11.3 

7    4.9    7  10.8 

8 

5.0 

1 

2 

1    0.6 

4  11.7 

5    3.6 

5    7.7 

6    0.1 

6    4.7 

6    9.6 

7    2.8'  7    8.3    8 

2.0 

8 

8.0 

2 

3 

1    7.3 

5    4.3 

5    8.0 

6    0.1 

6    4.3 

6    8.8 

7    1.6 

7    6.6    7  11.9;  8 

5.5 

8  11.3 

3 

4 

2    2.3 

5    9.2 

6    0.8 

6    4.7 

6    8.8 

7    1.1 

7    5.7 

7  10.6|  8    3.7 

8 

9.1 

9 

2.9 

4 

5 

2    9.5 

6    2.4 

6    5.9 

6    9.6 

7    1.6 

7    5.7 

7  10.1 

8    2.8   8    7.8 

9 

1.1 

9 

6.7 

5 

6 

3    5.0 

6    7.9 

6  11.3;  7    2.8 

7    6.6 

7  10.6 

8    2.8 

8    7.3   9    0.2 

9 

5.3 

9  10.7 

6 

7 

4    0.8 

7    1.8 

7    4.9 

7    8.3 

7  11.9 

8    3.7 

!  8    7.8l  9    0.2   9    4.8'  9 

9.7 

10 

2.9 

7 

8 

4    8.9 

7    7.8 

7  10.8 

8    2.0 

8    5.5 

8    9.1 

!  9    l.ll  9    5.3    9    9.710 

2.4 

10 

7.4 

8 

9 

5    5.2 

8    2.2 

8    5.0 

8    8.0 

8  11.3 

9    2.9 

!  9    6.7 

9  10.7  10    2.9jl0 

7.4 

11 

0.2 

9 

10 

6    1.8 

8    8.8 

8  11.5 

9    2.5 

9    5.6 

9    9.0 

|lO    0.510    4.3'l0    8.4I1I 

0.8 

11 

5.3 

10 

11 

6  10.6 

9    3.7 

9    6.3 

9    9.1 

10    0.0 

10    3.2 

10    6.6;10  10.3J11    2.2 11 

6.4 

11  10.8 

11 

12 

7    7.6 

9  10.8 

10    1.3il0    4.0 

10    6.8 

10    9.8 

11    1.1  jll    4.5 

11    8.3!12 

0.2 

12 

4.4 

12 

13 

8    4.7 

10    6.4 

10    8.6IIO  11.0 

11    1.7 

11    4.6 

11    7.7|11  11.0 

12    2.412 

Q.2 

12  10.3 

13 

14 

9    2.0 

IL    2.0 

11    4.2111    6.5 

11    9.1 

11  11.8 

12    2.71I2    5.8 

1 

12    9.113 

0.7 

13 

4.5 

14 

15 

9  11.6 

11  10.0 

12    0.0|12    2.2 

12    4.6 

12    7.1 

12    9.8:13    0.813    4.013 

7.4 

13  11.0 

15 

16 

10    9.5 

12    6.2 

12    8.2I12  10.3 

13    0.5 

13    2.9 

13    5.5 '13    8.3  13  11.2  14 

2.4 

14 

5.8 

16 

17 

11    7.3!l3    2.6 

13    4.4;i3    6.4 

13    8.5 

13  10.7 

14    I.1I14    3.7|l4    6.614 

9.6 

15 

0.8 

17 

18 

12    5.5!l3  11.5 

14    1.214    3.0 

14    4.9 

14    7.0 

14    9.3 

14  11.715    2.5il5 

5.3 

15 

8.3 

18 

19 

13    3.714    8.4 

14    9.9  14  11.6 

15    1.4|15    3.4 

15    5.5 

15    7.8 15  10.3 

16 

1.0 

16 

3.9 

19 

20 

14    2.o'l5    5.5 

15    7.015    8.5 

15  10.2 

16    0.0 

16    2.0 

16    4.2116    6.5 

16 

9.0 

16  11.8 

20 

21 

15    0.616    2.9 

16    4.216    5.6 

16    7.2 

16    8.9 

16  10.8 

17    0.8!l7    3.0 

17 

5.4 

17 

8.0 

21 

22 

15  11.2  17    0.4 

17    1.6'17    2.9 

17    4.4 

17    6.0 

|17    7.7 

17    9.6;17  11.6 

18 

1.8 

18 

4.1 

22 

23 

16  10.0  17  10.1 

17  11.2  18    0.5 

18    1.9 

18    3.4 

il8    5.0 

18    6.718    8.6 

18  10.7 

19 

0.8 

23 

24 

17    8.818    7.9 

18    9.0  18  10.2 

18  11.4 

19    0.8 

19    2.3 

19    4.019    5.7 

19 

7.6 

19 

9.7 

24 

25 

18    7.719    6.0 

19    7.0' 19    8.0 

19    9.2 

19  10.5 

19  11.8 

20    1.320    3.0 

20 

4.8 

20 

6.7 

25 

26 

19    6.7120    4.2 

20    5.120    6.1 

20    7.2 

20    8.4 

20    9.6'20  11.0  21    0.5 

21 

2.2 

21 

4.0 

26 

27 

20    5.9  21    2.5 

21    3.4|21    4.3 

21    5.3 

21    6.4 

21    7.6121    8.921  10,3 

21  11.8 

22 

1.4 

27 

28 

21    5.022    1.1 

22    1.8*22    2.6 

22    3.6 

22    4.6 

22    5.6;22    6.8;22    8.1 

22 

9.5 

22  11.0 

28 

29 

22    4.3I22  11.6 

23    0.323    1.1 

23    2.0 

23    2.9 

23    3.9 

23    5.0  23    6.1 

23 

7.4 

23 

8.8 

29 

30 

23    3.6!23  10.3 

23  10.9  23  11.6 

24    0.5 

24    1.3 

24    2.2 

24    3.2124    4.3 

24 

5.5 

24 

6.8 

30 

31 

24    3.0'24    9.1 

24    9.7|24  10.4 

24  11.1 

24  11.9 

25    0.8 

25    1.7125    2.7 

25 

3.8 

25 

5.1 

31 

32 

25    2.425    8.0 

25    8.5|25    9.1 

25    9.8 

25  10.6 

25  11.4  26    0.2  26    1.2 

26 

2.2 

26 

3.2 

32 

33 

26    1.9,26    7.1 

26    7.6|26    8.2 

•i&    8.8 

26    9.4 

26  10.1  26  10.9  26  11.8 

27 

0.7 

27 

1.8 

33 

34 

27    1.4i27    6.1 

27    6.6 

27    7.1 

27    7.7 

27    8.3 

27    9.0  27    9.7  27  10.4  27  11-3 

28 

0.3 

34 

35 

28    1.0 

28    5.3 

28    5.7 

28    6.1 

28    6.7 

28    7.2' 

28    7.8  28    8.5  28    9.2  28  10.0 

28 

10.8 

35 

36 

29    0.6 

29    4.6 

29    4.9 

29    5.3 

29    5.7 

29    6.2 

29    6.8  29    7.4'29    8.129 

8.9 

29 

9.7 

36 

37 

30    0.2 

30    3.8 

30    4.2130    4.6 

30    5.0 

30    5.4 

30    5.930    6.5!30    7.130 

7.8 

30 

8.6 

37 

38 

30  11.9 

31    3.1 

31    3.4!  31    3.8 

31    4.3 

31    4.7 

31    5.1 

31    5.6  31    6.2  31 

6.8 

31 

7.5 

38 

39 

31  11.5 

32    2.5 

32    2.932    3.1 

32    3.4 

32    3.8 

32    4.3 

32    4.8  32    5.3  32 

5.9 

32 

6.5 

39 

40 

32  11.3 

33    2.0 

33    2.333    2.6 

33    2.8 

33    3.2 

33    3.6 

33    4.1 

33    4.5  33 

5.0 

33 

5.5 

40 

41 

33  11.0 

34    1.6i34    1.834    2.0^34    2.3 

34    2.6  134    3.0 

34    3.4 

34    3.834 

4.3 

34 

4.8 

41 

42 

34  10.8 

35    I.1L35    1.435    1.6|35    1.8 

35    2.0 

35    2.4 

35    2.8  35    3.2  35 

3.6 

35 

4.1 

42 

43 

35  10.6|36    0.6  36    0.9136    l.ll36    1.3 

36    1.6 

36    1.9 

36    2.2  36    2.5 

36 

2.9 

36 

3.3 

43 

44 

36  10.4  37    0.4  37    0.5  37    0.7 

37    0.9 

37    1.2 

37    1.5 
5 

37    1.8  37    2.1 

37 

2.4 

37 

2.8 

44 

Oil 

2 

3 

4      ' 

6          7 

8 

9      1 

^  =  1.099713375 J    %g^=l-\-qy-^.     For  Three  Lives,  2j<''=l  +  2'^~*  +  2^~*J    vs—v\ 


TABLE    LXY. 


♦305 


JOINT  LIVES  MALE.     CORRECTION  TO  BE  ADDED  TO  THE  YOUNGEST  AGE  FOR  REDUCING 
TWO  LIVES  X,  y,  AND  ALSO  THREE  LIVES  x,  y,  z  TO  THE  CASE  OP  TWO  EQUAL  AGES. 


Diff. 

Difference  of  Tears  or  Ages  z  —  x. 

Diff 

Ages. 

y—x. 

Ages. 

y—x. 

10 

12 

14 

16 

18 

20 

25 

30 

Y.  M. 

35 

40 

Years. 

Y.  M. 

Y.  M. 

Y.  M. 

Y.  M. 

Y.  M. 

Y.  M. 

Y.  M. 

Y. 

M. 

Y. 

M. 

Years. 

0 

8  8.8 

9  10.8 

11  2.0 

12  6.2 

13  11.5 

15  5.5 

19  6.0 

23  10.3 

28 

5.3 

33 

2.0 

0 

1 

8  11.5 

10  1.3 

11  4.2 

12  8.2 

14  1.2 

15  7.0 

19  7.0 

23  10.9 

28 

5.7 

33 

2.3 

1 

2 

9  2.5 

10  4.0 

11  6.5 

12  10.3 

14  3.0 

15  8.5 

19  8.0 

23  11.6 

28 

6.1 

33 

2.6 

2 

3 

9  5.6 

10  6.8 

11  9.1 

13  0.5 

14  4.9 

15  10.2 

19  9.2 

24  0.5 

28 

6.7 

33 

2.8 

J   3 

4 

9  9.0 

10  9.8 

11  11.8 

13  2.9 

14  7.0 

16  0.0 

19  10.5 

24  1.3 

28 

7.2 

33 

3.2 

4 

5 

10  0.5 

11  1.1 

12  2.7 

13  5.5 

14  9.3 

16  2.0 

19  11.8 

24  2.2 

28 

7.8 

33 

3.6 

5 

6 

10  4.3 

11  4.5 

12  5.8 

13  8.3 

14  11.7 

16  4.2 

20  1.3 

24  3.2 

28 

8.5 

33 

4.1 

1   6 

7 

10  8.4 

11  8.3 

12  9.1 

13  11.2 

15  2.5 

16  6.5 

20  3.0 

24  4.3 

28 

9.2 

33 

4.5 

7 

8 

11  0.8 

12  0.2 

13  0.7 

14  2.4 

15  5.3 

16  9.0 

20  4.8 

24  5.5 

28  10.0 

33 

5.0 

8 

9 

11  5.3 

12  4.4 

13  4.5 

14  5.8 

15  8.3 

16  11.8 

20  6.7 

24  6.8 

28  10.8 

33 

5.5 

9 

10 

11  10.3 

12  9.0 

13  8.6 

14  9.6 

15  11.5 

17  2.7 

20  8.8 

24  8.3 

28  11.8 

33 

6.2 

10 

11 

12  3.5 

13  1.7 

14  1.1 

15  1.4 

16  3.1 

17  5.9 

20  11.2 

24  9.8 

29 

0.8 

33 

7.0 

11 

12 

12  9.0 

13  6.7 

14  5.6 

15  5.6 

16  6.8 

17  9.2 

21  1.5 

24  11.5 

29 

2.0 

33 

7.7 

12 

13 

13  2.6 

14  0.0 

14  10.4 

15  10.1 

16  10.8 

18  0.7 

21  4.1 

25  1.3 

29 

3.1 

33 

8.4 

13 

14 

13  8.6 

14  5.6 

15  3.6 

16  2.8 

17  3.0 

18  4.5 

21  6.8 

25  3.3 

29 

4.5 

33 

9.3 

14 

15 

14  2.9 

14  11.4 

15  9.0 

16  7.8 

17  7.6 

18  8.5 

21  10.0 

25  5.4 

29 

5.9 

33  10.2 

15 

16 

14  9.6 

15  5.6 

16  2.8 

17  1.1 

18  0.5 

19  1.0 

22  1.2 

25  7.8 

29 

7.6 

33  11.3 

16 

17 

15  4.3 

16  0.0 

16  8.8 

17  6.6 

18  5.5 

19  5.5 

22  4.7 

25  10.2 

29 

9.2 

34 

0.4 

17 

18 

15  11.5 

16  6.8 

17  3.0 

18  0.5 

18  10.9 

19  10.5 

22  8.3 

26  1.0 

29  11.2 

34 

1.8 

18 

19 

16  7.0 

17  1.9 

17  9.7 

18  6.6 

19  4.6 

20  3.6 

23  0.4 

26  3.8 

30 

1.2 

34 

3.1 

19 

20 

17  2.7 

17  9.2 

18  4.5 

19  1.0 

19  10.5 

20  9.0 

23  4.5 

26  6.9 

30 

3.2 

34 

4.4 

20 

21 

17  10.7 

18  4.7 

18  11.8 

19  7.7 

20  4.7 

21  2.8 

23  9.0 

26  10.3 

30 

5.6 

34 

6.1 

21 

22 

18  6.7 

19  0.5 

19  7.1 

20  2.6 

20  11.2 

21  8.8 

24  1.7 

27  1.8 

30 

8.2 

34 

7.8 

22 

23 

19  3.2 

19  8.6 

20  2.8 

20  10.0 

21  6.0 

22  3.1 

24  6.8 

27  5.6 

30  10.9 

34 

9.7 

23 

24 

19  11.9 

20  4.9 

20  10.7 

21  5.4 

22  1.0 

22  9.6 

25  0.1 

27  9.6 

31 

1.8 

34  11.8 

24 

25 

20  8.8 

21  1.5 

21  6.8 

22  1.2 

22  8.3 

23  4.5 

25  5.6 

28  1.9 

31 

4.9 

35 

1.9 

25 

26 

21  5.9 

21  10.2 

22  3.4 

22  9.2 

23  4.0 

23  11.6 

25  11.5 

28  6.5 

31 

8.4 

35 

4.3 

26 

27 

22  3.2 

22  7.3 

23  0.0 

23  5.5 

23  11.9 

24  7.1 

26  5.8 

28  11.4 

32 

0.0 

35 

7.0 

27 

28 

23  0.7 

23  4.4 

23  8.9 

24  2.0 

24  7.9 

25  2.8 

27  0.2 

29  4.4 

32 

3.8 

35 

9.6 

28 

29 

23  10.4 

24  1.9 

24  6.0 

24  10.8 

25  4.3 

25  10.8 

27  7.0 

29  10.0 

32 

8.0 

36 

0.6 

29 

30 

24  8.3 

24  11.5 

25  3.3 

25  7.8 

26  1.0 

26  6.9 

28  1.9 

30  3.6 

33 

0.2 

36 

3.8 

30 

31 

25  6.4 

25  9.4 

26  0.8 

26  4.9 

26  9.7 

27  3.4 

28  9.2 

30  9.6 

33 

4.9 

36 

7.2 

31 

32 

26  4.4 

26  7.2 

26  10.4 

27  2.3 

27  6.8 

28  0.0 

29  4.8 

31  3.8 

33 

9.8 

36  10.8 

32 

33 

27  2.9 

27  5.4 

27  8.4 

27  11.9 

28  4.1 

28  8.9 

30  0.6 

31  10.4 

34 

3.0 

37 

2.8 

33 

34 

28  1.3 

28  3.6 

28  6.4 

28  9.7 

29  1.6; 

29  6.0 

30  8.8 

32  5.2 

34 

8.5 

37 

7.0 

34 

35 

28  11.8 

29  2.0 

29  4.5 

29  7.6 

29  11.2: 

30  3.2 

31  4.9 

33  0.2 

35 

2.2 

37  11.3 

35 

36  1 

29  10.6 

30  0.5 

30  2.9 

30  5.6 

30  8.9 

31  0.8 

32  1.6 

33  7.7 

35 

8.3 

38 

4.0 

3JS 

37 

30  9.4 

30  11.2 

31  1.3 

31  3.8 

31  7.0 

31  10.4 

32  10.3 

34  3.4 

36 

2.6 

38 

8.9 

37 

38  \ 

31  8.2 

31  9.831  11.9 

32  2.2 

32  5.0 

32  8.3 

33  7.3 

34  11.2 

36 

9.2 

39 

2.0 

38 

39 

32  7.1 

32  8.6 

32  10.4 

33  0.6 

33  3.2 

33  6.2 

34  4.4 

35  7.3 

37 

4.1 

39 

7.6 

39 

40 

33  6.2 

33  7.7 

33  9.3 

33  11.3 

34  l.s' 

34  4.4 

35  1.9 

36  3.8 

37  11.3| 

40 

1.3 

40 

41 

34  5.4 

34  6.7|34  8.2 

34  10.1 

35  0.2 

35  2.8 

35  11.5 

37  0.4 

38 

6.7 

40 

7.4 

41 

42 

35  4.6 

35  5.8 

35  7.2 

35  8.9 

35  10.8 

36  1.2 

36  9.2 

37  9.239 

2.4 

41 

1.8 

42 

43 

36  3.8 

36  4.9 

36  6.2 

36  7.8 

36  9.6! 

36  11.8 

37  7.2 

38  6.2  39  10.3| 

41 

8.4 

43 

44 

37  3.2 
10 

37  4.2 

37  5.4 

37  6.8 

37  8.5: 

37  10.6 

38  5.4 

39  3.6 

40 

6.6 

42 

3.4 

44 

12 

14 

16 

18  1 

20 

25 

30 

35 

40 

♦206 


TABLE    LXYI, 


COMMUTATION  COLUMNS  FOR  TWO  EQUAL  AGES.     MALE  LIFE. 

3  PER  CENT. 


H 

T)xx- 

^a^ 

^Daa. 

AJNjca;. 

1| 
55 

l^axc' 

^xx- 

^■^xx'        ^-"^  sex' 

10 

100,000.0  2,123,700.7 

5.000000 

6.327093 

11,622.5 

120,383.7 

1 
4.065300*5.080567 

11 

95,833.6  2,023,700.7 

4.981518 

.306146 

66 

10,860.8 

108,761.2 

.035862  .036474 

12 

91,836.2 

1,927,867.1 

.963014 

.285077 

57 

10,123.4 

97,900.4 

.005325  4.990785 

13 

88,003.5 

1,836,030.9 

.944500 

.263880 

58 

9,409.27 

87,776.97 

3.973556  .943381 

14 

84,326.7 

1,748,027.4 

.925965 

.242548 

59 

8,718.77 

78,367.70 

.940455  .894137 

15 

80,798.8 

1,663,700.7 

4. 907405 

6.221075 

60 

8,051.71 

69,648.93 

3.905888  4.842915 

16 

77,414.3 

1,582,901.9 

.888821 

.199454 

61 

7,407.95 

61,597.22 

.869698^  .789562 

17 

74,168.8 

1,505,487.6 

.870221 

.177677 

j62 

6,787.68 

54,189.27 

.831721  .733913 

18 

71,054.1 

1,431,318.8'  .851589 

.155737 

63 

6,191.56 

47,401.59 

.791800  .675793 

19 

68,065.5 

1,360,264.7 

.832927 

.133624 

64 

5,619.78 

41,210.03 

.749719  .615003 

20 

65,198.3 

1,292,199.2 

4.814236 

6.111330 

65 

5,073.05 

35,590.25 

3.705269  4.551331 

21 

62,446.2 

1,227,000.9 

.795506 

.088845 

66 

4,552.02 

30,517.20 

.658204  .484545 

22 

59,804.5 

1,164,554.7 

.776734 

.066160 

67 

4,057.79 

25,965.18 

.608289:  .414391 

23 

57,269.2 

1,104,750.2 

.757921 

.043264 

68 

3,590.89 

21,907.39 

.555202;  .340591 

24 

54,835.1 

1,047,481.0 

.739059 

.020146 

69 

3,152.73 

18,316.50 

.498687  .262843 

25 

52,498.3 

992,645.9 

4.720145 

5.996794 

70 

2,743.64 

15,163.77 

3.438327  4.180807 

261  50,254.7 

940,147.6 

.701177 

.973196 

71 

2,364.81 

12,420.13 

.373796  .094127 

27 

48,099.2 

889,892.9 

.682138 

.949337  72 

2,016.73 

10,055.32 

.304647  .002396 

28 

46,029.1 

841,793.7 

.663032 

.9252061  73 

1,699.97 

8,038.59 

.230440  3.905180 

29 

44,040.7 

795,764.6 

.643854 

.900785  74 

1 

1,414.76 

6,338.62 

.150684!  .801994 

1 

30 

42,128.7 

751,723.9 

4. 624578 

5.876058 

75 

1,160.79 

4,923.86 

3.064753 

3.692305 

31 

40,291.7 

709,595.2 

.605216 

.851011 

76 

937.787 

3,763.069 

2.972104 

.575542 

32 

38,525.6 

669,303.5 

.585749 

.825623 

77 

744.871 

2,825.282 

.872081 

.451062 

33'  36,827.7 

630,777.9 

.566175 

.799877 

78 

580.583 

2,080.411 

.763864 

.318149 

34  35,194.4 

593,950.2 

.546473 

.773750 

79 

443.298 

1,499.828 

.646696 

.176041 

35 

33,623.0 

558,755.8 

4.526637 

5.747222 

80 

330.883 

1056.530 

2.519675 

3.023882 

36 

32,109.7 

525,132.8 

.506636 

.720269 

81 

240.883 

725.647 

.381806 

2.860725! 

37 

30,653.6 

493,023.1 

.486481 

.692867 

82 

170.630 

484.764 

.232055 

.685531 

38 

29,251.6 

462,369.5 

.466150 

.664990 

83 

117.251 

314.134 

.069115 

.497115 

39 

27,900.6 

433,117.9 

.445613 

.636606 

84 

77.9575 

196.8833 

1.891858 

.294209 

40 

26,598.4 

405,217.3 

4.424856 

5.607688 

85 

49.9624 

118.9258 

1.698643 

2.075276 

41 

25,342.5 

378,618.9 

.403850 

.578203 

86 

30.7632 

68.9634 

.488032 

1.838618 

42 

24,132.0 

353,276.4 

.382593 

.548115: 

87 

18.1321 

38.2002 

.258447 

.582065 

43 

22,963.0 

329,144.4 

.361029 

.517387 

88 

10.1711 

20.0681 

.007367 

.302506 

44 

21,835.0 

306,181.4 

.339153 

.485979 

89 

5.41405 

9.89699 

0.733522 

0.995504 

45 

20,745.2 

284,346.4 

4.316917 

5.453848 

90 

2.63036 

4.48294 

0.420015 

0.651563 

46 

19,692.3 

263,601.2 

.294296 

.420947 

91 

1.15271 

1.85258 

.061718 

.267777 

47 

18,674.3 

243,908.9 

.271245 

.387228 

92 

.460488 

.699874 

1.663218 

1.845020 

48 

17,689.8 

225,234.6 

.247723 

.352635 

93 

.166501 

.239386 

.221417 

.379099 

49 

16,737.2 

207,544.8 

.223683 

.317112 

94 

.053446 

.072885 

2.727916 

2.862638 

50 

15,815.3 

190,807.6 

4.199077 

5.280595 

95 

.0149939 

.0194392 

2.175915 

2.288678 

51 

14,922.4 

174,992.3 

.173838 

.243019 

96 

.0036393 

.0044453 

3.561017 

3.647901 

52 

14,057.7 

160,069.9  .147913 

.204310 

97 

.0006877 

.0008060 

4.837404 

4.906335 

53 

13,220.0 

146,012.2 

.121230 

.164389 

98 

.0001068 

.0001183 

.028687 

.072985 

54 

12,408.5 

132,792.2 

.093720 

.123172 

99 

.0000115 

.0000115 

5.061608 

5.060698 

Formula,    Da^  = 


Ixix^         tx  l^a 


7    «io 


D. 


*207 


TABLE    LXYII. 


COMMUTATION  COLUMNS  FOR  TWO  EQUAL  AGES.    MALE  LIFE. 

3i  PER  CENT. 


jyccx. 

Na^ 

ADa^. 

ANa^. 

1,6}) 

T)xx. 

.,  Na:^.. 

ADxa;.     ANa;a;. 

10 

100,000.0 

1,961,020.2 

5.000000 

6.292482 

55 

9,346.69 

93,597.81. 

3.970658  4.971266 

11 

95,370.3 

1,861,020.2 

4.979413 

.269751 

56 

8,691.95 

84,251.12 

.939117!  .925576 

12 

90,950.9 

1,765,649.9 

.958807 

.246904 

157 

8,062.64 

75,559.17 

.906477j  .878287 

13 

86,733.9 

1,674,699.0 

.938189 

.223937 

:  58 17,457.70 

67,496.53 

.872605  .829281 

14 

82,708.9 

1,587,965.1 

.917552 

.200841 

59  6,877.02 

60,038.83 

.837400 

.778432 

15 

78,865.7 

1,505,256.2 

4.896888 

6.177610 

60  6,320.19 

53,161.81 

3.800730 

4.725599 

16 

75,197.1 

1,426,390.5 

.876201 

.154238 

61 

5,786.79 

46,841.62 

.762438 

.670632 

17 

71,696.4 

1,351,193.4 

.855497 

.130718 

62 

5,276.63 

41,054.83 

.722357 

.613364 

18 

68,353.9 

1,279,497.0 

.834763 

.107039 

63 

4,789.97 

35,778.20 

.680333 

.553618 

19  65,162.5 

1,211,143.1 

.813998 

.083196 

64 

4,326.61 

30,988.23 

.636148 

.491197 

20  62,116.1 

1,145,980.6 

4.793204 

6.059178 

65 

3,886.83 

26,661.62 

3.589596 

4.425887 

21  59,206.6 

1,083,864.5 

.772370 

.034975 

66 

3,470.79 

22,774.79 

.540428 

.357454 

22;  56,428.0 

1,024,657.9 

.751495 

.010579 

67 

3,079.00 

19,304.00 

.488410 

.285647 

23  53,774.8 

968,229.9 

.730579 

5.985979 

68 

2,711.56 

16,225.00 

.433219 

.210185 

24  51,240.7 

914,455.1 

.709615 

.961163 

69 

2,369.20 

13,513.44 

.374601 

.130766 

25  48,819.8 

863,214.4 

4.688596 

5.936118 

70 

2,051.82 

11,144.24 

3.312139 

4.047050 

26  46,507.8 

814,394.6 

.667526 

.910835 

71 

1,759.97 

9,092.42 

.245504 

3.958680 

27 

44,298.0 

767,886.8 

.646384 

.885297 

72 

1,493.66 

7,332.45 

.174252 

.865249 

28 

42,186.7 

723,588.8 

.625175 

.859492 

73 

1,252.97 

5,838.79 

.097942 

.766323 

29 

40,169.1 

681,402.1 

.603892 

.833403 

74 

1,037.73 

4,585.82 

.016083 

.661417 

30 

38,239.7 

641,233.0 

4.582514 

5.807016 

75 

847.323 

3,548.091 

2.928049 

3.549995 

31 

36,395.5 

602,993.3 

.561048 

.780312 

76 

681.234 

2,700.768 

.833296 

.431487 

32 

34,632.2 

566,597.8 

.539480 

.753275 

77 

538.481 

2,019.534 

.731170 

.305251 

33 

32,946.0 

531,965.6 

.517802 

.725883 

78 

417.686 

1,481.053 

.620850 

.170570 

34 

31,332.6 

499,019.6 

.495997 

.698118 

79 

317.380 

1,063.367 

.501579 

.026683 

35 

29,789.1 

467,687.0 

4.474057 

5.669955 

80 

235.752 

745.987 

2.372455 

2.872731 

36 

28,310.9 

437,897.9 

.451954 

.641372 

81 

170.798 

510.235 

.232483 

.707771 

37 

26,896.5 

409,587.0 

.429696 

.612346 

82 

120.400 

339.437 

.080628 

.530759 

38 

25,542.4 

382,690.5 

.407262 

.582848 

83 

82.3353 

219.0374 

1.915586 

.340518 

39 

24,244.9 

357,148.1 

.384621 

.552849 

84 

54.4786 

136.7021 

.736226 

.135776 

40 

23,001.8 

332,903.2 

4.361761 

5.522318 

85 

34.7462 

82.2235 

1.540907 

1.914996 

41 

21,809.9 

309,901.4 

.338653 

.491224 

86 

21.2909 

47.4773 

.328193 

.676486 

42 

20,667.7 

288,091.5 

.315292 

.459530 

87 

12.4884 

26.1864 

.096505 

.418076 

43 

19,571.5 

267,423.8 

.291624 

.427200 

88 

6.97143 

13.69801 

0.843322 

.136657 

44 

18,520.2 

247,852.3 

.267646 

.394193 

89 

3.69296 

6.72658 

.567374 

0.827795 

45 

17,510.8 

229,332.1 

4.243307 

5.360465 

90 

1.78552 

3.03362 

0.251764 

0.481961 

46 

16,541.7 

211,821.3 

.218581 

.325970 

91 

.778687 

1.248099 

1.891363 

.096249 

47 

15,610.9 

195,279.6 

.193429 

.290657 

92 

.309572 

.469412 

.490761 

1.671554 

48 

14,716.4 

179,668.7 

.167802 

.254473 

93 

.111393 

.159840 

.046857 

.203685 

49 

13,856.7 

164,952.3 

.141660 

.217358 

94 

.035584 

.048447 

2.551252  2.685267. 

50 

13,030.2 

151,095.6 

4.114950 

5.179252 

95 

.0099346 

.0128629 

3.997148  2.109339 

51 

12,235.1 

138,065.4 

.087609 

.140085 

96 

.0023997 

.0029283 

.380147  3.466616 

52 

11,470.5 

125,830.3 

.059581 

.099785 

97 

.0004513 

.0005286 

4.654431  4.723127 

53 

10,734.8 

114,359.8 

.030795 

.058273 

98 

.0000698 

.0000773 

5.843611  5.888179 

54 

10,027.2 

103,625.0 

.001180 

.015465 

99 

.0000075 

.0000075 

6.87442816.875061 

^308 


TABLE    LXYIII 


CJOMMUTATION  COLUMNS  FOR  TWO  EQUAL  AGES.     MALE  LIFE, 

4  PER  CENT. 


fe 

Daa. 

Na^ 

ADo,,. 

ANa^.  ! 

II  ^^ 

Naxr. 

^^OCX'           ^^XX' 

10 

100,000 

1,819,554.9 

5.000000 

6.259966 

'55  7,524.42 

72,918.61 

3.876473  4.862838 

11 

94,911.8 

1,719,554.9 

4.977320 

.235416156  6,963.70 

65,394.19 

.842840  .815539 

12 

90,078.5 

1,624,643.1 

.954621 

.210758 

15716,428.46 

58,430.49 

.808107  .766639 

13 

85,488.9 

1,534,564.6 

.931910 

.185985 

s  58  5,917.54 

52,002.03 

.772141  .716029 

14 

81,129.7 

1,449,075.7 

.909180 

.161091 

59  5,430.55 

46,084.49 

.734844 

.663555 

15 

76,988.0 

1,367,946.0 

4.886423 

6.136069 

60 '4,966.85 

40,653.94 

3.696081 

4.609108 

16 

73,054.0 

1,290,958.0 

.863644 

.110912 

61  4,525.80 

35,687.09 

.655695 

.552511 

17 

69,318.0 

1,217,904.0 

.840846 

.085613 

6214,106.97 

31,161.29 

.613522 

.493615 

18 

65,768.7 

1,148,586.0 

.818019 

.060164 

63  3,710.27 

27,054.32 

.569405 

.432237 

19 

62,396.8 

1,082,817.3 

.795162 

.034555 

64  3,335.24 

23,344.05 

.523127 

.368176 

20 

59,193.5 

1,020,420.5 

4.772274 

6.008779 

65 

2,981.82 

20,008.81 

3.474482 

4.301221 

21 

56,149.6 

961,227.0 

.749347 

5.982826 

66 

2,649.85 

17,026.99 

.423221 

.231138 

22 

53,257-4 

905,077.4 

.726380 

.956686 

67 

2,339.42 

14,377.14 

.369109 

.157673 

23 

50,509.1 

851,820.0 

.703370 

.930348 

68 '2,050.34 

12,037.72 

.311826 

.080544 

24 

47,897.5 

801,310.9 

.680313 

.903801 

69 

1,782.85 

9,987.38 

.251115 

3.999451 

25 

45,415.3 

753,413.4 

4.657202 

5.877033 

70 

1,536.59 

8,204.53 

3.186559 

3.914054 

26 

43,056.4 

707,998.1 

.634038 

.850032 

71 

1,311.69 

6,667.94 

.117832 

.823992 

27 

40,813.4 

664,941.7 

.610803 

.822783 

72 

1,107.87 

5,356.25 

.044487 

.728861 

28 

38,681.4 

624,128.3 

.587502 

.795274 

73 

924.875 

4,248.381 

2.966083 

.628223 

29 

36,654.4 

585,446.9 

.564126 

.767488 

1 

74 

762.311 

3,323.506 

.882132 

.521597 

30 

34,726.0 

548,792.5 

4.540655 

5.739408^ 

75 

619.448 

2,561.195 

2.792005 

3.408443 

31 

32,892.4 

514,066.5 

.517096 

.711019 

76 

495.632 

1,941.747 

.695159 

.288193 

32 

31,148.3 

481,174.1 

.493434 

.682303' 

77 

389.888 

1,446.115 

.590940 

.160203 

33 

29,489.2 

450,025.8 

.469663 

.653237 

78 

300.973 

1,056.227 

.478527 

.023757 

34 

27,910.4 

420,536.6 

.445766 

.623804 

79 

227.595 

755.254 

.357163 

2.878093 

35 

26,407.8 

392,626.2 

4.421732 

5.593979 

80 

168.247 

527.659 

2.225946 

2.722353 

36 

24,976.8 

366,218.4 

397537 

.5637401 

81 

121.306 

359.412 

.083881 

.555593 

37 

23,614.8 

341,241.6 

.373185 

.533062! 

82 

85.1007 

238.1057 

1.929933 

.376770 

38 

22,318.1 

317,626.8 

.348658 

.501918 

83 

57.9159 

153.0050 

.762798 

.184706 

39 

21,082.6 

295,308.7 

.323925 

.470276 

84 

38.1369 

95.0891 

.581345 

1.978131 

40 

19,905.4 

274,226.1 

4.298971 

5.438109 

85 

24.2066 

56.9522 

1.383933 

1.755511 

41 

18,783.2 

254,320.7 

.273770 

.405392, 

86 

14.7613 

32.7456 

.169126 

.515153 

42 

17,714.0 

235,537.5 

.248317 

.372060 

87 

8.61678 

17.98425 

0.935345 

.254892 

43 

16,693.8 

217,823.5 

.222555 

.338105 

88 

4.78706 

9.36747 

.680069 

0.971622 

44 

15,721.1 

201,129.7 

.196484 

.303476 

89 

2.52364 

4.58041 

.402027 

.660904 

45 

14,792.9 

185,408.6 

4.170053 

5.268130 

90  1.21430 

2.05677  0.084325 

0.313186 

46 

13,907.0 

170,615.7 

.143233 

.232019; 

91 

.52702 

.84247 

1.721831 

1.925554 

47 

13,061.3 

156,708.7 

.115988 

.195093 

92 

.20851 

.31545 

.319136 

.498930 

48 

12,253.8 

143,647.4 

.088269 

.157298 

93 

.07467 

.10694 

2.873138 

.029140 

49 

11,482.4 

131,393.6 

.060033 

.118574 

94 

.023738 

.032266 

.375441 

2.508745 

50 

10,745.6 

119,911.2 

4.031230 

5.078860 

95 

.0065954 

.008528 

3.819244 

3.930847 

51 

10,041.5 

109,165.6 

.001797 

.038086 

96 

.0015854 

.0019326,  .200150 

.286152 

52 

9,368.61 

99,124.1 

3.971675 

4.996179 

97 

.0002967 

.0003472  4.472341 

4.540637 

53 

8,725.61 

89,755.4 

.940796 

.953061 

98 

.0000456 

.0000505  5.659427 

5.703515 

54 

8,111.27 

81,029.8 

.909089 

.908645 

99 

.0000049 

.0000049  6.688152 

1 

6.688153 

FOBMULA,     Dasc  = 


IxlxV^         Ix^x 


ho^'' 


D 


10 


"^09 


TABLE    LXIX. 


COMMUTATION  COLUMNS  FOR  TWO  EQUAL  AGES.    MALE  LIFE. 

4i  PER  CENT. 


1?' 

Do^. 

N^. 

^iJsxc 

^^xa> 

Da.,. 

Nara;. 

XBaxc- 

ANa^o:. 

10 

100,000 

1,695,834.4 

5.000000 

6.339381 

55 

6,063.75 

56,930.00 

3.783741 

4.755265 

11  94,457.8 

1,595,834.4 

4.975338 

.202985 

56  5,585.03 

50,856.35 

.747035 

.706344 

12  89,218.7 

1,501,366.6 

.950456 

.176487 

i  57  5,131.07 

45,371.33 

.710208 

.655833 

13  84,267.7 

1,412,147.9 

.935661 

.149880 

158,4,700.67 

40,140.16 

.672160 

.603579 

14  79,588.3 

1,327,880.3 

.900849 

.133159 

59  4,393.19 

35,439.49 

.632780 

.549487 

15  75,163.8 

1,248,291.9 

4.876009 

6.096316 

60 '3,907.83 

31,146.30 

3.591934 

4.493407 

16;  70,981.6 

1,173,128.1 

.851146 

.069345!  6li3,543.76 

37,338.48 

.549465 

.435183 

17 i  67,039.5 

1,102,146.5 

.836366 

.043339 

62  3,300.44 

33,694.73 

.505209 

.374653 

18 i  63,293.0 

1,035,117.0 

.801356 

.014989 

63j3,877.46 

30,494.28 

.459009 

.311633 

19  59,760.6 

971,834.0 

.776415 

5.987588 

64 

3,574.33 

17,616.82 

.410648 

.345937 

20  56,421.6 

913,063.4 

4.751445 

5.960035 

65  2,290.45 

15,042.59 

3.359930 

4.177333 

21  53,364.1 

855,641.8 

.726435 

.933393 

!66|3,035.70 

12,752.14 

.306576 

.105583 

22  50,278.7 

802,377.7 

.701384 

.904379 

67 

1,779.84 

10,726.44 

.350383 

.030456 

23  47,456.1 

752,099.0 

.676393 

.876375  68 

1,552.44 

8,946.60 

.191015 

3.951658 

24  44,787.0 

704,643.9 

.651153 

.847969 

69 

1,343.45 

7,394.16 

.138331 

.868889 

25'  43,363.8 

659,855.9 

4.625958 

5.819449 

70 

1,152.34 

6,050.71 

3.061583 

3.781806 

26 

39,875.9 

617,593.1 

.600711 

.790703 

71   978.976 

4,898.367 

2.990772 

.690051 

27 

37,617.8 

577,717.3 

.575393 

.761715 

72  833.894 

3,919.391 

.915344 

.593319 

28 

35,482.1 

540,099.4 

.550009 

.733474 

73 1  683.688 

3,096.497 

.834858 

.490871 

29 

33,461.9 

504,617.3 

.524551 

.703963 

74 

560.831 

2,412.809 

.748824 

.383533 

30 

31,549.8 

471,155.4 

4.498996 

5.673164 

75 

453.537 

1,851.988 

2.656613 

3.367638 

31 

29,740.9 

439,605.6 

.473354 

.643063 

76 

361.148 

1,398.451 

.557685 

.145647 

32 

28,029.2 

409,864.7 

.447610 

.613640 

77 

383.737 

1,037.303 

.451383 

.015906 

33 

26,409.2 

381,835.5 

.421755 

.581876 

78 

317.313 

754.566 

.336886 

3.877697 

34 

24,875.7 

355,436.3 

.395775 

.550750 

79 

163.471 

537.353 

.213440 

.730360 

35 

23,423.9 

330,550.6 

4.369659 

5.519338 

80 

130.365 

373.883 

2.080140 

3.573735 

36 

22,048.6 

307,136.7 

.343381 

.487317 

81 

86.2963 

353.6169 

1.935992 

.404178 

37 

20,746.6 

385,078.1 

.316946 

.454964 

82 

60.3506 

167.3306 

.779961 

.223550 

38 

19,513.5 

364,331.5 

.290336 

.422149 

83 

40.8078 

107.0700 

.610743 

.029668 

39 

18,345.1 

344,818.0 

.263520 

.388843 

84 

36.7438 

66.3623 

.427207 

1.821366 

40 

17,237.9 

326,472.9 

4.236483 

5.355016 

85 

16.8933 

39.5194 

1.337713 

1.596810 

41 

16,188.2 

209,335.0 

.209199 

.320634 

86 

10.2533 

23.6362 

.010832 

.354612 

42 

15,193.7 

193,046.8 

.181663 

.285663 

87 

5.95604 

12.37393 

0.774958 

.092508 

43 

14,250.1 

177,853.1 

.153819 

.350061 

88 

3.29306 

6.41789 

.517599 

0.807392 

44 

13,355.6 

163,603.0 

.125664 

.213791 

89 

1.737736 

3.124835 

.337475 

.494826 

45 

12,506.9 

150,347.4 

4.097150 

5.176807 

90 

.8373495 

1.3971089 

T.917689 

0.145230 

46 

11,701.7 

137,740.5 

.068248 

.139062 

91 

.3573668 

.5697594 

.553113 

1.755693 

47 

10,937.5 

136,038.8 

.038919 

.100504 

92 

.1407139 

.3133926 

.148334 

.337139 

48 

10,212.1 

115,101.3 

.009117 

.061080 

93 

.0501480 

.0716797 

2.700354 

3.855396 

49 

9,533.53 

104,889.19 

3.978798 

.030731 

94 

.0158663 

.0315317 

.300474 

.333078 

50 

8,869.78 

95,365.66 

3.947913 

4.979393 

95 

.0043873 

.0056654 

3.643193 

3.753334 

51 

8,348.90 

86,495.88 

.916396 

.936995 

96 

.0010496 

.0012783 

.031017 

.106595 

52 

7,659.35 

78,346.98 

.884192 

.893468 

97 

.0001954 

.0003386 

4.391135 

4.359084 

53 

7,099.54 

70,587.63 

.851230 

.848739 

98 

.0000299 

.0000331 

5.476139  5.530012 

54 

6,568.09 

63,488.09 

.817439 

.803693 

99 

.0000031 

.0000033 

6.503770  6.503770 
J 

*210 


TABLE    LXX 


COMMUTATION  COLUMNS  FOR  TWO  EQUAL  AGES.     MALE  LEFK 

5  PER  CENT. 


^ 

jy^ 

N«B. 

XT)^. 

ANaa:. 

M  ^- 

N«^ 

AjUaa;. 

ANasr. 

10 

100,000 

1,587,002.3 

5.000000 

6.200578 

55  4,891.66 

44,516.96 

3.689456 

4.648526 

11 

94,008.0 

1,487,002.3 

4.973165 

.172312 

56  4,484.00 

39,625.30 

.65M66  .5979731 

12 

88,369.2 

1,392,994.3 

.946309 

.143949 

57  4,099.94 

35,141.30 

.612777  .545818 

13 

83,069.6 

1,304,625.1 

.919442 

.115486 

58  3,738.14 

31,041.36 

.572656  .491941 

14 

78,083.1 

1,221,555.5 

.892557 

.086913 

59  3,397.83 

27,303.22 

.531202  .436214 

15 

73,391.2 

1,143,472.4 

4.865644 

6.058226 

60  3,078.10 

23,905.39 

3.488283  4.378496 

16 

68,977.6 

1,070,081.2 

.838708 

.029417 

61 '2,778.06 

20,827.29 

.443742i  .318633 

17 

64,826.9 

1,001,103.6 

.811755 

.000479 

62  i2, 496.97 

18,049.23 

.397413 

.256459 

18 

60,921.7 

936,276.7 

.784772 

5.971404 

63  2,234.29 

15,552.26 

.349139 

.191792 

19 

57,247.7 

875,355.0 

.757758 

.942184 

64 

1,989.33 

13,317.97 

.298706 

.124438 

20 

53,791.7 

818,107.3 

4,730715 

5.912810 

65 

1,761.59  • 

11,328.64 

3.245905'4.054178 

21 

50,539.6 

764,315.6 

.703632 

.883273 

66 

1,550.55 

9,567.05 

.190487  3.980778 

22 

47,479.7 

713,776.0 

.676508 

.853562 

67 

1,355.88 

8,016.50 

.132220  .903985 

23 

44,600.8 

666,296.3 

.649343 

.823667 

68 

1,177.01 

6,660.62 

.070781!  .823515 

24 

41,891.9 

621,695.5 

.622130 

.793578 

69 

1,013.71 

5,483.61 

.005913  .739067 

25 

39,342.6 

579,803.6 

4.594863 

5.763281 

70 

865.370 

4,469.901 

2.937202  3.650298 

26 

36,943.9 

540,461.0 

.567543 

.732764 

71 

731.675 

3,604.531 

.864318 

.556849 

27 

34,685.8 

503,517.1 

.540152 

.702014 

72 

612.094 

2,872.856 

.786818 

.458314 

28 

32,560.8 

468,831.3 

.512695 

.671017 

73 

506.125 

2,260.762 

.704258 

.354255 

29 

30,560.7 

436,270.5 

.485163 

.639756 

74 

413.191 

1,754.637 

.616151  .2441871 

30 

28,677.1 

405,709.8 

4.457536 

5.608215 

75 

332.558 

1,341.446 

2.521868  3.1275731 

31 

26,904.3 

377,032.7 

.429821 

.576379 

76 

263.552 

1,008.888 

.420866 

.003843 

32 

25,235.0 

350,128.4 

.402003 

.544227! 

77 

205.348 

745.336 

.312491 

2.872352 

33 

23,663.3 

324,893.4 

.374076 

.511741' 

78 

157.008 

539.988 

.195922 

.732384 

34 

22,183.1 

301,230.1 

.346023 

.478898; 

79 

117.599 

382.980 

.070402 

.583176 

35 

20,789.0 

279,047.0 

4.317834 

5.445677 

80 

86.1051 

265.3809 

1.935029 

2.423870 

36 

19,475.2 

258,258.0 

.289482 

.412054 

81 

61.4905 

179.2758 

.788808 

.253522 

37 

18,237.9 

238,782.8 

.260975 

.378003 

82 

42.7273 

117.7853 

.630705 

.071091 

38 

17,072.3 

220,544.9 

.232292 

.343497 

83 

28.8014 

75.0580 

.459413 

1.875397 

39 

15,973.9 

203,472.6 

.203402 

.308506 

84 

18.7847 

46.2566 

.273804 

.665174 

40 

14,938.0 

187,498.7 

4.174293 

5.272998 

85 

11.8096 

27.4719 

1.072237 

1.438889 

41 

13,961.6 

172,560.7 

.144936 

.236942 

86 

7.13301 

15.66231 

0.853273 

.194856 

42 

13,041.5 

158,599.1 

.115326 

.200301' 

87 

4.12417 

8.52930 

.615336 

0.930913 

43 

12,173.3 

145,557.6 

.085409 

.163035 

88 

2.26937 

4.40513 

.355905 

.643959 

44 

11,354.9 

133,384.3 

.055182 

.125104 

89 

1.18497 

2.13576 

.073707 

.329552 

45 

10,582.7 

122,029.4 

4.024595 

5.086464 

90 

.564739 

.950788 

T.751848 

T.978084 

46 

9,854.15 

111,446.70 

3.993619 

.0470671 

91 

.242772 

.386049 

.385199 

.586642 

47 

9,166.80 

101,592.55 

.962218 

.006858 

92 

.0951367 

.1432769 

2.978348 

.156176 

48 

8,518.11 

92,425.75 

.930343 

4.965793 

93 

.0337438 

.0481402 

.528194 

2.682508 

49 

7,905.89 

83,907.64 

.897951 

.923801 

94 

.0106253 

.0143964 

.026341 

.158254 

50 

7,328.11 

76,001.75 

3.864992 

4.880824 

95 

.0029241 

.0037711 

3.465988 

3.576466 

51 

6,782.71 

68,673.64 

.831403 

.836790 

96 

.0006962 

.0008470 

4.842738 

4.927886 

52 

6,267.95 

61,890.93 

.797125 

.791627 

97 

.0001291 

.0001508 

.110773 

.178401 

53 

5,782.16 

55,622.98 

.762090 

.745254 

98 

.0000197 

.0000217 

5.293704 

5.337379 

54 

5,323.86 

49,840.82 

.726227 

.697585 

99 

.  .0000021 

.0000021 

6.318272 

6.318272 

♦^11 


TABLE    LXXI. 


COMMUTATION  COLUMNS  FOR  TWO  EQUAL  AGES.    MALE  LIFE. 

6  PER  CENT. 


DaxB. 

N«^ 

^iJxX' 

A^a-g. 

T>a^. 

^xx- 

ADa:aj. 

ANa^. 

10 

100,000.0 

1,405,298.1 

5.000000 

6.147768 

55 

3,193.08 

27,382.81 

3.504210 

4.437478 

11 

93,121.3 

1,305,298.1 

4.969049 

.115710 

56 

2,899.38 

24,189.73 

.462305!  .3836311 

12 

86,711.6 

1,212,176.8 

.938077 

.083566 

57  2,626.03 

21,290.35 

.419299 

.328183 

13 

80,740.8 

1,125,465.2 

.907093 

.051332 

58  2,371.71 

18,664.32 

.375061 

.271012 

14 

75,178.0 

1,044,724.4 

.876091 

.019002 

59 

2,135.46 

16,292.61 

.329491 

.211991 

15 

69,994.0 

969,546.4 

4.845061 

5.986569 

60 

1,916.26 

14,157.15 

3.282455 

4.150976 

16 

65,164.2 

899,552.4 

.814009 

.954027 

6111,713.16 

12,240.89 

.233797!  .087813] 

17 

60,665.1 

834,388.2 

.782939 

.921368 

62 

1,525.29 

10,527.73 

.183351 

.022335 

18 

56,472.8 

773,723.1 

.751839 

.888585 

63 

1,351.95 

9,002.44 

.130962 

3.954360 

19 

52,566.6 

717,250.3 

.720710 

.855671 

64 

1,192.37 

7,650.49 

.076412 

.883689 

20 

48,927.2 

664,683.7 

4.689550 

5.822615 

65 

1,045.91 

6,458.12 

3.019494 

3.810106 

21 

45,535.5 

615,756.5 

.658350 

.789409 

66 

911.927 

5,412.212 

2.959960  .733375 

22 

42,375.0 

570,221.0 

.627110 

.756043 

67 

789.907 

4,500.285 

.897576  .653240 

23 

39,430.1 

527,846.0 

.595828 

.722507 

68 

679.235 

3,710.378 

.832020  .569418! 

24 

36,685.8 

488,415.9 

.564498 

.688790 

69 

579.477 

3,031.143 

.763036 

.481606 

25 

34,128.3 

451,730.1 

4.533114 

5.654879 

70 

490.013 

2,451.666 

2.690208 

3.389461 

26  31,745.3 

417,601.8  .501679 

.620762 

71 

410.402 

1,961.653:  .613209 

.292622 

27 

29,523.7 

385,856.5i  .470171 

.586426 

72 

340.088 

1,551.251 

.531591 

.190682 

28 

27,453.5 

356,332.8 

.438597 

.551856 

73 

278.558 

1,211.163 

.444915 

.083203 

29 

25,524.0 

328,879.3 

.406948 

.517036 

74 

225.264 

932.605 

.35269112.969698 

30 

23,724.9 

303,355.3 

4.375205 

5.481952 

75 

179.594 

707.341 

2.254291 

2.849629 

31 

22,048.2 

279,630.4 

.343373 

.446584 

76 

140.985 

527.747 

.149173 

.722426 

32 

20,485.1 

257,582.2 

.311439 

.410916 

77 

108.813 

386.762 

.036681 

.587444 

33  19,028.1 

237,097.1  .279395 

.374926 

78 

82.4131 

277.9488il.915996 

.443965 

34 

17,669.6 

218,069.0 

.247226 

.338594 

79 

61.1449 

195.5357 

.786360 

.291226 

35 

16,402.9 

200,399.4 

4.214920 

5.301896 

80 

44.3476 

134.3908 

1.646870 

2.128370 

36 

15,221.3 

183,996.5 

.182452 

.264810 

81 

31.3713 

90.0432 

.496532 

1.954451 

37 

14,119.8 

168,775.2 

.149828 

.227309 

82 

21.5930 

58.6719 

.334312 

.768430 

38  i  13,092.7 

154,655.4 

.117028 

.189365 

83 

14.4180 

37.0789 

.158904 

.569127 

39 

12,134.5 

141,562.7 

.084022 

.150949 

84 

9.314896 

22.660866 

0.969178 

.355277 

40 

11,240.8 

129,428.2 

4.050796 

5.112029 

85 

5.800895 

13.345970 

0.763495 

1.125350 

41 

10,406.9 

118,187.4 

.017323 

.072571 

86 

3.470683 

7.545075 

.540415 

0.877664 

42 

9,629.35 

107,780.51 

3.983597 

.032540 

87 

1.987747 

4.074392 

.298361 

.610063 

43 

8,903.55 

98,151.16 

.949563 

4.991895 

88 

1.083460 

2.086645 

.034813 

.319448 

44 

8,226.57 

89,247.61 

.915219 

.950597 

89 

.560401 

1.003185 

1.748499 

.001381 

45 

7,594.78 

81,021.04 

3.880515 

4.908598 

90 

.264559 

.442783 

1.422523 

1.646191 

46 

7,005.24 

73,426.26 

.845423 

.865851 

91 

.112657 

.178224 

.051757 

.250966 

47 

6,455.13 

66,421.02 

.809905 

.822306 

92 

.043731 

.065567 

2.640789  2.8166851 

48 

5,941.73 

59,965.89 

.773913 

.777904 

93 

.015364 

.021836 

.186520 

.339173 

49 

5,462.67 

54,024.16 

.737405 

.732588' 

94 

.004792 

.006472 

3.680550 

3.811038 

50 

5,015.68 

48,561.49 

3.700330 

4.686292 

95 

.001306 

.001680 

3.116080 

3.225309 

51 

4,598.58 

43,545.81 

.662624 

.638946 

96 

.000308 

.000374 

4.488714 

4.572872 

52 

4,209.50 

38,947.23 

.624230 

.590477^ 

97 

.000057 

.000066 

5.752632 

5.819544 

53 

3,846.61 

34,737.73 

.585078 

.540801' 

98 

.0000085 

.0000094 

6.931446 

6.974733 

54 

3,508.31 

30,891.12 

.545098 

.4898341 

1 

99 

.0000009 

.0000009 

7.951898 

7.951898 

♦212 


TABLE     LXXII. 


JOINT  LIFE  ANNUITIES.    PRESENT  VALUE  {ttxx)  OF  1,  PAYABLE  AT  THE  END  OF  EACH 
YEAR  DURING  THE  JOINT  CONTINUANCE  OF  TWO  MALE  LIVES. 


1 


^•4  ;  Per  Ct. 


Per  Ct. 


10 

11 

12 
13 
14 

15 
16 
17 
18 
19 

20 
21 
22 
23 
24 

25 
26 
27 
28 
29 

30 
31 
32 
33 
34 

35 
36 
37 
38 
39 

40 
41 
42 
43 

44 

45 
46 
47 
48 
49 

50 
51 
52 
53 
54 


20.237 
20.117 
19.992 
19.863 
19.729 

19.591 
19.447 
19.298 
19.144 

18.985 

18.820 
18.649 
18.473 
18.291 
18.102 

17.908 
17.708 
17.501 
17.288 
17.069 

16.844 
16.612 
16.373 
16.128 
15.876 

15.618 
15.354 
15.084 
14.807 
14.524 

14.235 
13.940 
13.639 
13.334 
13.023 

12.707 
12.388 
12.061 
11.733 
11.400 


4 
PerCt. 


PerCt. 


5 
PerCt. 


6 
PerCt. 


18.610  17.1956  15.9583  14.870  13.053' 
18.514ll7.1174'l5.8946,14.818|13.017 
18.413:17.0359115.827914.76312.979; 
18.309'l6.9504 15. 7579il4.705  12.939' 
18.200'l6.8612ll5.6844'l4.644|12.897| 

18.08616.7683  15.6076  14.58l!l2.852! 
17.969!l6.6713jl5.5272|l4.514ll2.804| 
17.846!l6.5698il5.4427|l4. 443112.754 
17.719!l6.4640l5.3543  14.369^12. 70l| 
17.587J16.3537il5.262014.291il2.645i 


I7.449!l6.2387  15.1652 
17.307|16.1190il5.0641 
17.159  15.9944!l4  9586 


17.005 
16.846 


15.864714.8483 
15.7297il4.7332 


16.68215.589414.6132 


16.511 
16.335 
16.152 
15.963 

15.769 
15.568 
15.360 


15.443514.4878 
15.292214.3579 
15.135l!l4.2218 


14.209ll2.585 
14.12312.523 
14.03312.457 
13.939ll2.387 
13.841 12.314 

13.73712.236 


13.629 
13.517 
13.399 


14.9721 14.0803  13.276 


14.8035 
14.6287 
14.4479 
15.147|14.2607 
14.927114.0674 

14.700ll3.8678 
14.467  13.6623 


14.228 
13.983 
13.731 

13.473 
13.209 
12.939 
12.664 
12.383 


13.4503 
13.2318 
13.0072 

12.7765 
12.5401 
12.2967 
12.0482 
11.7936 


13.9337 
13.7812 
13.6228 
13.4584 


12155 
12.069 
11.980 
11.885 


13.148  11.786 
13.014 11.683i 

12.875 


12.730 


11.574 
11.460; 


13.2881 12.57911.342 


12.097J11.5.336 
11.805  11.2684 


11.509 
11.209 
10.904 


ll.€65  10.596 
10.72710.284 
10.3871  9.970 
10.045!  9.653 
9.702'  9.334 


10.9979 
10.7227 
10.4430 

101591 

9.8715 
9.5805 
9.2864 
8.9898 


131117 
12.9295 
12.7410 
12.5461 
12.3451 

121381 
11.9251 
11.7057 
11.4808 
11.2497 

11.0131 
10.7710 
10.5235 
10.2710 
10.0137 

9.7518 
9.4857 
9.2159 
8.9426 
8.6661 


12.42311.217 
12.26l!ll.088 
12.093il0.953| 
11.91810.812 
11.73810.666 


11.552 
11.360 
11.161 
10.957 
10.747 

10.531 

10.310 

10.083 

9.851 

9.613 

9.371 
9.125 

8.874 
8.620 
8.362 


10.514! 
10.3571 
10.1931 
10.024| 
9.849 

9.668 
9.482 
9.290 
9.092 
8.890| 

8.682! 
8.469' 
8.252: 
8.031| 
7.805 ! 


55 
56 
57 
58 
59 

60 
61 
62 
63 
64 

65 
66 
67 
68 
69 

70 

71 
72 
73 

74 

75 
76 
77 
78 
79 

80 
81 
82 
83 
84 

85 
86 
87 
88 
89 

90 
91 
92 
93 
94 

95 
96 
97 
98 
99 


3     ^ 

PerCt.  PerCt. 

9.3589.014 
9.014  8.693 

8.67l!8.372 
8.3298.051 
7.988  7.730 


4 
PerCt. 


8.6909 
8.3907 
8.0893 

7.7880 
7.4862 


7.650  7. 41117.1851 
7.3157.095  6.8853 


6.983:6.780 
6.65616.469 
6.333:6.162 

6.016:5.859 


O.704 
5.399 
5.101 
4.810 

4.527 
4.252 
3.986 
3.729 
3.480 

3.242 
3.013 
2.793 
2.583 
2.383 

2.193 
2.012 
1.841 
1.679 
1.526 


380 

242 

1.107 

.973 

.828 

.704 
.607 
.520 
.438 
.364 

.296 
.221 
.172 
.107 


5.562 
5.270 
4.984 
4.704 

4.431 
4.166 
3.909 
3.660 
3.419 

3.187 
2.965 
2.750 
2.546 
2.350 

2.164 
1.987 
1.819 
1.660 
1.509 

1.366 

1.230 

1.097 

.965 

.821 

.699 
.603 
.516 
.435 
.361 

.295 
.220 
.171 
.108 
.001 


6.5874 
6.2918 
5.9992 

5.7103 
5.4257 
5.1456 
4.8711 
4.6019 

4.3394 
4.0835 
3.8348 
3.5935 
3.3598 

3.1346 
2.9177 
2.7091 
2.5094 
2.3184 

2.1362 
1.9629 
1.7979 
1.6419 


PerCt. 


8.3869 
8.1058 
7.8230 
7.5392 


5 
PerCt. 


8.101 

7.837 
7.571 
7.304 


7.254817.035 


6 
PerCt. 


7.576 
7.343 
.107 
6.870 
6.630 


6.9703  6.766 
6.68636.497 
6.4036:6.228 
6.1224  5.9615.659 
5.8435  5.695  5.416 


6.388 
6.145 
5.902 


5.5675:5.431 
5.29525.170 
5.0266;4.912 
4.7629  4.659 
4.5039  4.409 

4.2508  4,165 
4.0036L3.926 
3.762913.693 
3.5291:3.467 
3.3023!3.247 


5.175 
4.935 
4.697 
4.463 
4.231 

4.003 
3.780 
3.561 
3.348 
3.140 


3.0834;3.034  2.939 

2.8722!2;828;2.743 
2.6688!2.630  2.554 
2.4739  2. 439j2. 373 
2.2872-2.257  2.198 


2.108812.082 
1.93891.916 

1.777l|l.757 
1.62381.606 


1.49341.47781.462 


1.35281.3394 
1.2183il.2069 
1.08711.0775 


.9568 
.8150 

.6938 
.5985 
.5128 
.4322 
.3593 

.2930 
.2190 
.1703 
.1069 
.0000 


.9489 
.8086 

.6887 
.5943 
.5094 
.4294 
.3571 

.2913 

.2178 
.1694 
.1063 
.0000 


1.326 

1.196 

1.068 

.941 


2.0301 
1.870 
1.717 
1.572 
1.433 

1.301 
1.174 

1.050 
926 


.802    .790 


.684 
.590 
.506 
.427 
.355 

.290 
.217 
.169 
.106 
.000 


.674 
.582 
.499 
.421 
.350 

.286 
.214 
.167 
.105 
.000 


K 


x+l .x+1 


FOBMIJLA,  Oxa;  = fT^- 

Vqcx 


TABLE     LXXIII. 


213 


ANNUAL   PREMIUM  (rr)  FOR  THE   INSURANCE  OF  1,000  ON  TWO  JOINT  LIVES  MALE, 
PAYABLE  AT  THE  END  OF  THE  YEAR  OF  THE  FIRST  DEATH. 


10 

11 

12 
13 
14 

15 
16 
17 
18 
19 

20 
21 
22 
23 
24 

25 
26 
27 
28 
29 

30 
31 
32 
33 
34 

35 
36 
37 
38 
39 

40 
41 
42 
43 
44 

45 
46 
47 
48 
49 

50 
51 
52 
53 
54 


3 
Per  Ct, 


17.97 
18.23 
18.52 
18.80 
19.11 

19.44 
19.78 
20.14 
20.52 
20.91 

21.33 
21.77 
22.23 
22.71 
23.22 

23.76 
24.33 
24.93 
25.56 
26.21 

26.92 
27.66 
28.44 
29.26 
30.13 

31.05 
32.02 
33.05 
34.14 
35.30 

36.51 
37.81 
39.18 
40.64 
42.19 

43.83 
45.58 
47.44 
49.41 
51.52 


34 
Per  Ct. 

17.18 
17.43 

17.69 
17.98 
18.27 

18.58 
18.90 
19.25 
19.61 
19.99 

20.39 
30.81 
21.26 
21.72 
22.22 

22.74 

23.29 
23.87 
24.49 
25.14 

25.82 
26.54 
27.31 
28.12 
28.98 

29.88 
30.84 
31.85 
32.93 
34.07 

35.28 
36.56 
37.92 
39.37 
40.91 


4 
PerCt. 


16.49 
16.74 
16.98 
17.25 
17.53 

17.82 
18.13 
18.45 
18.80 
19.17 

19.55 
19.95 
20.38 
20.84 
21.31 

21.82 
22.36 
22.92 
23.51 
24.15 

24.82 
25.53 
26,27 
27.07 
27.91 

28.80 
29.74 
30.74 
31.80 
32.93 

34.13 
35.39 
36.75 
38.18 
39.70 


42.54  41.32 

44. 28:43.05 


46.12 
48.09 
50.19 


53.76  52.43 
56.1554.80 
58.70  57.34 
61.4160.05 
64.3262.95 


44.88 
46.84 
48.93 


PerCt, 


15.91 
16.12 
16.37 
10.61 
16.87 

17.15 
17.44 
17.76 
18.08 
18.43 

18.80 
19.19 
19.60 
20.04 
20.50 

20.99 
21.51 
22.05 
22.63 
23.25 

23.90 
24.59 
25.33 
26.10 
26.93 

27.80 
28.73 
29.71 
30.76 
31.87 

33.05 
.34.31 
35.65 
37.06 
38.57 


5. 
Per  Ct. 


15.39 
15.60 
15.82 
16.06 
16.30 

16.57 
16.84 
17.14 
17.45 

17.78 

18.13 
18.51 
18.90 
19.32 

19.77 

20.23 
20.73 
21.27 
21.84 
22.43 

23.06 
23.74 
24.46 
25.21 
26.02 

26.88 

27.79 
28.76 


6 
PerCt. 


14.55 
14.73 
14.93 
15.13 
15.36 

15.59 
15.84 
16.10 
16.39 
16.69 

17.00 
17.35 
17.71 
18.10 
18.51 

18.95 
19.41 
19.91 
20.44 
21.01 

21.60 
22.24 
22.93 
23.65 
24.42 

25.25 
26.12 
27.06 
29.79128.05 
30.88  29.12 


32.05 
33.29 
34.61 
36.01 
37.51 


40.18  39.10 
41.89  40.80 
43.7242.61 
45.66  44.55 
^7.74  46.61 


51.15  49.95  48.79 
53.52  52.3151.14 
56.06  54.83  53.65 
58.75|57.51|56.33 
61.64  60. 40159. 20 


30.25 
31.45 
32.74 
34.11 
35.58 

37.14 

38.80 
40,58 
42.48 
44.51 

46.69 
49.00 
51.48 
54.13 
56.97 


5<bp 


55 
56 
57 
58 
59 

60 
61 
62 
63 
64 

65 
66 
67 
68 
69 

70 
71 
72 
73 

74 

75 
76 

77 
78 
79 

80 
81 
82 
83 
84 

85 
86 
87 
88 
89 

90 
91 
92 
93 
94 

95 
96 
97 
98 
99 


3 
Per  Ct. 


67.42 
70.73 

74.28 
77.97 
82.14 

86.48 

91.14 

96.13 

101.50 

107.25 

113.42 
120.05 
127.15 
134.80 
143.01 

151.81 
161.28 
171.45 
182.35 
194.08 

206.63 
220.09 
234.52 
249.94 
266.44 

284.06 
302.84 
322.87 
344.13 
366.84 

391.00 
416.96 
445.53 

477.71 
517.93 

557.64 
593.09 
628.84 
666.42 
704.16 

742.21 
789.56 
824.12 

873.91 


3i 
Per  Ct. 


66.04 
69.35 
72.89 
76.67 
80.73 

85.07 

89.72 

94.71 

100.06 

105.81 

111.97 
118.58 
125.69 
133.31 
141.51 

150.30 
159.75 
169.89 
180.78 
192.48 

205.00 
218.42 
232.82 
248.20 
264.65 

282.21 
300.93 
320.89 
342.08 
364.70 

388.77 
414.62 
443.09 
475.14 
515.21 

554.77 
590.08 
625.68 
663.10 
700.67 

738.53 

785.66 
819.89 
868.65 


4 
Per  Ct. 


64.73 
68.02 
71.56 
75.33 

79.37 

83.71 
88.36 
93.33 
98.68 


PerCt. 


5 
Per  Ct. 


63.47 

66.75 
70.28 
74.04 
78.08 

82.41 

87.04 
92.01 
97.34 


104.42  103.06 


110.56 
117.16 
124.25 
131.87 
140.05 

148.82 
158.25 
168.38 
179.24 
190.91 

203.40 
216.79 
231.15 
246.49 
262.89 

280.39 
299.05 
318.94 
.340.06 
362.61 

.386.57 
412.33 

440.67 
472.57 
512.50 

551.93 
587.11 
622.55 

659.77 
697.23 

734.92 

781.89 
816.03 
865.011860.83 
96L  54  956.94 


109.20 
115.79 
122.87 
130.46 
138.63 

147.38 
156.79 
166.89 
177.73 
189.38 

201.83 
215.19 
229.51 
244.80 
261.16 

278.61 
297.20 
317.03 
338.07 
360.52 

384.40 
410.06 
438.28 
470.04 
509.85 

549.12 

584.17 
619.45 
656.55 
693.81 

731.33 

778.09 
812.10 


62.26 
65.54 
69.05 
72.80 
76.83 

81.14 
85.76 
90.63 
96.04 
101.75 

107.88 
114.46 
121.52 
129.09 
137.25 

145.98 
155.37 
165.43 
176.25 
187.86 

200.29 
213.61 
227.89 
243.14 
259.44 

276.84 
295.37 
315.14 
336.11 
35.8.47 

382.27 
407.81 
435.91 
467.55 
507.20 

546.35 
581.24 
616.39 
653.32 
690.43 

727.78 
774.34 
808.19 
856.70 
9.52.38 


6 
Per  Ct. 


60.01 
63.26 
66.74 
70.47 

74.47 

78.75 
83.36 
88.28 
93.58 
99.25 

105.36 
111.88 
118.92 
126.46 
134.57 

143.27 
152.61 
162.63 
173.38 
184.94 

197.31 
210.55 
224.75 
239.90 
256.10 

273.39 
291.80 
311.42 
332.24 
354.46 

378.05 
403.40 
431.26 
462.62 
502.02 

540.89 
575.51 
610.37 
G47.03 

683.88 

721.03 

767.24 
800.62 
848.53 
943.40 


Formula,  n^  =  1000 1  ^^  "  C^"^)  ]  =  ^^^^  j  fe  ~  ^^"''^  } 


♦214 


TABLE     LXXIY. 


SINGLE  PREMIUM  (A)  OR  RESERVE,  FOR  THE   INSURANCE  OF    1,000  ON   TWO  JOINT 
LIVES,  PAYABLE  AT  THE  END  OP  THE  YEAR  OP  THE  FIRST  DEATH. 


o3  m 

0    O 

o<to 

H^  Percent. 


10 

11 

12 
13 
14 

15 
16 
17 
18 
19 

20 
21 
22 
23 
24 

25 
26 
27 
28 
29 

30 
31 
32 
33 
34 

3^ 
36 
37 
38 
39 

40 
41 
42 
43 

44 

45 
46 
47 
48 
49 

50 
51 
52 
53 
54 


381.45 
384.95 
388.57 
392.34 
396.24 

400.27 
404.45 
408.79 
413.28 
417.92 


H  4 

Per  Cent.  I  Per  Cent. 


^   I    5 

Per  Cent.  I  Per  Cent. 


336.85 
340.12 
343.51 
347.06 
350.74 

354.57 
358.55 
362.69 
367.00 
371.47 


422.73  376.12 
427.70  380.94 
432. 83i  385.94 
438.141  391.13 
443.62  396.50 


449.28 
455.12 
461.13 
467.33 
473.72 

480.29 
487.05 
493.99 
501.13 
508.46 

515.97 
523.66 
531.54 
539.61 

547.86 

556.27 
564.85 
573.61 
582.51 
591.58 

600.78 
610.12 
619.58 
629.15 
638.83 

648. 6o' 
658.44 
668.35 
678.31 
688:30' 


402.07 
407.84 
413.81 
419.98 
426.36 

432.94 
439.74 

446.75 
4.53.98 
461.42 

469.08 
476.95 
485.03 
493.34 
501.85 

510.58 
519.49 
528.63 
537.93 
547.44 

557.12 
566.97 
576.98 
587.14 
597.44 

607.87 
618.40 
629.04 
639.75 
650.53 


300.17! 
303.17 
306.32 
309.60. 
313.03 

316.60 
320.33 
324.24 
328.31 
332.54 


269.75 
272.48 
275.35 
278.37 
281.53 


244.29 
246.77 
249.38 
252.13 
255.04 


284.84  258.08 
288.30  261.27 
291.94  264.63 
295.75  268.17 


299.72 


336.97;  303.88 
341. 57|  308.25 
346.37'  312.79!  284.14 


271.87 

275.77 
279.85 


351.36 
356.54 

361.941 
367.55 
373.37 
379.43 
385.69 

392.17 
398.89 
405.84 
413,05 
420.48 

428.16 
436.06 
444.22 
452.621 
461.26j 

470.13, 
479.23 
488.59 
498.14 
507.94 

517.94 
528.13 
538.54 
549.12 
559.88 

570.80 
581. 86| 
593.06 
604.37 
615.77 


317.54 
322.49 

327.66 
333.07 
338.66 
344.52 
350.61 

356.92 
363.49 
370.31 
377.39 
384.73 

392.32 
400.16 
408.29 
416.68 
425.33 

434.25 
443.42 
452.86 
462.55 
472.50 

482.69 
493.12 
503.57 
514.65 
525.73 

537.01 
548.46 
560.07 
571.84 
583.75 


288.61 
293.31 

298.23 
303.37 
308.74  I 
314.35  i 
320.21  I 

326.32  ! 
332.68  : 
339.30  i 
346.20  i 

353.37  i 

i 

360.81  I 

368.53  : 

376.54  ; 
384.85  I 
393.42  I 

! 

402.29  ' 
411.44  I 
420.89  ! 
430.62  j 
440.62 

450.89 
461.44 
472.25 
483.31 
494.61 

506.13 
517.87 
529.80 
541.91 
554.20 


55 
56 
57 
58 
59 

60 
61 
62 
63 
64 

65 
66 
67 
68 
69 

70 
71 
72 
73 

74 

75 
76 

77 
78 
79 

80 
81 
82 
83 
84 

85 
86 
87 
88 
89 

90 
91 
92 
93 
94 

95 
96 
97 
98 
99 


8 
Per  Cent. 


698.32 
708.33 
718.33 
728.29 
738.20 

748.05 
757.81 
767.47 
777.01 
786.42 

795.66 
804.73 
813.63 
822.31 
830.78 

839.02 
847.03 

854.78 
862.27 
869.50 

876.45 
883.12 
889.52 
895.63 
901.46 

907.00 
912.26 
917.25 
921.97 
926.44 

930.67 
934.71 
938.64 
942.53 
946.76 

950.36 
953.19 
955.73 
958.12 
960.28 

962.24 
964.42 
965.86 
967.75 


3i 
Per  Cent, 


4  4i  5 

Per  Cent.jPer  Cent.  Per  Cent, 


661.36 
672.22 
683.09 
693.94 
704.77 

715.56 
726.27 
736.89 
747.41 
757.80 

768.04 
778.10 
787.99 
797.65 
807.12 

816.33 
825.30 
833.99 
842.42 
850.56 

858.40 
865.93 
873.17 
880.09 
886.70 

892.99 
898.98 
904,66 
910.04 
915.14 

919.98 
924.59 
929.09 
933.55 
938.40 

942.55 
945.80 
948.72 
951.48 
953.96 

956.22 
958.73 
960.39 
962.53 
966.13 


627.27  595.78 
638.82,  607.88 
650.4l!  620.06 
662.00  632.28 
673.61  644.54 

685.19  656.78 
696.701  669.01 
708.18' 681.18 
719.55'  693.29 
730.79  705.30 


741.91! 

752.87 
763.64 
774.19 

784.54 


717.19 
728.91 
740.48 
751.83 
762.99 


794.63  773.89 
804.48  784.54 
814.05  794.89 


823.32 
832.31 


804.97 
814.73 


840.98  824.16 
849.32  833.25 


857,34 
865.02 
872.36 

879.38 
886.04 
892.38 
898.39 
904.10 

909.51 
914.68 
919.73 
924.74 
930.19 

934.85 
938.52 
941.81 
944.91 
947.72 

950.26 
953.11 
954.99 
957.43 
961.54 


842.02 
850.40 
858.45 

866.14 
873.45 
880.42 
887.02 
893.31 

899.36 
904.96 
910.54 
916.08 
922.12 

927.29 
931.35 
935.00 
938.44 
941.57 

944.40 
947.56 
949.64 
952.36 
956.94 


566.64 
579.19 
591.84 
604.57 
617.36 

630.18 
643.00 
655.79 
668.54 
681.21 

693.77 
706.19 
718.45 
730.53 
742,41 

754.04 
765.40 
776.51 
787,29 

797,78 

807.93 
817.72 
827.16 
836.23 
844.92 

853.23 
861.17 
868.73 
875.90 

882.74 

889.22 
895.43 
901.51 
907,56 
914.17 

919.83 
924.28 
928.28 
932.06 
935.48 

938.59 
942.06 
944.36 
947.34 
952.38 


FOEMULA,  Aa«  =  1000  j  1  -  {l-v)  (1  +a^)\  =  1000  1 1  -(1  -  v)  ^  I 


TABLE    LXXY. 


♦215 


TEN  PAYMENT  PREMIUM   (P)   ON   1,000,  WITH   VALUATION   FACTORS  FOR  THE  SAME, 

ALSO  FOR  ORDINARY   JOINT   POLICIES   ON   TWO   MALE   LIVES. 

FOR  THE  LATTER  POLICIES  P'  IS  0. 

4  PER  CENT. 


II 

Ord'y  Joint. 

Ten  Pay't  Joint  Life  Policies. 

Is 

Ord'y  Joint 

1 
Ten  Pay't  Joint  Life  Policies.  1 

XP". 

P. 

XV. 

AP". 

AP". 

P. 

AP'. 

AP". 

10 

1.740034 

37.562 

7.583526 

1.880948 

50 

1.952370 

77.388 

6.49777S 

2.063894 

11 

.741904 

37.945 

.561975 

.883130 

51 

.963711 

79.516 

.452967 

.071799 

12 

.743863 

38.347 

.540412 

.885409 

52 

.975496 

81.753 

.40611? 

.079957 

13 

.745925 

38.766 

.518801 

.887772 

53 

.987735 

84.105 

.357061 

.088372 

14 

.748089 

39.206 

.497150 

.890240 

54 

2.000444 

86.584 

.305615 

.097068 

15 

1.750354 

39.663 

7.475422 

1.892787 

55 

2.013635 

89.206 

6.251613 

2.106081 

16 

.752732 

40.142 

.453635 

.895442 

56 

.027301 

91.975 

.194806 

.115399 

17 

.755233 

40.646 

.431800 

.898218 

57 

.041468 

94.911 

.134988 

.125066 

18 

.757855 

41.171 

.409867 

.901091 

58 

.056112 

98.023 

.071871 

.135084 

19 

.760607 

41.718 

.387814 

.904064 

59 

.071289 

101.34 

.005232 

.145512 

20 

1.763495 

42.293 

7.365674 

1.907167 

60 

2.086978 

104.88 

5.934739 

2.156372 

21 

.766521 

42.891 

.343382 

.910371 

61 

.103184 

108.66 

.860049 

.167676 

22 

.769694 

43.516 

.320956 

.913695 

62 

.119907 

112.71 

.780822 

.179470 

23 

.773022 

44.169 

.298355 

.917141 

63 

.137168 

117.06 

.696641 

.191790 

24 

.776512 

44.849 

.275557 

.920700 

64 

.154951 

121.74 

.607041 

.204667 

25 

1.780169 

45.560 

7.252567 

1.924391 

65 

2.173261 

126.79 

5.511540 

2.218145 

26 

.784006 

46.303 

.229347 

.928214 

66 

.192083 

132.25 

.409582 

.232263 

27 

.788020 

47.076 

.205861 

.932157 

67 

.211436 

138.16 

.300568 

.247044 

28 

.792228 

47.885 

.182120 

.936245 

68 

.231282 

144.55 

.183770 

.262479 

29 

.796638 

48.726 

.158035 

.940455 

69 

.251664 

151.51 

.058521 

.278689 

30 

1.801247 

49.600 

7.133591 

1.944787 

70 

2.272505 

159.05 

4.923893 

2.295592 

31 

.806077 

50.513 

.108792 

.949266 

71 

.293840 

167.27 

.779012 

.313301 

32 

.811131 

51.463 

.083556 

.953878 

72 

.315626 

176.21 

.622795 

.331774 

33 

.816426 

52.457 

.057905 

.958653 

73 

.337860 

185.93 

.454064 

.351006 

34 

.821962 

53.489 

.031737 

.963554 

74 

.360535 

196.53 

.271559 

.371052 

35 

1.827753 

54.565 

7.005041 

1.968607 

75 

2.383562 

208.03 

4.073626 

2.391802 

36 

.833797 

55.681 

6.977727 

.973786 

76 

.406966 

220.51 

3.858577 

.413252 

37 

.840123 

56.847 

.949802 

.979132 

77 

.430737 

234.06 

.624217 

.435400 

38 

.846740 

58.062 

.921192 

.984633 

78 

.454770 

248.69 

.367287 

.458111 

39 

.853649 

59.327 

.891826 

.990288 

79 

.479070 

264.49 

.083312 

.481373 

40 

1.860862 

60.643 

6.861641 

1.996094 

80 

2.503593 

281.49 

2.762652 

2.505084 

41 

.868378 

62.013 

.830568 

2.002056 

81 

.528288 

299.75 

.402315 

.529188 

42 

.876257 

63.446 

.798584 

.008206 

82 

.553163 

319.37 

.003219 

.553679 

43 

.884450 

64.933 

.765527 

.014498 

83 

.578092 

340.30 

1.561001 

.578366 

44 

.893008 

66.490 

.731399 

.020988 

84 

.603214 

362.73 

.068323 

.603352 

45 

1.901923 

68.111 

6.696056 

2.027645 

85 

2.628422 

386.63 

0.518142 

2.628483 

46 

.911214 

69.802 

.659409 

.034482 

86 

.653973 

412.35 

1.901420 

.653995 

47 

.920895 

71.573 

.621388 

.041529 

87 

.680453 

440.67 

.184758 

.680454 

48 

.930971 

73.422 

.581854 

.0487661 

88 

.708447 

472.57 

3.377984 

.708447 

49 

.941459 

75.358 

.540687 

.056217 

89 

.741123 

512.50 

3.397848 

.7U121 

Formula,    Fxx  = 


-ii'r.'R.  iJa 


S\ncx -IN5 


P'xx={Pxx-^x^)^ccx^       P"a:«:=Pa=«-M000a      ^v). 


♦216  TABLE    LXXVI. 

t 

GENERAL  VALUATION  OF  JOINT  LIFE  POLICIES  BY  ANNUAL  PREMIUM  ON  1,000. 

Note.     Ten  or  Limited  Premium  Policies  are  valued  by  this  Table  only  till  the  end  of  the  year 
after  Payment  of  the  last  Premium,  and  afterwards  by  Single  Premium  Table. 

4  PER  CENT. 


Equal 
Ages. 

x-\-n. 

h  =  4^111 

.  *Dec. 

l^m.  Nov. 

2jm.  Oct.    : 

dim. 

Equal 
Ages. 

X-\-?l. 

f" 

963.141 

966.346 

969.551     ■ 

972.756 

kb. 

kb'. 

AS. 

Xb'. 

kb. 

W.      1 

Xb. 

10 

5.000969 

1.236385 

5.002901  1.238317 

5.004824 

1.240240 

5.006739 

10 

11 

.023650 

.234408 

.025584:  .236342 

.027508 

.238266 

.029424 

11 

12 

.046350 

.232335 

.048284  .234269 

.050209  1  .236194; 

.052127 

12 

13 

.069062 

.230153 

.070998 

.232089 

.072925 

.234016  i 

.074843 

13 

14 

.091793 

.227862 

.093731 

.229800 

.095660 

.231729 

.097582 

14 

15 

5.114550 

1.225462 

5.116491 

1.227403 

0.118422 

1.229334: 

5.120346 

15 

16 

.137330 

.222943 

.139272 

.224885 

.141205 

.226818 

.143130 

16 

17 

.160129 

.220293 

.162074 

.222238 

.164010 

.224174 

.165937 

17 

18 

.182957 

.217512 

.184905 

.219460 

.186843 

.221398 

.188773 

18 

19 

.205817 

.214596 

.207766 

.216545 

.209707 

.218486 

.211639 

19 

20 

0. 228706 

1.211532 

0. 230659 

1.213485 

5.232604 

1.215430 

5.234540 

20 

21 

.251635 

.208321 

.253591 

.210277 

.255539 

.212225  > 

.257479 

21 

22 

.274604 

.204952 

.276564 

.206912 

.278515 

.208863  , 

.280459 

22 

23 

.297615 

.201416 

.299580 

.203381 

.301536 

.205337 

.303482 

2G 

24 

.320675 

.197708 

.322644 

.199677 

.324605 

.201638 

.326556 

24 

25 

5.343789 

1.193821 

5.345762 

1.195794 

5.347727 

1.197759 

5.349683 

25 

26 

.366956 

.189739 

.368935 

.191718 

.370907 

.193690 

.372868 

26 

27 

.390193 

.185467 

.392179 

.187453 

.394156 

.189430 

.396124 

27 

28 

.413498 

.180986 

.415490 

.182978 

.417473 

.184961 

.419448 

28 

29 

.436878 

.176286 

.438878 

.178286 

.440870 

.180278 

.442852 

29 

30 

5.460353 

1.171372 

0.462361 

1.173380 

5.464360 

1.175379 

5.466350 

30 

31 

.483916 

.166219 

.485933 

.168236 

.487941 

.170244 

.489939 

31 

32 

.507583 

.160820 

.509610 

.162847 

.511627 

.164864 

.513635 

32 

33 

.531360 

.155164 

.533397 

.157201 

.535425 

.159229 

.537444 

33 

34 

.555263 

.149242 

.557313 

.151292 

.559352 

.153331 

.561383 

34 

35 

5.579303 

1.143043 

0.581367 

1.145107 

5.583422 

1.147162 

0.585466 

35 

36 

.603506 

.136568 

.605583 

.138645 

.607650 

.140712 

.609708 

36 

37 

.627865 

.129783 

.629958 

.131876 

.632040 

.133958 

.634113 

37 

38 

.652401 

.122677 

.654512 

.124788  i 

.656613 

.126889 

.658703 

38 

39 

.677144 

.115253 

.679274 

.117383 

.681394 

.119503 

.683502 

39 

40 

5.702109 

1.107501 

5.704260 

1.109652 

0. 706401 

1.111793 

5.708531 

40 

41 

.727321 

.099381  : 

.729495 

.101555 

.731657 

.103717 

.733809 

41 

42 

.752788 

.090893  ^ 

.754988 

.093093 

.757178 

.095283 

.759356 

42 

43 

.778564 

.082040 

.780791 

.084267 

.783008 

.086484 

.785212 

43 

44 

.804650 

.072780 

.806909 

.075039 

.809157 

.077287 

.811393 

44 

45 

5.831099 

1.063118 

0.833392 

1.065411 

5.835673 

1.067692 

5.837942 

45 

46 

.857937 

.053030 

.860268 

.055361 

.862586 

.057679  1 

.864892 

46 

i  47 

.885203 

.042501 

.887575 

.044873 ! 

.889934 

.047232 

.892281 

47 

48 

.912945 

.031519 

.915363 

.033937 

.917767 

.036341 

.920158 

48 

49 

.941206 

.020066 

.943674 

.022534 

.946127 

.024987 

.948567 

49  1 

50 

5.970037 

1.008123 

5.972560 

1.010646 

5.975069 

1.013155 

5.977563 

50 

51 

.999501 

0.995680 

4.002085 

0.998264 

:  4.004653 

.000832 

4.007207 

51 

52 

4  029657 

.982718 

.032307 

.985368 

i  .034942 

0.988003 

.037561 

52 

53 

.060573 

.969218 

.063297 

.971942 

'  .066003 

.974648 

.068693 

53 

Formula,  V  =  /"  f  P;  •  b^^^  -  P^  •  5;,„ ;        F^  =  (P.  -  -x)  N.. 

The  suffix  is  not  here  repeated  for  equal  Ages,  Page  270.  I^  =  Pa:  +  1000  (1  —  v). 


nil 


TABLE    LXXYI. 


GENERAL  VALUATION  OP  JOINT  LIFE  POLICIES  BY  ANNUAL  PREMIUM  ON  1,000. 

4  PER  CENT. 


Equal 

*Sept. 

4|-rn.  Aug. 

5^in.  July. 

6m. 

Equal 

Ages. 
x-^n. 

975.962 

979.167 

980.769 

Ages. 
x+n. 

10 

Xb'. 

Xb. 

Xb'. 

Xb. 

Xb'. 

Xb. 

Xb'. 

10 

1.242155 

0. 008645  1.244061 

5.010542 

1.245958 

5.011488 

1.246904 

11 

.240182 

.031332 

.242090 

.033232 

.243990 

.034178 

.244936 

11 

12 

.238112 

.054035 

.240020 

.055936 

.241921 

.056883 

• .242868 

12 

13 

.235934 

.076754 

.237845 

.078656 

.239747 

.079604 

.240695 

13 

14 

.233651 

.099494 

.235563 

.101398 

.237467 

.102348 

.238417 

14 

15 

1.231258 

0. 122260 

1.233172 

0.124166 

1.235078 

5.125116 

1.236028 

15 

16 

.228743 

.145046 

.230659 

.146954 

.232567 

.147905 

.233518 

16 

17 

.226101 

.167855 

.228019 

.169766 

.229930 

.170718 

.230882 

17 

18 

.223328 

.190694 

.225249 

.192607 

.227162 

.193560 

.228115 

18 

19 

.22.0418 

.213563 

.222342 

.215479 

.224258 

.216433 

.225212 

19 

20 

1.217366 

5.236467 

1.219293 

0.238384 

1.221210 

5.239341 

1.222167 

20 

21 

.214165 

.259409 

.216095 

.261330 

.218016 

.262289 

.218975 

21 

^  22 

.210807 

.282393 

.212741 

.284318 

.214666 

.285278 

.215626 

22 

23 

.207283 

.305421 

.209222 

.307350 

.211151 

.308312 

.212113 

23 

24 

.203589  ! 

.328499 

.205532 

.330433 

.207466 

.331397 

.208430 

24 

25 

1.199715 

5.351630 

1.201662 

5.353569 

1.203601 

6.354535 

1.204567 

25 

26 

.195651 

.374822 

.197605  . 

.376766 

.199549 

.377735 

.200518 

26 

27 

.191398 

.398082 

.193356 

.400032 

.195306 

.401004 

.196278 

27 

28 

.186936 

.421412 

.  .188900' 

.423369 

.190857 

.424344 

.191832 

28 

29 

.182260 

.444825 

.184233 

.446790 

.186198 

.447769 

.187177 

29 

30 

1.177369 

5.468331 

1.179350 

0. 470302 

1.181321 

5.471285 

1.182304 

30 

31 

.172242 

.491930 

.174233 

.493910 

.176213 

.494897 

.177200 

31 

32 

.166872 

.515633 

.168870 

.517623 

.170860 

.518614 

.171851 

32 

33 

.161248 

.539453 

.163257 

.541453 

.165257 

.542450 

.166254 

33 

34 

.155362 

.563404 

.157383 

.565415 

.159394 

.566418 

.160397. 

34 

35 

1.149206 

5.587500 

1.151240 

5.589525 

1.153265 

5.590534 

1.154274 

35 

36 

.142770 

.611756 

.144818 

.613795 

.146857 

.614810 

.147872 

36 

37 

.136031 

.636176 

.138094 

.638229 

.140147 

.639252 

.141170 

37 

38 

.128979 

.660783 

.131059 

.662853 

.133129 

.663885 

.134161 

38 

39 

.121611 

.685601 

.123710 

.687690 

.125799 

.688731 

.126840 

39 

40 

1.113923 

5.710651 

1.116043 

0.712762 

1.118154 

5.713813 

1.119205 

40 

41 

.105869 

.735951 

.108011 

.738082 

.110142 

.739143 

.111203 

41 

42 

.097461 

.761524 

.099629 

.763681 

.101786 

.764755 

.102860 

42 

43 

.088688 

.787406 

.090882 

.789589 

.093065 

.790676 

.094152 

43 

44 

.079523 

.813617 

.081747 

.815830 

.083960 

.816933 

.085063 

44 

45 

1.069961 

5.840200 

1.072219 

5.842446 

1.074465 

5.843564 

1.076583 

45 

46 

.059985 

.867186 

.062279 

.869467 

.064560 

.870604 

.065697 

46 

47 

.049579 

.894615 

.051913 

.896937 

.054235 

.898093 

.066391 

47 

48 

.038732 

.922536 

.041110 

.924901 

.043475 

.926079 

.044653 

48 

49 

.027427 

.950993 

.029853 

.953406 

.032266 

.954607 

.033467 

49 

50 

1.015649 

0. 980043 

1.018129 

5.982508 

1.020594 

0.983736 

1.021822 

50 

51 

.003386 

4.009745 

.005924 

4.012269 

.008448 

4.013525 

.009704 

51 

52 

0.990622 

.040164 

0.993225 

.042751 

0.995812 

.044039 

0.997100 

52 

53 

.977338 

.071367 

.980012 

.074024 

.982669 

.075347 

.983992 

53 

■*  Months  of  Entry  corresponding  to  Annual  Valuation,  Dec.  31. 
Here  x  +  n  +  h=  Present  Age  in  years  and  fraction  ;  f"  =:  1000  J7i  +  (1  —  ^)  V^  ; 

_  h  +  (l—h)  vpx+n~l  .  b'        =  b        'N 


*x+n  = 


*2id 


TABLE     LXXTI 


GENERAL  VALUATION  OF  JOINT  LIFE  POLICIES  BY  ANNUAL  PREMIUM  ON  1,000. 

4  PER   CENT. 


Equal 

AgM. 

X+n. 

7^=6Jra 

.  June. 

7^in.  May. 

8^in.  April. 

9|in. 

Equal  1 
Ages,  j 

x-\-n. 

/"  =  982.372. 

985.577. 

988.782. 

991.987. 

Xb. 

Xb'. 

Xb. 

Xb'. 

Xb. 

Xb'. 

Xb. 

10 

5.012432 

1.247848 

O.014313 

1.249729 

0.016187 

1.251603 

5.018052 

10 

11 

.035122 

.245880 

.037006 

.247764 

■  .038880 

.249638 

.040747 

U 

12 

.057828 

.243813 

.059712 

.245697 

.061588 

.247573 

.063456 

12 

13 

.080549 

.241640 

.082435 

.243526 

.084313 

.245404 

.086182 

13 

14 

.103294 

.239363 

.105182 

.241251 

.107062 

.243131 

.108933 

14 

15 

5.126063 

1.236975  ' 

0.127954 

1.238866 

0.129835 

1.24074t 

5.131708 

15 

16 

.148853 

.234466 

.150744 

.236357 

.152628 

.238241 

.154502 

16 

17 

.171667 

.23183] 

.173561 

.233725  ' 

.175446 

.235610 

.177323 

17 

18 

.194511 

.229066 

.196407 

.230962 

.198295 

.232850 

.200175 

18 

19 

.217386 

.226165 

.219284 

.228063 

.221174 

.229953 

.223056 

19 

20 

5.240295 

1.223121 

0.242196 

1.225022 

5.244090 

1.226916 

5.245975 

20 

21 

.263244 

.219930 

.265149 

.221835 

.267046 

.223732 

.268935 

21 

22 

.286235 

.216583 

.288143 

.218491 

.290044 

.220392 

.291936 

22 

23 

.309271 

.213072 

.311183 

.214984 

.313087 

.216888 

.314984 

23 

24 

.332358 

.209391  ; 

.334275 

.211308 

.336183 

.213216 

1  .338084 

24 

25 

5.355499 

1.205531 

0. 357420 

1.207452 

0.359333 

1.209365 

5.361238 

25 

26 

.378702 

.201485  ; 

.380629 

.203412 

.382548 

.205331 

.384458 

26 

27 

.401974 

.197248  i 

.403906 

.199180 

.405830 

.201104 

;  .407746 

27 

28 

.425316 

.192804 

.427255 

.194743 

.429185 

.196673 

!  .431107 

28 

29 

.448745 

.188153 

.450691 

.190099 

.452630 

.192038 

;  .454559 

29 

30 

5.472265 

1.183284 

5.474218 

1.185237 

5.476164 

1.187183 

5.478101 

30 

31 

.495881 

.178184 

.497844 

.180147 

.499797 

.182100 

.501742 

31 

32 

.519604 

.172841  1 

.521575 

.174812 

.523537 

.176774 

.525491 

32 

33 

.543444 

.167248  i 

.545426 

.169230 

.547399 

.171203 

,549363 

33 

34 

.567418 

.161397 

.569411 

.163390 

.571394 

.165373 

.573370 

34 

35 

5.591541 

1.155281  ^ 

0.593548 

1.157288 

5.595544 

1.159284 

5.597533 

35 

36 

.615823 

.148885 

.617843 

.150905 

.619853 

.152915 

.621853 

36 

37 

.640273 

.142191 

.642306 

.144224 

.644330 

.146248 

.646346 

37 

38 

.664913 

.135189 

.666965 

.137241 

.669006 

.139282 

.671037 

38 

39 

.689769 

.127878  i 

.691839 

.129948 

.693898 

.132007 

.695947 

39 

40 

5.714861 

1.120253 

0. 716950 

1.122342 

5.719030 

1.124422 

5.721099 

40 

41 

.740202 

.112262 

.742313 

.114373 

.744412 

.116472 

.746502 

41 

42 

.765827 

.103932 

.767962 

.106067 

.770088 

.108193 

.772202 

42 

43 

.791761 

.095237 

.793922 

.097398 

.796073 

.099549 

.798212 

43 

44 

.818032 

.086162 

.820223 

.088353 

.822403 

.090533 

.824572 

44 

45 

5.844680 

1.076699 

0. 846903 

1.078922 

5.849114 

1.081133 

0.851314 

45 

46 

.871736 

.066829 

.873994 

.069087 

.876241 

.071334 

.878476 

46 

47 

.899246 

.056544 

.901543 

.058841 

.903828 

.061126 

.906100 

47 

48 

.927253 

.045827 

.929593 

.048167 

.931919 

.050493 

.934234 

48 

49 

.955805 

.034665 

.958192 

.037052 

.960565 

.039425 

.962925 

49 

50 

5.984960 

1.023046 

5.987398 

1.025484 

5.989822 

1.027908 

5.992234 

50 

51 

4.014778 

.010957 

4.017273 

.013452 

4.019753 

.015932 

4.022220 

51 

52 

.045323 

0.998384 

.047881 

.000942 

.050422 

.003483 

.052950 

52 

53 

.076665 

.985310 

.079291 

0.987936 

.081900 

0.990545 

.084494 

53 

♦219 


TABLE     LXXYI. 


GENERAL  VALUATION  OF  JOINT  LIFE   POLICIES  BY  ANNUAL  PREMIUM    ON  1,000, 

4  PER  CENT. 


Equal 
Ages. 

March. 

lOjm.  Feb. 

llj^m.  Jan. 

12m. 

Equal 
Ages. 

x-\-n. 

995.192. 

998.397. 

1000.000. 

x-\-n. 

kb'. 

kb. 

W. 

A5. 

Xb'. 

U. 

AJ'. 

10 

1.253468 

5.019909 

1.255325 

0. 021759 

1.257175 

5.022680 

1.258096 

10 

11 

.351505 

'  .042606 

.253364 

.044456 

.255214 

.045379 

.256137 

11 

12 

.249441 

1  .065315 

.251300 

.067167 

.253152  ; 

.068090 

.254075 

12 

13 

.247273 

.088043 

.249134 

.089896 

.250987  ! 

.090820 

.251911 

13 

14 

.245002 

.110797 

.246866 

.112653 

.248722 

.113577 

.249646 

14 

15 

1. 242620 

5.133573 

1.244485 

5.135431 

1.246343 

5.136356 

1.247268 

15 

16 

.240115 

.156368 

.241981 

.158228 

.243841 

.159154 

.244767 

16 

17 

.237487 

.179192 

.239356 

.181054 

.241218 

.181981 

.242145 

17 

18 

.234730 

.202046 

.236601 

.203910 

.238465 

.204838 

.239393 

18 

19 

.231835 

.224930 

.233709 

.226796 

.235575 

.227726 

.236505 

19 

20 

1.^^.28801 

0.247853 

1.230679 

5.249722 

1.232548 

15.250653 

1.233479 

20 

21 

.225621 

.270815 

.227501 

.272687 

.229373 

.273620 

.230306 

21 

22 

.222284 

..293819 

.224167 

.295695 

.226043 

1  .296630 

.226978 

22 

23 

.218785 

.316872 

.220673 

.318751 

.222552 

!  .319687 

.223488 

23 

24 

.215117 

.339976 

.217009 

.341860 

.218893 

.342798 

.219831 

24 

25 

1.211270 

5.363134 

1.213166 

0. 365022 

1.215054 

5.365962 

1.215994 

25 

26 

.207241 

.386360 

.209143 

.388253 

.211036 

.389197 

.211980 

26 

27 

.203020 

.409653 

.204927 

.411552 

.206826 

.412498 

.207772 

27 

28 

.138595 

.433020 

.200508 

.434925 

.202413 

.435874 

.203362 

28 

29 

.193967 

.456479 

.195887 

.458392 

.197800 

i  .459345 

.198753 

29 

30 

1.189120 

5.480028 

1.191047 

0.481948  il.  192967 

5.482904 

1.193923 

30 

31 

.184045 

.503678 

.185981 

.505606 

.187909 

.506566 

.188869 

31 

32 

.178728 

.527436 

.180673 

.529372 

.182609 

.530337 

.183574 

32 

33 

.173167 

.551318 

.175122 

1  .553264 

.177068 

.554234 

.178038 

33 

34 

.167349 

.575336 

.169315 

.577293 

.171272 

.578268 

.172247 

34 

35 

1.161273 

0.599512 

1.163252 

0. 601481 

1.165221 

5.602463 

1.166203 

35 

36 

.154915 

.623845 

.156907 

.625828 

.158890 

.626815 

.159877 

36 

37 

.148264 

.648351 

.150269 

.650347 

.152^65 

.651342 

.153260 

37 

38 

.141313 

.  .673060 

.143336 

.675072 

.145348 

.676075 

.146351 

38 

39 

.134056 

.697987 

.136096 

.700018 

.138127 

.701029 

.139138 

39 

40 

1.126491 

0.723159 

1.128551 

5.725209 

1.130601 

5.726230 

1.131622 

40 

41 

.118562 

.748582 

.120642 

.750652 

.122712 

.751683 

.123743 

41 

42 

.110307 

.774307 

.112412 

.776401 

.114506 

.777445 

.115550 

42 

43 

.101688 

.800342 

.103818 

.802461 

.105937 

.803516 

.106992 

43 

44 

.092702 

.826730 

.094860 

.828877 

.097007 

.829947 

.098077 

44 

45 

1.083333 

0. 853504 

1.085523 

0.855683 

1.087702 

5.856767 

1.088786 

45 

46 

.073569 

.880698 

.075791 

.882910 

.078003  1 

.884012 

.079105 

46 

47 

.063398 

.908362 

.065660 

.910611 

.067909 

.911731 

.069029 

47 

48 

.052808 

.936537 

.055111 

.938827 

.057401 

.939967 

.058541 

48 

49 

.041785 

.965272 

.044132 

.967608 

.046468 

.968770 

.047630 

49 

50 

1.030320 

5.994631 

1.032717 

5.997016  1.035102  i 

5.998203 

1.036289 

50 

51 

.018399 

4.024672 

.020851 

4.027111 

.023290 

4.028325  i  .024504 

51 

52 

.006011 

.055463 

.008524 

.057960 

.011021 

.059204  1  .012265 

52 

53 

0.993139 

.087072 

0.995717 

.089635 

0.998280 

.090911  0.999556 

53 

*320 


TABLE    LXXYI. 


GENERAL  VALUATION  OF  JOINT  LIFE  POLICIES  BY  ANNUAL  PREMIUM  ON  1,000. 

4  PER  CENT. 


Equal 

h  =  ^m.  *Dec. 

l^ni.  Nov. 

2|-m.  Oct. 

d^m. 

Eaual 

Ages. 
x-^n. 

/"  =  963.141 

i     966.346 

969.551 

972.756 

Ages. 
x-\-n. 

Xb. 

Ab'. 

U. 

W. 

Xb. 

Xb'. 

Xb. 

54 

4.092330 

0.955158 

4.095124 

0.957962 

4.097911 

0.960749 

4.100680 

54 

55 

4.124982 

0.940521 

4.127877 

0.943416 

4.130752  0.946291 

4.133609 

55 

56 

.158664 

.925303 

.161656 

.928295 

.164628  1  .931267 

.167580 

56 

57 

.193453 

.909482  '  .196555 

.912584 

.199635  .  .915664 

.202694 

57 

58 

.229479 

.893034   .232700 

.896255 

.235898  '  .899453 

.239072 

58 

59 

.266842 

.875945  '  .270196 

.879299 

.273523   .882626 

.276824 

59 

60 

4.305679 

0.858190 

4.309178 

0.861689 

:  4.312648 

0.865159 

!  3.316091 

60 

61 

.346147 

.839762 

.349806 

.843421 

.353435 

.847050 

.357035 

61 

62 

.388409 

.820646 

.392245 

.824482 

.396046 

.828283 

.399815 

62 

63 

.432626 

.800802 

.436657 

.804833 

.440651 

.808827 

.444610 

63 

64 

.479013 

.780234 

.483260 

.784481 

.487467  .788688 

.491633 

64 

65 

4.527780 

0.758918 

4.532266 

0.763404 

4.536708  0.767846 

4.541105 

65 

66 

.579173 

.736846 

.583924 

.741597 

.588622 

.746295 

.593270 

66 

67 

.633435 

.713979 

.638478 

.719022 

.643465 

.724009 

.648393 

67 

68 

.690881 

.690332 

.696244 

.695695 

.701541 

.700992 

.706775 

68 

69 

.751776 

.665830) 

.757499 

.671553 

.763149 

.677203 

.768725 

69 

70 

4.816533 

0.640525 

4.822651 

0.646643 

4.828684  0.652676 

4.834634 

70 

71 

.885485 

.614346  1 

.892043 

.620904 

.898503   .627364 

.904869 

71 

72 

.959079 

.587302  1 

.966124 

.594347 

.973056 

.601279 

.979879 

72 

73 

3.037759 

.559356  i 

3.045342 

.566939 

3.052795 

.574392 

3.060123 

73 

74 

.122022 

.530465  i 

.130211 

.538654 

.138250 

.546693 

.146141 

74 

75 

3.212493 

0.500686 

3.221349 

0.509542 

3.230029 

0.518222 

3.238540 

75 

76 

.309721 

.469924 

.319320 

.479523 

.328712 

.488915 

.337904 

76 

77 

.414374 

.438131 

.424809 

.448566 

.435000 

.458757 

.444957 

77 

78 

.527269 

.405362 

.538632 

.416725  1 

.549706 

.427799 

.560504 

78 

79 

.649174 

.371527 

.661577 

.383930  ; 

.673635 

.395988 

.685367 

79 

80 

3.781001 

0.336594 

3.794569 

0.350162 

3.807726 

0.363319 

3.820496 

80 

81 

.923750 

.300520 

.938622 

.315392 

.953001 

.329771 

.966919 

81 

82 

2.078479 

.263185 

2.094829 

.279535 

2.110586 

.295292 

2.125791 

82 

83 

.246487 

.224618 

.264482 

.242613 

.281761 

.259892 

.298379 

83 

84 

.428946 

.184457 

.448823 

.204334 

.467831 

.223342 

.486042 

84 

85 

2.627494 

0.142647 

2.649484 

0.164637 

2.670414 

0.185567 

2.690381 

85 

86 

.843590 

.098482 

.867956 

.122848 

.891028 

.145920 

.912936 

86 

87 

1.078896 

.050518 

1.106049 

.077671 

1.131603 

.103225 

1.155737 

87 

88 

.335865 

1.996769 

.366080 

.026984 

.394328 

.055232 

.420851 

88 

89 

.617059 

.930245 

.652886 

1.966072 

.685981 

1.999167 

.716732 

89 

90 

T.  938654 

T.  864208 

T.  981258 

T.  906812 

0.020053 

T.  945607 

0.055665 

90 

91 

0.304967 

.803897 

0.354059 

.852989 

.398162 

.897092 

.438196 

91 

92 

.712147 

.741287 

.768670 

.797810 

.818675 

.847815 

.863513 

92 

93 

1.164049 

.672794 

1.230048 

.738793 

1.287328 

.796073 

1.337926 

93 

94 

.669216 

.600063 

.746739 

.677586 

.812499 

.743346 

.869597 

94 

95 

2.234475 

T.  520627 

2.325331 

T.  611483 

2.400428 

T.  686580 

2.464435 

95 

96 

.872089 

.412726 

.988191 

.528828 

3.079712 

.620349 

3.155262 

96 

97 

3.617270 

.320785 

3.754903 

.458418 

.859255 

.562770 

.943328 

97 

98 

4.470370 

.158523 

4.651266 

.339419 

4.778587 

.466740 

4.876920 

98 

*  Mouths  of  Entry  corresponding  to  Annual  Valuation  Dec.  31. 


n2\ 


TABLE    LXXYI. 


GENERAL  VALUATION  OP  JOINT  LIFE  POLICIES  BY  ANNUAL  PREMIUM  ON  1,000. 

4  PER  CENT. 


Equal 

Sept. 

4^m.  Aug. 

5-^m.  July. 

6m. 

Equal 

Ages. 

x-\-n. 

975.962 

979.167 

980.769 

Ages. 
x-\-n. 

W. 

Xh.             W. 

U. 

XV. 

Xh. 

XV. 

54 

0.963518 

4.103431 

0.966269 

4.106165 

0.969008 

4.107525 

0.970363 

54 

55 

0.949148 

4.136447 

0.951986 

4.139266 

0.954805 

4.140669 

0.956208 

55 

56 

.934219 

.170513 

.937152 

.173425 

.940064 

.174874 

.941513 

56 

57 

.918723 

.205732 

.921761 

.208748 

.924777 

.210248 

.926277 

57 

58 

.902627 

.242223 

.905778 

.245352 

.908907 

.246908 

.910463 

58 

59 

.885927 

.280101 

.889204 

.283353 

.892456 

.284970 

.894073 

59 

60 

0.868602 

4.319507 

0.872018 

4.322897 

0.875408 

4.324582 

0.877093 

60 

61 

.850650 

.360603 

.854218 

.364144 

.857759 

.365904 

.859519 

61 

62 

.832052 

.403551 

.835788 

.407256 

.839493 

.409096 

.841333 

62 

63 

.812786 

.448532 

.816708 

.436819 

.804995 

.454351 

.822527 

63 

64 

.792854 

.495759 

.796980 

.499847 

.801068 

.501876 

.803097 

64 

65 

0.772243 

4.545457 

0.776595 

4.549766 

0.780904 

4.551904 

0.783042 

65 

66 

.750943 

.597869 

.755542 

.602420 

.760093 

.604678 

.762351 

66 

67 

.728937 

.653267 

.733811 

.658087 

.738631 

.660477 

.741021 

67 

68 

.706226 

.711947 

.711398 

.717057 

.716508 

.719590 

.719041 

68 

69 

.682779 

.774231 

.688285 

.779669 

.693723 

.782362 

.696416 

69 

70 

0.658626 

4.840504 

0.664496 

4.846296 

0.670288 

4.849162 

0.673154 

70 

71 

.633730 

.911143 

.640004 

.917328 

.646189 

.920387 

.649248 

71 

72 

.608102 

.986597 

.614820 

.993212 

.621435 

.996482 

.624705 

72 

73 

.581720 

3.067329 

.588926 

3.074417 

.596014 

3.077918 

.599515 

73 

74 

.554504 

.153892 

.562335 

.161508 

.569951 

.165266 

.573709 

74 

75 

0.526733 

3.246886 

0.535079  \ 

3.255074 

0.543267 

3.259112 

0.547305 

75 

76 

.498107 

.346906 

.507109 

.355726 

.515929 

.360069 

.520272 

76 

77 

.468714 

.454690 

.478447 

.464210 

.487967 

.468894 

.492651 

77 

78 

.438597 

.571041 

.449134 

.581328 

.459421 

.586381 

.464474 

78 

79 

.407720 

.696791 

.419144 

.707922 

.430275 

.713382 

.435735 

79 

80 

0.376089 

3.832902 

0.388495 

3.844963 

0.400556 

3.850870 

0.406463 

80 

81 

.343689 

.980404 

.357174 

.993484 

.370254 

.999879 

.376649 

81 

82 

.310497 

2.140482 

.325188 

2.154691 

.339397 

2.161626 

.346332 

82  1 

83 

.276510 

.314384 

.292515 

.329820 

.307951 

.337337 

.315468 

83  1 

84 

.241553 

.503518 

.259029 

.520320 

.275831 

.528483 

.283994 

84 

85 

0.205534 

2.709470 

0.224623 

2.727757 

0.242910 

2.736619 

0.251772 

85 

86 

.167828 

.933791 

.188683 

.953691 

.208583 

.963309 

.218201 

86 

87 

.127359 

1.178600 

.150222 

1.200320 

.171942 

1.210785 

.182407 

87 

88 

.081755 

.445846 

.106750 

.469481 

.130385 

.480833 

.141737 

88 

89 

.029918 

.745449 

.058635 

.772384 

.085570 

.785250 

.098436 

89 

90 

T.  981219 

0.088577 

0.014131 

0.119169 

0.044723 

0.133694 

0.059248 

90 

91 

.937126 

.474848 

1.973778 

.508647 

.007577 

.524609 

.023539 

91 

92 

.892653 

.904153 

.933293 

.941312 

1.970452 

.958764 

1.987904 

92 

93 

.846671 

1.383239 

.891984 

1.424268 

.933013 

1.443415 

.952160 

93 

94 

.800444 

.920054 

.850901 

.965254 

.896101 

.986205 

.917052 

94 

95 

T.  750587 

2.520208 

T.  806360 

2.569627 

1.855779 

2.592377 

1.878529 

95 

96 

.695899 

3.219597 

.760234 

3.275620 

.816257 

3.301135 

.841772 

96 

97 

.646843 

4.013736 

.717251 

4.074305 

.777820 

4.101691 

.805206 

97 

98 

.565073 

.957048 

.645201 

5.024669 

.712822 

5.054902 

.743055 

98 

n%% 


TABLE    LXXYI, 


GENERAL  VALUATION  OF  JOINT  LIFE  POLICIES  BY  ANNUAL  PREMIUM  ON  1,000, 


4  PER  CENT. 

Eaual 

h  =  6^m.    June. 

7^m.  May. 

8^m.  April. 

9^m. 

1 
Equal  1 

Ages. 

/"  = 

982.372 

985.577 

988.782 

991.987 

Ages.  1 
x-\-n. 

Xb. 

kb'. 

1  - 

kb. 

Xb'. 

Xb. 

Xb'. 

Xb. 

54 

4.108881 

0.971719 

4.111582 

0.974420 

4.114264 

0.977102 

4.116932 

54 

55 

4.142067 

0.957606 

4.144851 

0.960390 

4.147616 

0.963155 

4.150365 

55 

56 

.176318 

.942957 

.179191 

.945830 

.182047 

.948686 

.184883 

56 

57 

.211743 

.927772 

.214718 

.930747 

.217673 

.933702 

.220608 

57 

58 

.248458 

.912013 

.251543 

.915098 

.254605 

.918160 

.257646 

58 

59 

.286581 

.895684 

.289786 

.898889 

.292967 

.902070 

.296123 

1 

59 

60 

4.326260 

0.878771 

4.329597 

0.882108 

4.332909 

0.885420 

i  4.336195 

60 

61 

.367656 

.861271 

.371139 

.864754 

.374595 

.868210 

.378023 

61 

62 

.410929 

.843166 

.414572 

.846809 

.418184 

.850421 

.421766 

62 

63 

.456273 

.824449 

.460092 

.828268 

.463877 

.832053 

.467630 

63 

64 

.503897 

.805118 

.507909 

.809130 

.511884 

.813105 

.515824 

64 

65 

4.554033 

0.785171 

4.558258 

0.789396 

4.562443 

0.793581 

4.566588 

65 

66 

.606924 

.764597 

.611381 

.769054 

.615793 

.773466 

.620160 

66 

67 

.662853 

.743397 

.667568 

.748112 

.672232 

.752776 

.676847 

67 

68 

.722108 

.721559 

.727101 

.726552 

.732038 

.731489 

.736918 

68 

69 

.785038 

.699092 

.790342 

.704396 

.795583 

.709637 

.800760 

69 

70 

4.852011 

0.676003 

4.857652 

0.681644 

4.863221 

0.687213 

4.868720 

70 

i  71 

.923425 

.652286 

.929438 

.658299 

.935370 

.664231 

.941221 

71 

72 

.999728 

.627951 

3.006148 

.634371 

3.012474 

.640697 

3.018709 

72 

73 

3.081391 

.602988 

.088255 

.609852 

.095013 

.616610 

.101667 

73 

74 

.168991 

.577434 

.176349 

.584792 

.183583 

.592026 

.190699 

74 

75 

3.263112 

0.551305 

3.271004 

t).559197 

3.278755 

0.566948 

3.286369 

75 

76 

.364369 

.524572 

.372845 

.533048 

.381157 

.541360 

.389315 

76 

77 

.473527 

.497284 

.482647 

.506404 

.491580 

.515337 

.500334 

77 

78 

.591376 

.469469 

.601198 

.479291 

.610802 

.488895 

.620199 

78 

79 

.718776 

.441129 

.729363 

.451716 

.739700 

.462053 

.749795 

79 

80 

3.856698 

0.412291 

3.868124 

0.423717 

3.879257 

0.434850 

3.890112 

80 

81 

2.006181 

.382951 

2.018518 

.395288 

2.030514 

.407284 

2.042187 

81 

82 

-.168451 

.353157 

.181788 

.366494 

.194728 

.379434 

.207293 

82 

83 

.344726 

.322857 

.359138 

.337269 

.373087 

.351218 

.386601 

83 

84 

.536495 

.292006 

.552090 

.307601 

.567143 

.322654 

.581693 

84 

85 

2.745303 

0.260456 

2.762168 

0.277321 

2.778403 

0.293556 

2.794053 

85 

86 

.972718 

.227610 

.990948 

.245840  ' 1.008442 

.263334 

1.025259 

86 

87 

1.221005 

.192627 

1.240749 

.212371  1 

.259635 

.231257 

.277733 

87 

88 

.491896 

.152800 

.513211 

.174115 

.533528 

.194432 

.552937 

88 

89 

.797745 

.110931 

.821707 

.134893 

.844416 

.157602 

.865997 

89 

90 

0.147748 

0.073.302 

0.174561 

0.100115 

0.199815 

0.125369 

0.223681 

90 

91 

.540005 

.038935 

.569250 

.068180 

.596649 

.095579  i 

.622422 

91 

92 

.975541 

.004681 

1.007268 

.036408 

1.036834 

.065974 

1.064516 

92 

93 

1.461753 

1.970498 

.496258 

.005003 

.528222 

.036967 

.557995 

93 

94 

2.006190 

.937037 

2.043598 

1.974445 

2.078038 

.008885 

2.109946 

94 

95 

2.613993 

T.  900145 

2.654244 

1.940396 

2.691078 

T.  977230 

2.725031 

95 

96 

3.325234 

.865871 

3.369758 

.910395 

3.410138 

.950775 

3.447080 

96  1 

97 

4.327452 

.830967 

4.174798 

.878313 

4.217486 

.921001 

4.256352 

97 

98 

5.083166 

.771319 

5.134712 

.822865 

5.180783 

.868936 

5.222432 

98 

♦223 


TABLE    LXXYI. 


GENERAL  VALUATION  OP  JOINT  LIFE  POLICIES  BY  ANNUAL  PREMIUM  ON  1,000. 

4  PER  CENT. 


Equal 
Ages. 

x-\-n. 

March. 

lO^m.  Feb. 

ll^m.  Jan. 

12m. 

Equal 
Ages. 

x  +  n. 

995.192 

998.397 

1000.000 

Xb'. 

AJ. 

W. 

U. 

Xb'. 

Xb. 

Xb'. 

54 

0.979770 

4.119582 

0.982420 

4.122216 

0.985054 

4.123527 

0.986365 

54 

55 

0.965904 

4.153096 

0.968635 

4.155809 

0.971348 

4.157160 

0.972699 

55 

56 

.951522 

.187700 

.954339 

.190500 

.957139 

.191893 

.958532 

56 

57 

.936637 

.223523 

.939552  \ 

.226418 

.942447 

.227859 

.943888 

57 

58 

.921201 

.260666 

.924221 

.263665 

.927220 

.265156 

.928711 

58 

59 

.905226 

.299259 

.908362 

.302371 

.911474 

.303919 

.913022 

59 

60 

0.888706 

4.339457 

0.891968 

4.342695 

0.895206 

"4.344305 

0.896816 

60 

61 

.871638 

.381425 

.875040 

.384800 

.878415 

.386478 

.880093 

61 

62 

.854003 

.425319 

.857556 

.428844 

.861081 

.430595 

.862832 

62 

63 

.835806 

.471351 

.839527 

.475040 

.843216 

.476873 

.845049 

63 

64 

.817045 

.519727 

.820948 

.523596 

.824817 

.525518 

.826739 

64 

65 

0.797726 

4.570693 

0.801831 

4.574760 

0.805898 

4.576779 

0.807917 

65 

66 

.777833 

.624484 

.782157 

.628766 

.786439 

.630891 

.788564 

66 

67 

.757391 

.681414 

.761958 

.685933 

.766477 

.688174 

.768718 

67 

68 

.736369 

.741744 

.741195 

.746518 

.745969 

.748885 

.748336 

68 

69 

.714814 

.805878 

.719932 

.810935 

.724989 

.813441 

.727495 

69 

70 

0.692712 

4.874149 

0.698141 

4.879511 

0.703503 

i.  882168 

0.706160 

70 

71 

.670082 

.946994 

.675855 

.952692 

.681553 

.955513 

.684374 

71 

72 

.646932 

3.024857 

.653080 

3.030918 

.659141 

3.033917 

.662140 

72 

73 

.623264 

.108221 

.629818 

.114676 

.636273 

.117868 

.639465 

73 

74 

.599142 

.197701 

.606144 

.204590 

.613033 

.207995 

.616438 

74 

75 

0.574562 

3.293853 

0.582046 

3.301209 

0.589402 

3.304841 

0.593034 

75 

76 

.549518 

.397321 

.557524 

.405183 

.565386 

.409060 

.569263 

76 

77 

.524091 

.508913 

.532670 

.517327 

.541084 

.521473 

.545230 

77 

78 

.498292 

.629396 

.507489  1 

.638403 

.516496 

.642837 

.520930 

78 

79 

.472148 

.759662 

.482015 

.769310 

.491663 

.774054 

.496407 

79 

80 

0.445705 

3.900703 

0.456296  ! 

3.911041 

0.466634 

3.916119 

0.471712 

80 

81 

.418957 

2.053555 

.430325  ! 

2.064633 

.441403 

2.070067 

.446837 

81 

82 

.391999 

.219505 

.404211 

.231383 

.416089 

.237202 

.421908 

82 

83 

.364732 

.399708 

.377839 

.412431 

.390562 

.418655 

.396786 

83 

84 

.337204 

.595771 

.351282 

.609406 

.364917 

.616067 

.371578 

84 

85 

0.309206 

2.809158 

0.324311 

2.823756 

0.338909 

2.830874 

0.346027 

85 

86 

.280151 

1.041449 

.296341 

1.057056 

.311948 

1.064655 

.319547 

86 

87 

.249355 

.295107 

.266729 

.311813 

.283435 

.319931 

.291553 

87 

88 

.213841 

.571515 

.232419 

.589332 

.250236  ! 

.597973 

.258877 

88 

89 

.179183 

.886555 

.199741 

.906184 

.219370 

.915675 

.228861 

89 

90 

0.149235 

0.246303 

0.171857 

0.267805 

0.193359 

0.278169 

0.203723 

90 

91 

.121352 

.646751 

.145681 

.669788 

.168718 

.680864 

.179794 

91 

92 

.093656 

1.090538 

.119678 

1.115089 

.144229 

1.126862 

.156002 

92 

93 

.066740 

.585856 

.094601 

.612038 

.120783 

.624559 

.133304 

93 

94 

.040793 

2.139669 

.070516 

2.167488 

.098335 

2.180756 

.111603 

94 

95 

0.011183 

2.756522 

0.042674 

2.785883 

0.072035 

2.799850 

0.086002 

95 

96 

1.987717 

3.481126 

.021763 

3.512695 

.053332 

3.527659 

.068296 

96 

97 

.959867 

4.292022 

1.995537 

4.324985 

.028500 

4.340573 

.044088 

97 

98 

.910585 

5.260434 

.948587 

5.295377 

1.983530 

5.311848 

-.000001 

98 

*224 


TABLE     LXXVIT. 


FEMALE    UFE     TABLE.     FROM    THIRTY    OFFICES'    EXPERIENCE    OF    LOSSES     AND 

AMOUNTS  INSURED. 


AGE. 
X. 

Living. 

Decre- 
ment. 

dx- 

Expectation 
of  Life. 

Prob.  of  Dec. 
d. 

Ix 

Prob.  Living. 

Px  —  ,  • 
Ix 

^Px- 

AZa;. 

AGE. 

X.    1 

10 

10 

100,000 

314 

48.05 

0.003140 

0.996860 

T.998634 

5.000000 

11 

99,686 

420 

47.21 

.004212 

.995788 

.998167 

4.998634 

11 

12 

99,266 

510 

46.40 

.005140 

.994860 

.997762 

4.996801 

12 

13 

98,756 

581 

45.64 

.005882 

.994118 

.997438 

4.994563 

13 

14 

98,175 

631 

44.91 

.006426 

.993574 

.997200 

4.992001 

14 

15 

97,544 

644 

44.19 

0.006603 

0.993397 

T.997123 

4.989201 

15 

16 

96,900 

678 

43.48 

.006998 

.993002 

.996950 

4.986324 

16 

17 

96,222 

745 

42.79 

.007741 

.992259 

.996625 

4.983274 

17 

18 

95,477 

792 

42.12 

.008296 

.991704 

.996382 

4.979899 

18 

19 

94,685 

820 

41.46 

.008659 

.991341 

.996223 

4.976281 

19 

I  20 

93,865 

856 

40.82 

0.009120 

0.990880 

T.996021 

4.972504 

20 

21 

93,009 

847 

40.19 

.009106 

.990894 

.996027 

4.968525 

21 

22 

92,162 

943 

39.56 

.010233 

.989767 

.995533 

4.964552 

22 

23 

91,219 

992 

38.96 

.010873 

.989127 

.995252 

4.960085 

23 

24 

90,227 

990 

38.38 

.010973 

.989027 

.995208 

4.955337 

24 

25 

89,237 

1,006 

37.80 

0.011274 

0.988726 

T.995076 

4.950545 

25 

26 

88,231 

1,024 

87.23 

.011606 

.988394 

.994930 

4.945621 

26 

27 

87,207 

998 

36.66 

.011442 

.988558 

.995002 

4.940551 

27 

28 

86,209 

977 

36.08 

.011333 

.988667 

.995050 

4.935553 

28 

28 

85,232 

975 

35.49 

.011440 

.988560 

.995003 

4.930603 

29 

30 

84,257 

971 

34.89 

0.011524 

0.988476 

T.994966 

4.925606 

30 

31 

83,286 

966 

34.29 

.011599 

.988401 

.994933 

4.920572 

31 

32 

82,320 

916 

33.69 

.011126 

.988874 

.995141 

4.915505 

32 

i  33 

81,404 

869 

33.06 

.010675 

.989325 

.995339 

4.910646 

33 

34 

80,535 

903 

32.42 

.011212 

.988788 

.995103 

4.905985 

34 

35 

79,632 

882 

31.78 

0.011076 

0.988924 

T.995163 

4.901088 

35 

36 

78,750 

877 

3L13 

.011137 

.988863 

.995136 

4.896251 

36  1 

37 

77,873 

878 

30.47 

.011274 

.988726 

.995076 

4.891387 

37  i 

38 

76,995 

887 

29.81 

.011522 

.988478 

.994967 

4.886463 

38  i 

39 

76,108 

863 

29.16 

.011338 

.988662 

.995048 

4.881430 

39  i 

'  40 

75,245 

885 

28.48 

0.011763 

0.988237 

T.994861 

4.876478 

40 

41 

74,360 

893 

27.82 

.012009 

.987991 

.994753 

4.871339 

41 

1  42 

73,467 

821 

27.15 

.011174 

.988826 

.995120 

4.866092 

42 

1  43 

72,646 

791 

26.45 

.010889 

.989111 

.995245 

4.861212 

43  1 

44 

71,855 

805 

25.74 

.011203 

.988797 

1  .995107 

4.856457 

44 

45 

71,050 

799 

25.02 

0.011244 

0.988756 

T.995089 

4.851564 

45 

46 

70,251 

792 

24.30 

.011274 

.988726 

.995076 

4.846653 

46 

47 

69,459 

757 

23.57 

.010900 

.989100 

.995240 

4.841729 

47  1 

48 

68,702 

766 

22.83 

.011149 

.988851 

.995131 

4.836969 

48 

49 

67,936 

803 

22.08 

.011820 

.988180 

.994836 

4.832100 

49 

50 

67,133 

821 

21.33 

0.012230 

0.987770 

T.994656 

4.826936 

50 

51 

66,312 

889 

20.59 

.013407 

.986593 

.994138 

4.821592 

51 

52 

65,423 

955 

19.87 

.014597 

; 985403 

.993614 

4.815730 

52 

53 

64,468 

.  976 

19.15 

.015139 

.984861 

.993375 

4.809344 

53 

54 

63,492 

1,009 

18.44 

.015891 

.984109 

.993043 

4.802719 

54 

TABLE     LXXVIl. 


*Z26 


FEMALE    LIFE     TABLE.     FROM    THIRTY    OFFICES'    EXPERIENCE    OF    LOSSES    AND 

AMOUNTS  INSURED. 


Decre- 

Prob. of  Dec. 

Prob.  Living. 

AGE. 
'X. 

Living. 

ment. 
dx. 

Expectation 
of  Life. 

dx 

n    — ^*^^ 

Xpx. 

Xlx. 

A&E. 

X. 

55 

62,483 

1,082 

17.73 

0.017318 

0.982682 

T.  992413 

4.795762 

55 

56 

61,401 

1,138 

17.03 

.018533 

.981468 

.991876 

4.788175 

56 

57 

60,363 

1,221 

16.35 

.030363 

.979738 

.991110 

4.780051 

57 

58 

59,042 

1,302 

15.67 

.033051 

.977949 

.990316 

4.771161 

58 

59 

57,740 

1,360 

15.03 

.023554 

.976446 

.989648 

4.761477 

59 

60 

56,380 

1,429 

14.37 

0.025345 

0.974655 

T.  988851 

4.751135 

60 

61 

54,951 

1,501 

13.73 

.027315 

.972685 

.987972 

4.739976 

61 

62 

53,450 

1,617 

13.10 

.030254 

.969746 

.986658 

4.737948 

62 

63 

51,833 

1,690 

13.49 

.032605 

.967395 

.985604 

4.714606 

63 

64 

50,143 

1,771 

11.90 

.035318 

.964682 

.984384 

4.700310 

64 

65 

48,372 

1,856 

11.31 

0.038370 

0.961630 

1.983008 

4.684594 

65 

66 

46,516 

1,940 

10.74 

.041705 

.958295 

.981499 

4.667603 

66 

67 

44,576 

2,024 

10.19 

.045405 

.954595 

.979819 

4.649101 

67 

68 

42,552 

2,107 

9.65 

.049515 

.950485 

.977945 

4.638930 

68 

69 

40,445 

2,185 

9.13 

.054034 

.945976 

.975880 

4.606865 

69 

70 

38,260 

2,257 

8.63 

0.058991 

0.941009 

T.  973594 

4.583745 

70 

71 

36,003 

2,323 

8.13 

.064495 

.935505 

.971046 

4.556339 

71 

72 

33,681 

2,376 

7.65 

.070544 

.929456 

.968229 

4.537385 

72 

73 

31,305 

3,416 

7.30 

.077176 

.922824 

.965119 

4.495614 

73 

74 

28,889 

2,442 

6.76 

.084533 

.915468 

.961643 

4.460733 

74 

75 

26,447 

2,449 

6.34 

0.093599 

0.907401 

T.  957799 

4.422376 

75 

76 

23,998 

2,435 

5.93 

.101467 

.898533 

.953534 

4.380175 

76 

77 

21,563 

2.397 

5.55 

.111163 

.888837 

.948823 

4.333709 

77 

78 

19,166 

2,335 

5.18 

.131839 

.878171 

.943579 

4.282531 

78 

79 

16,831 

2,246 

4.83 

.133445 

.866555 

.937796 

4.226110 

79 

80 

14.585 

2,133 

4.49 

0.146345 

0.853755 

T.  931333 

4.163906 

80 

81 

12,453 

1,994 

4.17 

.160134 

.839866 

.924210 

4.095239 

81 

82 

10.458 

1,833 

3.88 

.175373 

.824727 

.916310 

4.019449 

82 

83 

8,635 

1,654 

3.59 

.191768 

.808232 

.907536 

3.935759 

83 

84 

6,971 

1,462 

3.33 

.209725 

.790275 

.897778 

3.843295 

84 

35 

5,509 

1,262 

3.08 

0.229081 

0.770919 

T.  887009 

3.741073 

85. 

86 

4,247 

1,062 

3.84 

.250059 

.749941 

.875027 

3.628082 

86 

87 

3,185 

868 

2.62 

.272527 

.727473 

.861817 

3.503109 

87 

88 

2,317 

687 

2.42 

.296503 

.703497 

.847262 

3.364936 

88 

89 

1,630 

526 

2.23 

.322700 

.677300 

.830781 

3.313188 

89 

90 

1,104 

387 

2.05 

0.350544 

0.649456 

T.  812550 

3.042969 

90 

91 

717 

272 

1.89 

.379358 

.620643 

.792841 

2.855519 

91 

92 

445 

183 

1.73 

.411236 

.588764 

.769941 

2.648360 

92 

93 

262 

116 

1.59 

.442747 

.557353 

.746052 

2.418301 

93 

94 

146 

70 

1.46 

.479452 

.530548 

.716461 

2.164353 

94 

95 

76 

39 

1.34 

0.513158 

0.486842 

1.687388 

1.880814 

95 

96 

37 

20 

1.33 

.540541 

.459459 

.662247 

1.568202 

96 

97 

17 

10 

1.09 

.588235 

.411765 

.614649 

1.330449 

97 

98 

7 

4 

.93 

.571429 

.428571 

.632023 

0.845098 

98 

99 

3 

3 

.50 

1.000000 

.000000 

00 

! 

0.477131 

99 

^336 


TABLE    LXXYIII. 

FEMALE  LIFE.     D,  N,  Ox,  AND  CORRECTION  OF  AGE. 


Example.     An  actual  Age,  32  years  3  months,  added  to  its  Correction,  gives  34  years,  the  equivalent. 
Age  at  which  the  equal  Life  Annuity  and  Premium  are  found  in  the  preceding  tables  for  Male  Life. 

4  PER  CENT. 


AGE. 
X. 

Life  An'y.. 

Correction 

AGE. 

X. 

^x. 

XDx- 

■Na,. 

XEx- 

AJN  /p  —  AxJ/p, 

ttx- 

(.). 

10 

67,556.5 

4.829667 

1,372,039.3 

6.137366 

1.307699 

19.3095 

Y. 

5 

M. 

0.6 

10 

11 

64,754.1 

.811267 

1,304,482.8 

.115438 

.304171 

19.1452 

5 

9.1 

11 

12 

62,001.3 

.792401 

1,239,728.7 

.093327 

.300926 

18.9952 

6 

2.7 

12  i 

13 

59,310.3 

.773130 

1,177,727.4 

.071045 

.297915 

18.8571 

6 

6.1 

13 

14 

56,693.6 

.753534 

1,118,417.1 

.048604 

.295070 

18.7274 

6 

7.9 

14 

15 

54,162.8 

4.733701 

1,061,723.5 

6.026012 

1.292311 

18.6025 

6 

8.6 

15 

16 

51,735.8 

.713791 

1,007,560.7 

.003271 

.289480 

18.4751 

6 

9.1 

16 

17 

49,397.7 

.693707 

955,824.9 

5.980378 

.286671 

18.3496 

6 

8.9 

17 

18 

47,130.2 

.673299 

906,427.2 

.957333 

.284034 

18.2324 

6 

7.5 

18 

19 

44,941.5 

.652648 

859,297.0 

.934144 

.281496 

18.1204 

6 

5.4 

19 

20 

42,838.8 

4.631837 

814,355.5 

5.910814 

1.278977 

18.0098 

6 

2.9 

20 

21 

40,815.5 

.610825 

771,516.7 

.887345 

.276520 

17.9025 

5  11.8 

21 

22 

38,888.3 

.589819 

730,701.2 

-863740 

.273921 

17.7898 

5 

8.9 

22 

23 

37,009.9 

.568318 

691,812.9 

.839989 

.271671 

17.6927 

5 

4.5 

23 

24 

35,199.5 

.546537 

654,803.0 

.816111 

.269574 

17.6026 

4  11.5 

24 

25 

33,474.3 

4.524712 

619,603.5 

5.792113 

1.267401 

17.5098 

4 

6.5 

25 

26 

31,823.9 

.502754 

586,129.2 

.767993 

.265239 

17.4179 

4 

1.3 

26 

27 

30,244.8 

.480651 

554,305.3 

.743749 

.263098 

17.3273 

3 

7.9 

27 

28 

28,748.8 

.458620 

524,060.5 

.719381 

.260761 

17.2289 

3 

2.9 

28 

29 

27,329.6 

.436633 

495,311.7 

.694879 

.258246 

17.1237 

2  10.3 

29 

30 

25,978.0 

4.414606 

467,982.1 

5.670229 

1.255623 

17.0145 

2 

5.7 

30 

31 

24,691.0 

.392539 

442,004.1 

.645426 

.252887 

16.9014 

2 

1.3 

31 

32 

23,465.9 

.370438 

417,313.1 

.620462 

.250024 

16.7838 

1 

9.0 

32 

33 

22,312.4 

.348546 

393,847.2 

.595328 

.246782 

16.6515 

1 

5.5 

33 

34 

21,225.2 

.326852 

371,534.8 

.570000 

.243148 

16.5044 

1 

2.7 

34 

35 

20,180.0 

4.304921 

350,309.6 

5.544452 

1.239531 

16.3593 

0  11.6 

35 

36 

19,188.9 

.283051 

330,129.6 

.518684 

.235633 

16.2041 

0 

8.8 

36 

37 

18,245.4 

.261153 

310,940.7 

.492678 

.231525 

16.0422 

0 

6.3 

37 

38 

17,345.9 

.239196 

292,695.3 

.466416 

.227220 

15.8741 

0 

3.8 

38 

39 

16,486.6 

.217130 

275,349.4 

.439884 

.222754 

15.7014 

0 

1.4 

39 

40 

15,672.7 

4.195144 

258,862.8 

5.413070 

1.217926 

15.5168 

0 

.0 

40 

41 

14,892.7 

.172972 

243,190.1 

.385946 

.212974 

15.3295 

0 

.0 

41 

42 

14,147.9 

.150692 

228,297.4 

.358501 

.207809 

15.1365 

0 

.0 

42 

43 

13,451.7 

.128778 

214,149.5 

.330717 

.201939 

14.9199 

0 

.0 

43 

44 

12,793.5 

.106990 

200,697.8 

.302542 

.195552 

14.6874 

0 

.0 

44 

45 

12,163.7 

4.085064 

187,904.3 

5.273937 

1.188873 

14.4480 

0 

.0 

45 

46 

11,564.3 

.063119 

175,740.6 

.244872 

.181753 

14.1968 

0 

.0 

46 

47 

10,994.2 

.041162 

164,176.3 

.215310 

.174148 

13.9330 

0 

.0 

47 

48 

10,456.1 

.019369 

153,182.1 

.185208 

.165839 

13.6500 

0 

.0 

48 

49 

9,941.82 

3.997466 

142,725.97 

.154503 

.157037 

13.3561 

0 

.0 

49 

50 

9,446.46 

3.975269 

132,784.15 

5.123146 

1.147877 

13.0565 

0 

.0 

50 

51 

8,972.06 

.952892 

123,337.69 

.091096 

.138204 

12.7469 

0 

.0 

51 

52 

8,511.30 

.929996 

114,365.63 

.058295 

.128299 

12.4369 

0 

.0 

52 

53 

8,064.49 

.906577 

105,854.33  .024709 

.118132 

12.1260 

0 

.0 

53 

54 

7,636.93 

.882919 

97,789.84  4.990293 

.107374 

11.8048 

0 

.0 

54 

Formula,    Dj^  =  «;« Za,  j 


l  +  «.  =  P^; 


Female  Ox  =  %+<  Male  Life. 


lABLE    LXXYIII. 


*227 


FEMALE  LIFE,    D,  N,  a,.,  AND  CORRECTION  OF  AGE. 


4  PER  CENT. 


A  OTI 

Life  An'y. 

Correction 

AGE. 

X. 

AftE. 
X. 

r>x. 

ADa,. 

^x. 

ANa,. 

ANa;  —  ADa;. 

ax- 

{c). 

Y. 

M. 

55 

7,226.50 

3.858928 

90,152.91 

4.954980 

1.096052 

11.4753 

0 

.0 

55 

56 

6,828.23 

.834308 

82,926.41 

.918693 

.084385 

11.1447 

0 

.0 

56 

57 

6,443.93 

.809151 

76,098.18 

.881374 

.072223 

10.8093 

0 

.8 

67 

58 

6,070.54 

.783227 

69,654.25 

.842948 

.059721 

10.4742 

0 

1.4 

58 

59 

5,708.34 

.756510 

63,583.71 

.803346 

.046836 

10.1387 

0 

1.9 

59 

60 

5,359.51 

3.729125 

57,875.37 

4.762494 

1.033369 

9.7986 

0 

2.5 

60 

61 

5,022.76 

.700942 

52,515.86 

.720291 

.019349 

9.4556 

0 

3.1 

61 

62 

4,697.65 

.671881 

47,493.10 

.676631 

.004750 

9.1100 

0 

3.7 

62 

63 

4,380.32 

.641506 

42,795.45 

.631398 

0.989892 

8.76994 

0 

4.2 

63 

64 

4,074.52 

.610076 

38,415.13 

.^84502 

.974426 

8.42814 

0 

4.7 

64 

65 

3,779.44 

3.577427 

34,340.61 

4.535808 

0.958381 

8.08617 

0 

5.2 

65 

66 

3,494.64 

.543402 

30,561.17 

.485170 

.941768 

7.74517 

0 

5.8 

66 

67 

3,220.08 

.507867 

27,066.53 

.432432 

.924565 

7.40553 

0 

6.3 

67 

68 

2,955. 6o 

.470653 

23,846.45 

.377424 

.906771 

7.06810 

0 

6.9 

68 

69 

2,701.25 

.431565 

20,890.80 

.319955 

.888390 

6.73375 

0 

7.5 

69 

70 

2,457.03 

3.390411 

18,189.55 

4.259822 

0.869411 

6.40306 

0 

8.1 

70 

71 

2,223.17 

.346972 

15,732.52 

.196799 

.849827 

6.07664 

0 

8.7 

71 

72 

1,999.79 

.300985 

13,509.35 

.130634 

.829649 

5.75537 

0 

9.3 

72 

73 

1,787.23 

.252180 

11,509.56 

.061059  { 

.808879 

5.43990 

i  ^ 

9.9 

73 

74 

1,585.86 

.200266 

9,722.33 

3.987770 

.787504 

5.13061 

0  10.6 

74 

75 

1,395.97 

3.144876 

8,136.47 

3.910436 

0.765560 

4.82854 

!  0  11.2  . 

75 

76 

1,217.98 

.085641 

6,740.50 

.828692 

.743051 

4.53415 

1  0  11.8 

76 

77 

1,052.31 

.022142 

5,522.52 

.742138 

.719996 

4.24803 

.5 

77 

78 

899.355 

2.953931  ; 

4,470.212 

.650328 

.696397 

3.97047 

1.1 

78 

79 

759.410 

.880476 

3,570.857 

.552773 

.672297 

3.70216 

1.7 

79 

80 

632.760 

2.801239 

2,811.447 

3.448930 

0.647691 

3.44315 

2.3 

80 

81 

519.444 

.715539 

2,178.6^7 

.338194 

.622655 

3.19426 

2.8 

81 

82 

419.484 

.622715 

1,659.243 

.219910 

.597195 

2.95544 

3.2 

82 

83 

332.653 

.521992 

1,239.759 

.093338 

.571346 

2.72689 

3.4 

83 

84 

258.520 

.412495 

907.106 

2.957658 

.545163 

2.50884 

3.5 

84 

85 

196.444 

2.293239 

648.586 

2.811968 

0.518729 

2.30163 

3.1 

85 

86 

145.618 

.163215 

452.142 

.655275 

.492060 

2.10499 

2.3 

86 

87 

105.005 

.021208 

306.524 

.486465 

.465257 

1.91915 

.9 

87 

88 

73.4501 

1.865992 

201.5189 

.304316 

.438324 

1.74362 

0  10.6 

88 

89 

49.6845 

.696221 

128.0688 

.107443 

.411222 

1.57764 

0 

8.8 

89 

90 

32.3571 

1.509969 

78.3843 

1.894229 

0.384260 

1.42248 

0 

7.7 

90 

91 

20.2062 

.305485 

46.0272 

.663015 

.357530 

1.27788 

0 

6.8 

91 

92 

12.0585 

.081293 

25.8210 

.411973 

.330680 

1.14131 

0 

5.7 

92 

93 

6.82653 

0.834200 

13.76251 

.138698 

.304498 

1.01604 

0 

4.1 

93 

94 

3.65779 

.563219 

6.93598 

0.841108 

.277889 

.89622 

0 

2.5 

94 

95 

1.83083 

0.262647 

3.27819 

0.515634 

0.252987 

.79055 

0 

.0 

95 

96 

.857040 

1.933001 

1.447356 

.160576 

.227575 

.68879 

I  0 

.0 

96 

97 

.378630 

.578215 

.590316 

1.771084 

.192869 

.55908 

1  0 

.0 

97 

98 

.149910 

.175831 

.211686 

.325692 

.149861 

.41209 

0 

.0 

98 

99 

.061776 

2.790820 

.061776 

2.790820 

.000000 

.00000 

0 

.0 

99 

\ ' 


♦238 


TABLE    LXXIX. 


COMPARISON  OF  DIFFERENT  LIFE  TABLES. 


1  X. 

0 

Caxlisle. 

17  Offices. 

Am.  1858. 

English  Life  Table,  No.  3. 

20  Offices 

.  HM. 

AGE. 

X. 

Ix- 

Ix' 

Males,  Ix' 

dx- 

Fern.  Ix. 

dx. 

Ix. 

dx. 

10,000 

1,539 

511,745 

83,719 

488,255 

65,774 

0 

1 

8,461 

682 

428,026 

27,521 

422,481 

26,159 

1 

2 

7,779 

505 

400,505 

14,215 

396,322 

14,023 

2 

3 

7,274 

276 

386,290 

9,213 

382,299 

9,243 

3 

4 

6,998 

201 

377,077 

6,719 

373,056|  6,596 

4 

5 

6,797 

121 

370,358 

5,033 

366,460  4,866 

5 

6 

6,676 

82 

365,325 

3,953 

361,594  3,815 

e 

7 

6,594 

58 

361,372 

3,310 

357,779 

3,249 

7 

8 

6,536 

43 

358,062 

2,734 

354,530 

2,724 

8 

9 

6,493 

33 

355,328 

2,297 

351,806 

2,328 

9 

10 

6,460 

29 

100,000 

100,000 

353, 03r 

1,983 

349,478 

2,045 

100,000 

490 

10 

11 

6,431 

31 

99,324 

99,251 

351,048 

1,776 

347,433 

1,861 

99,510 

397 

11 

12 

6,400 

32 

98,650 

98,505  [ 

349,272 

1,666 

345,572 

1,765 

99,113 

329 

12 

13 

6,368 

33 

97,978 

97,762  i 

347,606 

1,637 

343,807 

1,745 

98,784 

288 

13 

14 

6,335 

35 

97,307 

97,022 

345,969 

1,679 

342,062 

1,789 

98,496 

272 

14 

15 

6,300 

39 

96,636 

96,285  1  344,290 

1,781 

340,273 

1,888 

98,224 

282 

15 

16 

6,261 

42 

95,965 

95,550  11342,509 

1,928 

338,385 

2,029 

97,942 

318 

16 

17 

6,219 

43  95,293 

94,818  : 

340,581 

2,112 

336,356 

2,205 

97,624 

379 

17 

18 

6,176 

43 

94,620 

94,089 

338,469 

2,320 

334,151 

2,400 

97,245 

466 

18 

19 

6,133 

43 

93,945 

93,362  1 

336,149 

2,541 

331,751 

2,609 

96,779 

556 

19 

20 

6,090 

43 

93,268 

92,637 

333,608 

2,764 

329,142 

2,819 

96,223 

609 

20 

21 

6,047 

42 

92,588 

91,914 

330,844 

2,801 

326,323  2,867 

95,614 

643 

21 

22 

6,005 

42 

91,905 

91,192  1 

328,043 

2,836 

323,456:  2,912 

94,971 

650 

22 

23 

5,963 

42 

91,219 

90,471  i 

325,207 

2,868 

320,544 

2,952 

94,321 

638 

23 

24 

5,921 

42 

90,529 

89,751  1 

322,339 

2,897 

317,592 

2,989 

93,683 

622 

24 

25 

5,879 

43 

89,835 

89,032 

319,442 

2,926 

314,603 

3,024 

93,061 

617 

25 

26 

5,836 

43 

89,137 

88,314  1 

316,516 

2,954 

311,579 

3,055 

92,444 

618 

26 

27 

5,793 

45 

88,434 

87,596  1 

313,562 

2,981 

308,524 

3,084 

91,826 

634 

27 

28 

5,748 

5o; 

87,726 

86,878  ; 

310,581 

3,009 

305,440 

3,112 

91,192 

654 

28 

29 

5,698 

56 

87,012 

86,160  ; 

307,572 

3,038 

302,328 

3,138 

90,538 

673 

29 

30 

5,642 

57 

86,292 

85,441 

304,534 

3,068 

299,190 

3,163 

89,865 

694 

30 

31 

5,585 

57 

85,565 

84,721 

301,466 

3,100 

296,027 

3,187 

1  89,171 

706 

31 

32 

5,528 

56 

84,831 

84,000 

298,366 

3,134 

292,840 

3,209 

1  88,465 

717 

32 

33 

5,472 

55 

84,089 

83,277 

295,232 

3,171 

289,631 

3,233!  87,748 

727 

33 

34 

5,417 

55 

83,339 

82,551 

292,061 

3,211 

286,398 

3,255  1  87,021 

740 

34 

35 

5,362 

55 

82,581 

81,822 

288,850 

3,254 

283,143 

3,279  86,281 

757 

35 

36 

5,307 

56 

81,814 

81,090 

285,596 

3,300 

279,864 

3,301  85,524 

779 

36 

37 

5,251 

57 

81,038 

80,353 

282,296 

3,352 

276,563 

3,326j  84,745 

802 

37 

38 

5,194 

58 

80,253 

79,611 

278,944 

3,406 

273,237 

3,350!i  83,943 

821 

38 

39 

5,136 

61 

79,458 

78,862 

275,538 

3,465 

269,887 

3,376 

83,122 

838 

39 

40 

5,075 

66 

78,653 

78,106 

272,073 

3,529 

266,511 

3,402 

82,284 

848 

40 

41 

5,009 

69 

77,838 

77,341 

268,544 

3,596 

263,109 

3,431 

81,436 

854 

41 

42 

4,940 

71 

77,012 

76,567 

264,948 

3,668 

259,678 

3,459 

80,582 

865 

42 

43 

4,869 

71 

76,173 

75,782 

261,280 

3,746 

256,219 

3,490 

79,717 

887 

43 

44 

4,798 

71 

75,316 

74,985 

257,534 

3,826 

252,729 

3,522 

78,830 

911 

44 

45 

4,727 

70 

74,435 

74,173 

253,708 

3,912 

249,207 

3,555 

77,919 

950 

45 

46 

4,657 

69 

73,526 

73,345 

249,796 

4,001 

245,652 

3,591 

76,969 

996 

46 

47 

4,588 

67 

72,582 

72,497 

245,795 

4,095 

242,061 

3,627 

75,973 

1,041 

47 

48 

4,521 

63 

71,601 

71,627 

241,700 

4,192 

238,434 

3,665 

74,932 

1,082 

48 

49 

4,458 

61 

70,580 

70,731 

237,508 

4,292 

234,769 

3,705 

73,850 

1,124 

49 

TABLE     LXXIX. 

COMPARISON  OF  DIFFERENT  LIFE  TABLES. 


*229 


AGE. 
X. 

Caxlisle. 

17  Offices. 

Am.  1858. 

Ix. 

English  Life  Table,  No.  3. 

20  Offices.  HM. 

AaE. 

X. 

Ix'            (*X' 

Males,  ly.. 

dx. 

Fem.  Ix' 

dx. 

Ix. 

dx. 

50 

4,397 

59 

69,517 

69,804 

233,216 

4,395 

231,064 

3,746 

72,726 

1,160 

50 

51 

4,338 

62 

68,409 

68,842 

228,821 

4,626 

227,318 

3,788 

71,566 

1,193 

51 

52 

4,276 

65 

67,253 

67,841 

224,195 

4,758 

223,530 

3,832 

70,373 

1,235 

52 

53 

4,211 

68 

66,046 

66,797 

219,437 

4,885 

219,698 

3,876 

69,138 

1,286 

53 

54 

4,143 

70 

64,785 

65,706 

214,552 

5,013 

215,822 

4,246 

67,852 

1,339 

54 

55 

4,073 

73 

63,469 

64,563 

209,539 

5,144 

211,576 

4,439 

66,513 

1,399 

55 

56 

4,000 

76 

62,094 

63,364 

204,395 

5,281 

207,137 

4,628 

65,114 

1,462 

56 

57 

3,924 

82 

60,658 

62,104 

199,114 

5,428 

202,509 

4,817 

63,652 

1,527 

57 

58 

3,842 

93 

59,161 

60,779 

193,686 

5,584 

197,692 

5,009 

62,125 

1.592 

58 

59 

3,749 

106 

57,600 

59,385 

188,102 

5,752 

192,683 

5,206 

60,533 

1,667 

59 

60 

3,643 

122 

55,973 

57,917 

182,350 

5,929 

187,477 

5,409 

58,866 

1,747 

60 

61 

3,521 

126 

54,275 

56,371 

176,421 

6,118 

182,068 

5,619 

57,119 

1,830 

61 

62 

3,395 

127 

52,505 

54,743 

170,303 

6,314 

176,449 

5,835 

55,289 

1,915 

62 

63 

3,268 

125 

50,661 

53,030 

163,989 

6,515 

170,614 

6,057 

53,374 

2,001 

63 

64 

3,143 

125 

48,744 

51,230 

157,474 

6,720 

164,557 

6,282 

51,373 

2,076 

64 

65 

3,018 

124 

46,754 

49,341 

150,754 

6,921 

158,275 

6,509 

49,297 

2,141 

65 

66 

2,894 

123 

44,693 

47,361 

143,833 

7,115 

151,766 

6,731 

47,156 

2,196 

66 

67 

2,771 

123 

42,565 

45,291 

136,718 

7,297 

145,035 

6,947 

44,960 

2,243 

67 

68 

2,648 

123 

40,374 

43,133 

129,421 

7,458 

138,088 

7,149 

42,717 

2,274 

68 

69 

2,525 

124 

38,128 

40,890 

121,963 

7,593 

130,939 

7,332 

40,443 

2,319 

69 

70 

2,401 

124 

35,837 

38,569 

114,370 

7,695 

123,607 

7,489 

38,124 

2,371 

70 

71 

2,277 

134 

33,510 

36,178 

106,675 

7,756 

116,118 

7,613 

35,753 

2,433 

71 

72 

2,143 

146 

31,159 

33,730 

98,919 

7,770 

108,505 

7,698 

33,320 

2,497 

72 

73 

1,997 

156 

28,797 

31,243 

91,149 

7,733 

100,807 

7,736 

30,823 

2,554 

73 

74 

1,841 

166 

26,439 

28,738 

83,416 

7,639 

93,071 

7,724 

28,269 

2,578 

74 

75 

1,675 

160 

24,100 

26,237 

75,777 

7,483 

85,347 

7,653 

25,691 

2,527 

75 

76 

1,515 

156 

21,797 

23,761 

68,294 

7,268 

77,694 

7,521 

23,164 

2,464 

76 

77 

1,359 

146 

19,548 

21,330 

61,026 

6,990 

70,173 

7,329 

20,700 

2,374 

77 

78 

1,213 

132 

17,369 

18,961 

54,036 

6,655 

62,844 

7,071 

18,326 

2,258 

78 

79 

1,081 

128 

15,277 

16,670 

47,381 

6,266 

55,773 

6,755 

16,068 

2,138 

79 

80 

953 

116 

13,290 

14,474 

41,115 

5,832 

49,018 

6,382 

13,930 

2,015 

80 

81 

837 

112 

11,424 

12,383 

35,283 

5,361 

42,636 

5,959 

11,915 

1,883 

81 

82 

725 

102 

9,694 

10,419 

29,922 

4,862 

36,677 

5,496 

10,032 

1,719 

82 

83 

623 

94 

8,112 

8,603 

25,060 

4,349 

31,181 

5,003 

8,313 

1,545 

83 

84 

529 

84 

6,685 

6,955 

20,711 

3,834 

26,178 

4,490 

6,768 

1,346 

84 

85 

445 

78 

5,417 

5,485 

16,877 

3,328 

21,688 

3,972 

5,422 

1,138 

85 

86 

367 

71 

4,306 

4,193 

13,549 

2,840 

17,716 

3,458 

4,284 

941 

86 

87 

296 

64 

3,348 

3,079 

10,709 

2,384 

14,258 

2,962 

3,343 

773 

87 

88 

232 

51 

2,537 

2,146 

8,325 

1,965 

11,296 

2,494 

2,570 

615 

88 

89 

181 

39 

1,864 

1,402 

6,360 

1,590 

8,802 

2,063 

1,955 

495 

89 

90 

142 

37 

1,319 

847 

4,770 

1,260 

6,739 

1,673 

1,460 

408 

90 

91 

105 

30 

892 

462 

3,510 

979 

5,066 

1,331 

1,052 

329 

91 

92 

75 

21 

570 

216 

2,531 

744 

3,735 

1,037 

723 

254 

92 

93 

54 

14 

339 

79 

1,787 

553 

2,698 

790 

469 

195 

93 

94 

40 

10 

184 

21 

1,234 

401 

1,908 

588 

274 

139 

94 

95 

30 

7 

89 

3 

833 

285 

1,320 

428 

135 

86 

95 

96 

23 

5 

37 

548 

196. 

892 

304 

49 

40 

96 

97 

18 

4 

13 

352 

132 

588 

210 

9 

9 

97 

98 

14 

3 

4 

220 

86 

378 

142 

96 

99 

11 

2 

1 

134 

55 

236 

92 

99 

100 

9 

2 

79 

33 

144 

69 

100 

1 

Beyond  100  Tears  :  Carlisle,  1-,  7,  5,  3, 1. 


English,  No.  3,  Males  l^,  46,  35,  14,  7,  4,  3,  1. 

"    _  Females  l^,  86,  49.  27,  15,  8,  4,  2, 1, 


♦230 


TABLE    LXXX. 

EXPECTATION   OF  LIFE   BY  VARIOUS  TABLES— YEARS  AND  DECIMALS. 


AGE. 

North- 

Carlisle. 

17 

Am. 

i 
English  Life,  No.  3.  j 

20  Offices.   HM. 

30  Am.  Offices. 

AGE. 

X. 

ampton. 

Offices. 

1858. 

Males. 

Females. 

Hales. 

Females, 

Males. 

Females. 

X. 

0 

25.18 

38.72 

39.91 

41.85 

0 

1 

32.74 

44.68 

46.65 

47.31 

1 

2 

37.79 

47.55 

48.83 

49.40 

2 

3 

39.55 

49.82 

49.61 

50.20 

3 

4 

40.58 

50.76 

49.81 

50.43 

4 

5 

40.84 

51.25 

49.71 

50.33 

5 

6 

41.07 

51.17 

49.39 

50.00 

6 

7 

41.03 

50.80 

48.92 

49.53 

7 

8 

40.79 

50.24 

48.37 

48.98 

8 

9 

40.36 

49.57 

47.74 

48.35 

9 

10 

39.78 

48.82 

48.36 

48.72 

47.05 

47.67 

I  50.29 

48.20 

49.99 

48.05 

10 

11 

39.14 

48.04 

47.68 

48.08 

46.31 

46.95 

49.54 

47.35 

49.32 

47.21 

11 

12 

38.49 

47.27 

47.01 

47.45 

45.54 

46.20 

48.73 

46.54 

48.64 

46.40 

12 

13 

37.83 

46.51 

46.33 

46.80 

44.76 

45.44 

47:89 

45.78 

47.95 

45.64 

13 

14 

37.17 

45.75 

45.64 

46.16 

43.97 

44.66 

47.03 

45.05 

47.26 

44.91 

14 

15 

36.51 

45.00 

44.96 

45.50 

43.18 

43.90 

46.16 

44.34 

46*.  57 

44.19 

15 

16 

35.85 

44.27 

44.27 

44.85 

42.40 

43.14 

45.29 

43.64 

45.88 

43.48 

16 

17 

35.20 

43.57 

43.58 

44.19 

41.64 

42.40 

44.44 

42.95 

45.18 

42.79 

17 

18 

34.58 

42.87 

42.88 

43.53 

40.90 

41.67 

43.61 

42.25 

44.48 

42.12 

18 

19 

33.99 

42.17 

42.19 

42.87 

40.17 

40.97 

42.82 

41.54 

43.78 

41. 4e 

19 

20 

33.43 

41.46 

41.49 

42.20 

39.48 

40.29 

42.06 

40.82 

43.07 

40.82 

20 

21 

32.90 

40.75 

40.79 

41.53 

38.80 

39.63 

41.33    40.09 

42.36 

40.19 

21 

22 

32.39 

40.04 

40.09 

40.85 

38.13 

38.98 

40.60  [  39.39 

41.65 

39.56 

22 

23 

31.88 

39.31 

39.39 

40.17 

37.46 

38.33 

39.88    38.70 

40.93 

38.96 

23 

24 

31.86 

38.59 

38.68 

39.49 

36.79 

37.68 

39.15    38.04 

40.21 

38.38 

24 

25 

30.85 

37.86 

37.98 

38.81 

36.12 

37.04 

38.41    37.41 

39.49 

37.80 

25 

26 

30.33 

37.14 

37.27 

38.12 

35.44 

36.39 

37.66    36.81 

38.77 

37.23 

26 

27 

29.82 

36.41 

36.56  37.43 

i   34.77 

35.75 

36.91    36.23 

38.04 

36.66 

27 

28 

29.30 

35.69 

35.86  36.73 

:   34.10 

35.10 

36.16    35.66 

37.31 

36.08 

28 

29 

28.79 

35.00 

35.15 

36.03 

33.43 

34.46 

35.42 

35.09 

36.58 

35.49 

29 

30 

28.27 

34.34 

34.43 

35.33 

32.76 

33.81 

34.68 

34.50 

35.85 

34.89 

30 

31 

27.76 

33.68 

33.72  34.63 

32.09 

33.17 

33.95 

33.91 

35.12 

34.29 

31 

32 

27.24 

33.03 

33.01 

33.92 

31.42 

32.53 

33.21 

33.31 

1  34.38 

33.69 

32 

33 

26.72 

32.36 

32.30 

33.21 

30.74 

31.88 

32.48 

32.69 

33.65 

33.06 

33 

34 

26.20 

31.68 

31.58 

32.50 

30.07 

31.23 

31.75 

32.07 

32.91 

32.42 

34 

35 

25.68 

31.00 

30.87 

31.78 

29.40 

30.59 

31.02 

31.45 

32.17 

31.78 

35 

36 

25.16 

30.32 

30.15 

31.07 

28.73 

29.94 

30.29 

30.81 

31.43 

ai.i3 

36 

37 

24.64 

29.64 

29.44 

30.35 

28.06 

29.29 

1  29.56 

30.18 

30.70 

30.47 

37 

38 

24.12 

28.96 

28.72 

29.62 

27.39 

28.64 

•  28.84 

29.54 

29.96 

29.81 

38 

39 

23.60 

28.28 

28.00 

28.90 

26.72 

27.99 

\  28.12 

28.90 

29.22 

29.16 

39 

40 

23.08 

27.61 

27.28 

28.18 

26.06 

27.34 

1  27.40 

28.25 

28.48 

28.48 

40 

41 

22.56 

26.97 

26.56  127.45 

25.^^ 

26.69 

'  26.68 

27.61     27.75 

27.82 

41 

42 

22.04 

26.34 

25.84  26.72 

24.73 

26.03 

i  25.96 

26.96 

27.01 

27.15 

42 

43 

21.54 

25.71 

25.12  26.00 

24.07 

25.38 

i 25.23 

26.30 

26.28 

26.45 

43 

44 

21.03 

25.09 

24.40  1 25.27 

23.41 

24.72 

\  24.51 

25.65 

25.55 

25.74 

44 

45 

20.52 

24.46 

23.69 

24.54 

22.76 

24.06 

123.79 

24.99 

24.82 

25.02 

45 

46 

20.02 

23.82 

22.97 

23.81 

22.11 

23.40 

23.08 

24.33 

24.09 

24.30 

46 

47 

19.51 

23.17 

22.27 

23.08 

21.46 

22.74 

22.38 

23.66 

23.38 

23.57 

47 

48 

19.00 

22.50 

21.56 

i  22.36 

i   20.82 

22.08 

21.68 

22.98 

22.66 

22.83 

48 

49 

18.49 

21.81 

20.87 

|21.63 

20.17 

21.42 

20.99 

22.30 

21.95 

22.08 

49 

TABLE    LXXX.  ♦231 

EXPECTATION   OF  LIFE  BY  VARIOUS  TABLES— YEARS  AND  DECIMALS. 


1 

AGE. 

North- 

17 

Am. 

English  Life,  No.  3. 

20  Offices.   HM. 

30  Am.  Offices. 

AGE. 

Carlisle. 

X. 

ampton. 

Offices. 

1858. 

Males. 

Females. 

Males. 

Females. 

Males. 

Females 

X. 

50 

17.99 

21.11 

20.18 

20.91 

19.54 

20.75 

20.31 

21.62 

21.24 

21.33 

50 

51 

17.50 

20.39 

19.50 

20.20 

18.90 

20.09 

19.63 

20.93 

20.54 

20.59 

51 

52 

17.02 

19.68 

18.82 

19.49 

18.28 

19.42 

18.95 

20.24 

19.84 

19.87 

52 

53 

16.54 

18.97 

18.16 

18.79 

17.67 

18.75 

18.28 

19.55 

19.15 

19.15 

53 

54 

16.06 

18.28 

17.50 

18.09 

17.06 

18.08 

17.62 

18.87 

18.47 

18.44 

54 

55 

15.58 

17.58 

16.86 

17.40 

16.45 

17.43 

16.96 

18.19 

17.80 

17.73 

55 

56 

15.10 

16.89 

16.22 

16.72 

15.86 

16.79 

16.32 

17.52 

17.13 

17.03 

56 

57 

1463 

16.21 

15.59 

16.05 

15.26 

16.17 

15.68 

16.85 

16.47 

16.35 

57 

58 

1415 

15.55 

1497 

15.39 

1468 

15.55 

15.05 

16.18 

15.83 

15.67 

58 

59 

13.68 

1492 

1437 

1474 

1410 

1494 

1444 

15.52 

15.19 

15.02 

59 

60 

13.21 

1434 

13.77 

1410 

13.53 

1434 

13.83 

1485 

1456 

1437 

60 

61 

12.75 

13.82 

13.18 

13.47 

12.96 

13.75 

13.24 

1420 

13.94 

13.73 

61 

62 

12.28 

13.31 

12.61 

12.86 

12.41 

13.17 

12.66 

13.56 

13.34 

13.10 

62 

63 

11.81 

12.81 

12.05 

12.26 

11.87 

12.60 

12.10 

12.95 

12.74 

12.49 

63 

64 

11.35 

12.30 

11.51 

11.67 

11.34 

12.05 

11.55 

12.35 

12.16 

11.90 

64 

65 

10.88 

11.79 

10.97 

11.10 

10.82 

11.51 

11.01 

11.77 

11.60 

11.31 

65 

66 

10.42 

11.27 

10.46 

10.54 

10.32 

10.98 

10.49 

11.21 

11.04 

10.74 

66 

67 

9.96 

10.75 

9.96 

10.00 

9.83 

10.47 

9.98 

10.66 

10.50 

10.19 

67 

68 

9.50 

10.23 

9.47 

9.47 

9.36 

9.97 

9.48 

10.12 

9.97 

9.65 

68 

69 

9.05 

9.70 

9.00 

8.97 

8.90 

9.48 

8.98 

9.59 

9.46 

9.13 

69 

70 

8.60 

9.18 

8.54 

8.48 

8.45 

9.02 

8.50 

9.08 

8.97 

8.62 

70 

71 

8.17 

8.65 

8.10 

8.00 

8.03 

8.57 

8.03 

8.59 

8.49 

8.13 

71 

72 

7.74 

8.16 

7.67 

7.55 

7.62 

8.13 

7.58 

8.12 

8.02 

7.65 

72 

73 

7.33 

7.72 

7.26 

7.11 

7.22 

7.71 

7.15 

7.69 

7.57 

7.20 

73 

74 

6.92 

7.33 

6.86 

6.68 

6.85 

7.31 

6.75 

7.29 

7.14 

6.76 

74 

75 

6.54 

7.01 

6.48 

6.27 

6.49 

6.93 

6.38 

6.93 

6.72 

6.34 

75 

76 

6.18 

6.69 

6.11 

5.88 

6.15 

6.56 

6.02 

6.60 

6.32 

5.93 

76 

77 

5.83 

6.40 

5.76 

'5.49 

5.82 

6.21 

5.67 

6.31 

5.93 

5.55 

77 

78 

5.48 

6.12 

5.42 

5.11 

5.51 

5.88 

5.34 

6.02 

5.57 

5.18 

78 

79 

5.11 

5.80 

5  09 

474 

5.21 

5.56 

5.03 

5.74 

5.21 

482 

79 

80 

475 

5.51 

478 

439 

493 

5.26 

472 

5.45 

487 

449 

80 

81 

441 

5.21 

448 

405 

466 

498 

443 

5.14 

455 

417 

81 

82 

409 

493 

418 

3.71 

441 

471 

417 

479 

424 

3.88 

82 

83 

3.80 

465 

3.90 

3.39 

4,17 

445 

3.93 

444 

3.95 

3.59 

83 

84 

3.58 

439 

3.63 

3.08 

3.95 

421 

3.71 

411 

3.67 

3.33 

84 

85 

3.37 

4.12 

3.36 

2.77 

3.73 

3.98 

3.51 

3.81 

3.40 

3.08 

85 

86 

3.19 

3.90 

3.10 

2.47 

3.53 

3.76 

3.31 

3.57 

3.14 

2.84 

86 

87 

3.01 

3.71 

2.84 

2.18 

3.34 

3.56 

3.10 

3.39 

2.89 

2.62 

87 

88 

2.86 

3.59 

2.59 

1.91 

3.16 

3.36 

2.88 

3.29 

2.64 

2.42 

88 

89 

2.66 

3.47 

2.35 

1.66 

3.00 

3,18 

2.63 

3.27 

2.39 

2.23 

89 

90 

2.41 

3.28 

2-11 

1.42 

2.84 

3.01 

2.36 

3.30 

2.17 

2.05 

90 

91 

2.09 

3.26 

1.89 

1.19 

•    2.69 

2.85 

2.08 

3.37 

1.98 

1.89 

91 

92 

1.75 

3.37 

1.67 

.98 

2.55 

2.70 

1.80 

3.42 

1.81 

1.73 

92 

93 

1.37 

3.48 

1.47 

.80 

2.41 

2.55 

1.50 

3.30 

1.64 

1.59 

93 

94 

1.05 

3.53 

1.28 

.64 

2.29 

2.42 

1.20 

2.91 

1.49 

1.46 

94 

95 

.75 

3.53 

1.12 

.50 

2.17 

2.29 

.93 

2.47 

1.34 

1.34 

95 

96 

.50 

3.46 

.99 

2.06 

2.17 

.68 

1.98 

1.18 

1.23 

96 

97 

3.28 

.89 

1.95 

2.06 

.50 

1.49 

1.03 

1.09 

97 

98 

3.07 

.75 

1.85 

1.96 

1.00 

.83 

.93 

98 

99 

2.77 

.50 

1.76 

1.86 

50 

.50 

V    .50 

99 

100 

2.28 

1.68 

1.76 

100 

*23a  TABLE    LXXXI; 

PERCENTAGE  OP  MORTALITY  BY  SEVERAL  LIFE  TABLES 


North- 

English Life,  No.  3. 

i 

17 

20  Offices. 

American, 

30  Offices, 

AGhE. 

Carlisle. 

Aa£. 

0 

ampton. 

Males. 

Females. 

Offices. 

HM 

1858. 

Am.Hales. 

25.7511 

15.3900 

18i326 

14.749 

0 

1 

15.8035 

8.0605 

6.680 

6.436 

1 

2 

6.8928 

^6.4918 

3.624 

3.603 

2 

3 

4.9403 

3.7943 

2.416 

2.450 

3 

4 

3.0562 

2.8723 

1.799 

1.785 

4 

5 

2.9445 

1.7810 

1.369 

1.337 

5 

6 

2.3084 

1.2283 

1.088 

1.061 

6 

7 

1.8565 

0.8796 

0.920 

0.912 

7 

8 

1.3757 

.6579 

.767 

.771 

8 

9 

1.0462 

.5082 

.649 

.664 

9 

10 

0.9163 

.4489 

.563 

.587 

0.6760 

0.4900 

0.7490 

0.6479 

10 

11 

.8892 

.  .4820 

.507 

.537 

.6786 

.3990 

.7516 

.6502 

11 

12 

.8973 

.5000 

.478 

.512 

.6812 

.3319 

.7542 

.6516 

12 

13 

.9053 

.5182 

.472 

.509 

1  .6848 

.2915 

.7569 

.6536 

13 

14 

.9136 

.5525 

.486 

.524 

.6896 

.2762 

.7596 

.6568 

14 

15 

.9220 

.6191 

.519 

.556 

.6944 

.2871 

.7633 

.6593 

15 

16 

.9864 

.6708 

.564 

.601 

.7003 

.3247 

..7660 

.6614 

16 

17 

1.0902 

.6914 

.622 

.658 

.7062 

.3882 

.7688 

.6648 

17 

18 

1.1972 

.6962 

.688 

.721 

.7134 

.4792 

.7726 

.6683 

18 

19 

1.2887 

.7011 

.759 

.789 

.7206 

.5745 

.7765 

.6717 

19 

20 

1.4030 

.7061 

.832 

.860 

.7291 

.6329 

.7804 

.6763 

20 

21 

1.4822 

.6946 

.850 

.882 

.7377 

.6725 

.7855 

.6808 

21 

22 

1.5045 

.6994 

.868 

.904 

.7464 

.6844 

.7906 

.6856 

22 

23 

1.5275 

.7043 

.886 

.925 

.7564 

.6764 

.7958 

.6911 

23 

24 

1.5512 

.7093 

.903 

.946 

.7666 

.6639 

.8011 

.6973 

24 

25 

1.5756 

.7314 

.920 

.966 

.7770 

.6630 

.8064 

.7032 

25 

26 

1.6009 

.7368 

.938 

.985 

.7887 

.6685 

.8130 

.7115 

26 

27 

1.6269 

.7768  : 

.955 

1.005 

.8006 

.6904 

.8196 

.7190 

27 

28 

1.6538 

.8699 

.974 

1.024 

.8139 

.7172 

.8264 

.7275 

.28 

29 

1.6816 

.9828 

.993 

1.043 

.8275 

.7473 

.8344 

.7385 

29 

30 

1.7104 

1.0103 

1.013 

1.063 

.8425 

.7723 

.8426 

.7485 

30 

31 

1.7401 

1.0206 

1.034 

1.082 

.8578 

.7917 

.8510 

.7602 

31 

32 

1.7710 

1.0130 

1.056 

1.102 

.8747 

.8105 

.8607 

.7727 

32 

33 

1.8029 

1.0051 

1.080 

1.123 

.8919 

.8285 

.8717 

.7871 

33 

34 

1.8360 

1.0151 

1.105 

1.143 

.9095 

.8504 

.8830 

.8027 

34 

35 

1.8704 

1.0257  , 

1.133 

1.165 

.9288 

.8774 

.8946 

.8212 

35 

36 

1.9060 

1.0552 

1.162 

1.186 

.9485 

.9109 

.9088 

.8390 

36 

37 

1.9430 

1.0855 

1.194 

1.210 

.9687 

.9464 

.9234 

.8591 

37 

38 

1.9815 

1.1167 

1.229 

1.234 

.9906 

.9780 

.9408 

.8826 

38 

39 

2.0216 

1.1877  1 

1.265 

1.259 

1.0131 

1.0082 

.9586 

.9077 

39 

40 

2.0908 

1.3005  ' 

1.306 

1.285 

1.0362 

1.0306 

.9794 

.9360 

40 

41 

2.1635 

1.3775 

1.348 

1.313 

1.0612 

1.0487 

1.0008 

.9647 

41 

42 

2.2401 

1.4373 

1.394 

1.341 

1.0894 

1.0734 

1.0252 

.9998 

42 

43 

2.2914 

1.4582 

1.444 

1.371 

1.1251 

1.1127 

1.0517 

1.0351 

43 

44 

2.3452 

1.4798  i 

1.497 

1.403  j 

1.1697 

1.1556 

1.0829 

1.0761 

44 

45 

2.4015 

1.4809  ' 

1.554 

1.437 

1.2212 

1.2192 

1.1163 

1.1203 

45 

46 

2.4606 

1.4816 

1.615 

1.473 

1.2839 

1.2940 

1.1562 

1.1688 

46 

47 

2.5227 

1.4603 

1.680 

1.510 

1.3516 

1.3702 

1.2000 

1.2227 

47 

48 

2.5879 

1.3935 

1.749 

1.549 

1.4260 

1.4440 

1.2509 

1.2814 

48 

49 

2.6908 

1.3683 

1.823 

1.591  j 

1.5061 

1.5220 

1.3106 

1.3459 

49 

Formula, 


100<?, 


-^— ^ ;  except  English  Life  No.  3,  from  Dr.  Farr. 

Ix 


TABLE    LXXXI. 

PERCENTAGE  OF  MORTALITY  BY  SEVERAL  LIFE  TABLES. 


*233 


i 

AQG. 

North- 

Carlisle. 

EngUsh  Life,  No.  3. 

17 

20  Offices. 

American, 

30  Officer, 

1           1  A  riTi 

!  AuE. 

ampton. 

Males. 

Females. 

Offices. 

HM. 

1858. 

AmiMales. 

50 

50 

2.8351 

1.3418 

1.902 

1.634 

1.5938 

1.5950 

1.3781 

1.4175 

61 

2.9539 

1.4292 

2.042 

1.680 

1.6898 

1.6670 

1.4541 

1.4955 

51 

52 

3.0438 

1.5201 

2.145 

1.739 

1.7947 

1.7549 

1.5389 

1.5814 

52 

53 

3.1394 

1.6148 

2.251 

1.780 

1.9093 

1.8600 

1.6333 

1.6752 

53 

54 

3.2411 

1.6896 

2.364 

1.987 

3.0313 

1.9734 

1.7396 

1.7779 

54 

55 

3.3497 

1.7923 

2.485 

2.120 

3.1664 

3.1033 

1.8571 

1.8930 

55 

56 

3.4658 

1.9000 

2.617 

2.259 

3.3136 

3.3453 

1.9885 

2.0172 

56 

57 

3.5902 

2.0897 

2.763 

2.407 

3.4679 

2.3990 

2.1335 

2.1560 

57 

58 

3.7239 

2.4206 

2.925 

2.566 

3.6386 

2.5626 

2.2936 

2.3060 

58 

59 

3.8679 

2.8274 

3.105 

2.738 

2.8246 

2.7539 

2.4730 

2.4707 

59 

60 

4.0235 

3.3489 

3.305 

2.927 

3.0336 

2.9678 

2.6693 

3.6527 

60 

61 

4.1922 

3.5785 

3.529 

3.134 

3.2612 

3.2038 

2.8880 

2.8529 

61 

62 

4.3223 

3.7408 

3.777 

3.362 

3.5131 

3.4636 

3.1292 

3.0700 

62 

63 

4.5176 

3.8250 

4.053 

3.614 

3.7840 

3.7490 

3.3943 

3.3108 

63 

64 

4.6729 

3.9771 

4.360 

3.891 

4.0836 

4.0410 

3.6873 

3.5740 

64 

65 

4.9020 

4.1087 

4.698 

4.198 

4.4083 

4.3431 

4.0129 

3.8640 

65 

66 

5.J546 

4.2502 

5.071 

4.535 

4.7614 

4.6569 

4.3707 

4.1789 

66 

67 

5.4348 

4.4388 

5.483 

4.906 

5.1474 

4.9889 

4.7647 

4.5282 

67 

68 

5.7471 

4.6450 

5.933 

5.314 

5.5630 

5.3334 

5.2002 

4.9043 

68 

69 

6.0975 

4.9109 

6.435 

5.760 

6.0087 

5.7340 

5.6762 

5.3242 

69 

70 

6.4935 

5.1645 

6.962 

6.247 

6.4933 

6.2192 

6.1993 

5.7778 

70 

71 

6.9444 

5.8849  ' 

7.545 

6.778 

7.0158 

6.8050 

6.7665 

6.2775 

71 

72 

7.4627 

6.8129 

8.176 

7.355 

7.5805 

7.4940 

7.3733 

6.8216 

72 

73 

8.0645 

7.8117 

8.861 

7.980 

8.1884 

8.2860 

8.0178 

7.4149 

73 

74 

8.7719 

9.0168 

9.599 

8.659 

8.8468 

9.1195 

8.7028 

8.0709 

74 

75 

9.6154 

9.5522 

10.391 

9.389 

9.5560 

9.8361 

9.4371 

8.7792 

75 

76 

10.2393 

10.2970 

11.346 

10.175 

10.3180 

10.6372 

10.2311 

9.5503 

76 

77 

10.8148 

10.7432 

13.158 

11.024 

11.1469 

11.4686 

11.1064 

10.3996 

77 

78 

11.2957 

10.8831  i 

13.136 

11.930 

12.0444 

12.3213 

12.0827 

11.3181 

78 

79 

12.1723 

11.8409 

14.178 

12.903 

13.0065 

13.3059 

13.1734 

13.3185  79 

80 

13.4328 

12.1721 

15.290 

13.942 

14.0406 

14.4653 

14.4466 

13.4068 

80 

81 

14.7783 

13.3811 

16.474 

15.048 

15.1436 

15.8036 

15.8605 

14.5833 

81 

82 

16.4740 

14.0690 

17.726 

16.227  , 

16.3194 

17.1353 

17.4397 

15.8704 

82 

83 

19.0311 

15.0883 

19.057 

17.483 

17.5913 

18.5853 

19.1561 

17.3458 

83 

84 

20.5128 

15.8790 

20.471 

18.812 

18.9678 

19.8877 

31.1359 

18.7523 

84 

85 

22.0430' 

17.5281 

31.966 

20.227 

20.5095 

30.9885 

33.5553 

20.3633 

85 

86 

23.4483 

19.3461 

23.539 

31.716 

22.2480 

21.9655 

36.5681 

22.0841 

86 

87 

25.2252 

21.6216 

25.196 

33.393 

24.2234 

23.1230 

30.3030 

23.9885 

87 

88 

25.3012 

21.9828 

26.947 

34.960 

26.5274 

23.9300 

34.6693 

25.9550 

88 

89 

25.8065 

21.5470 

28.799 

26.726 

29.3383 

25.3196 

39.5863 

29.3600 

89 

90 

26.0869 

26.0563 

30.717 

28.564 

32.3730 

^27.9452 

45.4546 

33.8154 

90 

91 

29.4118 

28.5714 

32.764 

30.521 

36.0987 

31.2737 

53.3468 

35.8544 

91 

92 

33.3333 

28.0000 

34.897 

32.579 

40.5263 

35.1314 

63.4259 

38.9736 

92 

93 

43.7500 

25.9259 

37.139 

34.735 

45.7237 

41.5778 

73.4177;  42.5000 

93 

94 

55.5556 

25.0000 

39.430 

36.935 

51.6304 

50.7300 

85.7143  46.2451 

94 

95 

75.0000 

23.3333 

42.035 

39.338 

58.4370 

63.7036 

100.000 

50.00001 

95 

96 

100.0000 

21.7391 

44.444 

41.873 

64.8649 

81.6327 

55.8834!  96 

97 

22.2222 

47.313 

44.397 

69.3308 

100.0000 

60.0000  97 

98 

21.4286 

50.000 

47.333 

75.0000 

66.6666  98 

99 

18.1818 

53.398 

49.730 

100.0000 

lOO.OOOOi  99 

100 

1 

22.2222 

55.000 

53.153 

100 

*334 


TABLE     LXXXII. 

ANTI-LOGARITHMS,  OR  NUMBERS  TO  LOGARITHMS. 


Log. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.P. 

.000 

10000  !  10002 

10005 

10007 

10009 

10012 

10014 

10016 

10018 

10021 

.001 

10023  1 10025 

10028 

10030 

10032 

10035 

10037 

10039 

10042 

10044 

1 

0 

.002 

10046 

10048 

10051 

10053 

10055 

10058 

10060 

10062 

10065 

10067 

2 

0 

1  .003 

10069 

10072 

10074 

10076 

10079 

10081 

10083 

10086 

10088 

10090 

3 

1 

1  .004 

10093 

10095 

10097 

10100 

10102 

10104 

10106 

10109 

10111 

10113 

4 

1 

.005 

10116 

10118 

10120 

10128 

10125 

10127 

10130 

10132 

10134 

10137 

5 

1 

.006 

10139 

10141 

10144 

10146 

10148 

10151 

10153 

10155 

10158 

10160 

6 

1 

.007 

10162 

10165 

10167 

10170 

10172 

10174 

10177 

10179 

10181 

10184 

7 

2 

.008 

10186 

10188 

10191 

10193 

10195 

10198 

10200 

10202 

10205 

10207 

8 

2 

.009 

10209 

10212 

10214 

10216 

10219 

10221 

10224 

10226 

10228 

10231 

9 

2 

.010 

10233 

10235 

10238 

10240 

10242 

10245 

10247 

10249 

10252 

10254 

.011 

10257 

10259 

10261 

10264 

10266 

10268 

10271 

10273 

10275 

10278 

1 

0 

.012 

10280 

10283 

10285 

10287 

10290 

10292 

10294 

10297 

10299 

10301 

2 

0 

.013 

10304 

10306 

10309 

10311 

10313 

10316 

10318 

10320 

10323 

10325 

3 

1 

.014 

10328 

10330 

10332 

10335 

10837 

10340 

10342 

10344 

10347 

10349 

4 

1 

.015 

10351 

10354 

10356 

10359 

10361 

10363 

10366 

10368 

10371 

10373 

5 

1 

.016 

10375 

10378 

10380 

10382 

10385 

10387 

10390 

10392 

10394 

10397 

6 

1 

.017 

10399 

10402 

10404 

10406 

10409 

10411 

10414 

10416 

10418 

10421 

7 

2 

.018 

10423 

10426 

10428 

10430 

10433 

10435 

10438 

10440 

10442 

10445 

8 

2 

.019 

10447 

10450 

10452 

10454 

10457 

10459 

10462 

10464 

10466 

10469 

9 

2 

.020 

10471 

10474 

10476 

10479 

10481 

10483 

10486 

10488 

10491 

10493 

.021 

10495 

10498 

10500 

10503 

10505 

10508 

10510 

10512 

10515 

1051.7 

1 

0 

.022 

10520 

10522 

10524 

10527 

10529 

10532 

10534 

10537 

10539 

10541 

2 

0 

.023 

10544 

10546 

10549 

10551 

10554 

10556 

10558 

10561 

10563 

10566 

3 

1 

.024 

10568 

10571 

10573 

10575 

10578 

10580 

10583 

10585 

10588 

10590 

4 

1 

.025 

10593 

10595 

10597 

10600 

10602 

10605 

10607 

10610 

10612 

10615 

5 

1 

.026 

10617 

10619 

10622 

10624 

10627 

10629 

10632 

10634 

10637 

10639 

6 

1 

.027 

10641 

10644 

10646 

10649 

10651 

10654 

10656 

10659 

10661 

10664 

7 

2 

.028 

10666 

10668 

10671 

10673 

10676 

10678 

10681 

10683 

10686 

10688 

8 

2 

.029 

10691 

10693 

10695 

10698 

10700 

10703 

10705 

10708 

10710 

10713 

9 

2 

.030 

10715 

10718 

10720 

10723  10725 

10728 

10730 

10732 

10735 

10737 

.031 

10740 

10742 

10745 

10747  10750 

10752 

10755 

10757 

10760 

10762 

1 

0 

.032 

10765 

10767 

10770 

10772  10775 

10777 

10780 

10782 

10784 

10787 

2 

1 

.033 

10789 

10792 

10794 

10797 

10799 

10802 

10804 

10807 

10809 

10812 

3 

1 

.034 

10814 

10817 

10819 

10822 

10824 

10827 

10829 

10832 

10834  10837 

4 

1 

.035 

10839 

10842 

10844 

10847 

10849 

10852 

10854 

10857 

10859 

10862 

5 

1 

.036 

10864 

10867 

10869 

10872 

10874 

10877 

10879 

10882 

10884 

10887 

6 

2 

037 

10889 

10892 

10894 

10897 

10899 

10902 

10904 

10907 

10909 

10912 

7 

2 

038 

10914 

10917 

10919 

10922 

10924 

10927 

10929 

10932 

10935 

10937 

8 

2 

039 

10940 

10942 

10945 

10947 

10950 

10952 

10955 

10957 

10960 

10962 

9 

2 

.040 

10965 

10967 

10970 

10972 

10975 

10977 

10980 

10982 

10985 

10988 

.041 

10990 

10993 

10995 

10998 

11000 

11003  11005  1 

11008 

11010 

11013 

1 

0 

.042 

11015 

11018 

11020 

11023 

11026 

11028 

11031 

11033 

11036 

11038 

2 

1 

.043 

11041 

11043 

11046 

11048 

11051 

11054 

11056 

11059 

11061 

11064 

3 

1 

.044 

11066 

11069 

11071 

11074 

11076 

11079 

11082 

11084 

11087 

11089 

4 

1 

.045 

11092 

11094 

11097 

11099 

11102 

11105 

11107 

11110 

11112 

11115 

5 

1 

.046 

11117 

11120 

11122 

11125 

11128 

11130  11133 

11135 

11138 

11140 

6 

2 

.047 

11143 

11146 

11148 

11151 

11153 

11156  !  11158 

11161 

11163  11166 

7 

2 

.048 

11169 

11171 

11174 

11176 

11179 

11181  i  11184 

11187 

11189 

11192 

8 

2 

.049 

11194 

11197 

11200 

11202 

11205 

11207  11210 

11212 

11215 

11218 

9 

2 

Log. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

TABLE    LXXXII. 

ANTI-LOGARITHMS,  OR  NUMBERS  TO  LOGARITHMS. 


*235 


Log. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.p. 

.050 

11220 

11223 

11225 

11228 

11231 

11233 

11236 

11238 

11241 

11243 

.051 

1124G 

11249 

11251 

11254  11256 

11259 

11262 

11264 

11267 

11269 

1  0 

.052 

11272 

11275 

11277 

11280  11282 

11285 

11288 

11290 

11293 

11295 

2  1 

.053 

11298 

11301 

11303 

11306 

11308 

11311 

11314 

11316 

11319 

11321 

3  1 

.054 

11324 

11327 

11329 

11332 

11334 

11337 

11340 

11342 

11345 

11347 

4  1 

.055 

11350 

11353 

11355 

11358 

11361 

11363 

11366 

11368 

11371 

11374 

5  1 

.056 

11376 

11379 

11382 

11384 

11387 

11389 

11392 

11395 

11397 

11400 

6  2 

.057 

11402 

11405 

11408 

11410 

11413 

11416 

11418 

11421 

11424 

11426 

7  2 

.058 

11429 

11431 

11434 

11437 

11439 

11442 

11445 

11447 

11450 

11452 

8  2 

.059 

11455 

11458 

11460 

11463 

11466 

11468 

11471 

11474 

11476 

11479 

9  2 

.060 

11482 

11484 

11487 

11489 

11492 

11495 

11497 

11500 

11503 

11505 

.061 

11508 

11511 

11513 

11516 

11519 

11521 

11524 

11527 

11529 

11532 

1  0 

.062 

11535 

11537 

11540 

11543 

11545 

11548 

11550 

11553 

11556 

11558 

2  1 

.063 

11561 

11564 

11566 

11569 

11572 

11574 

11577 

11580 

11582 

11585 

3  1 

.064 

11588 

11590 

11593 

11596 

11598 

11601 

11604 

11606 

11609 

11612 

4  1 

.065 

11614 

11617 

11620 

11623 

11625 

11628 

11631 

11633 

11636 

11639 

5  1 

.066 

11641 

11644 

11647 

11649 

11652 

11655 

11657 

11660 

11663 

11665 

6  2 

.067 

11668 

11671 

11673 

11676 

11679 

11682 

11684 

11687 

11690 

11692 

7  2 

.068 

11695 

11698 

11700 

11703 

11706 

11708 

11711 

11714 

.11717 

11719 

8  2 

.069 

11722 

11725 

11727 

11730 

11733 

11735 

11738 

11741 

11744 

11746 

9  2 

.070 

11749 

11752' 

11754 

11757 

11760 

11763 

11765 

11768 

11771 

11773 

.071 

11776 

11779 

11781 

11784 

11787 

11790 

11792 

11795 

11798 

11800 

1  0 

.072 

11805 

11806 

11809  11811 

11814 

11817 

11820 

11822 

11825 

11828 

V 

.073 

11830 

11833 

11836  11839 

11841 

11844 

11847 

11849 

11852 

11855 

3  1 

.074 

11858 

11860  11863  ; 11866 

11869 

11871 

11874 

11877 

11880 

11882 

4  1 

.075 

11885 

11888 

11890 

11893 

11896 

11899 

11901 

11904 

11907 

11910 

5  1 

.076 

11912 

11915 

11918 

11921 

11923 

11926 

11929 

11932 

11934 

11937 

6  2 

.077 

11940 

11943 

11945 

11948 

11951 

11954 

11956 

11959 

11962 

11965 

7  2 

.078 

11967 

11970 

11973 

11976 

11978 

11981 

11984 

11987 

11989 

11992 

8  2 

.079 

11995 

11998 

12001 

12003 

12006 

12009 

12012 

12014 

12017 

12020 

9  2 

.080 

12023 

12025 

12028 

12031 

12034 

12036 

12039 

12042 

12045 

12048 

.081 

12050 

12053  12056 

12059 

12061 

12064 

12067 

12070 

12073 

12075 

1  0 

.082 

12078 

12081 

12084 

12086 

12089 

12092 

12095 

12098 

12100 

12103 

2  1 

.083 

12106 

12109 

12112 

12114 

12117 

12120 

12123 

12126 

12128 

12131 

3  1 

.084 

12134 

12137 

12139 

12142 

12145 

12148 

12151 

12153 

12156 

12159 

4  1 

.085 

12162 

12165 

12167 

12170 

12173 

12176 

12179 

12181 

12184 

12187 

5  1 

.086 

12190 

12193 

12196 

12198 

12201 

12204 

12207 

12210 

12212 

12215 

6  2 

.087 

12218 

12221 

12224 

12226 

12229 

12232 

12235 

12238 

12241  i  12243 

7  2 

.088 

12246 

12249 

12252 

12255 

12257 

12260 

12263 

12266 

12269  '  12272 

8  2 

.089 

12274 

12277 

12280 

12283 

12286 

12289 

12291 

12294 

12297 

12300 

9  3 

.090 

12303 

12306 

12308 

12311 

12314 

12317 

12320 

12323 

12325 

12328 

.091 

12331 

12334 

12337 

12340 

12342 

12345 

12348 

12351 

12354 

12357 

1  0 

.092 

12359 

12362 

12365 

12368 

12371 

12374 

12377 

12379 

12382 

12385  i  2  1 

.093 

12388 

12391 

12394 

12397 

12399 

12402 

12405 

12408 

12411 

12414  1  3  1 

.094 

12417 

12419 

12422 

12425 

12428 

12431 

12434 

12437 

12439 

12442 

4  1 

.095 

12445 

12448 

12451 

12454 

12457 

12459 

12462 

12465 

12468 

12471 

5  1 

.096 

12474 

12477 

12480 

12482 

12485 

12488 

12491 

12494 

12497 

12500 

6  2 

.097 

12503 

12505 

12508 

12511 

12514 

12517 

12520 

12523 

12526 

12529 

7  2 

.098 

12531 

12534 

12537 

12540 

12543 

12546 

12549 

12552 

12555 

12557 

8  2 

.099 

12560 

12563 

12566 

12569 

12572 

12575 

12578 

12581 

12583 

12586 

9  3 

Loo. 

0 

1 

2 

3 

4 

6 

6 

7 

8 

9 

♦236 


TABLE     LXXXII. 

ANTI-LOGARITHMS,   OR  NUMBERS   TO  LOGARITHMS. 


Loo. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

\ 
P.P. 

.100 

12589 

12592 

12595 

12598 

12601 

12604 

12607 

12610 

12612  12615 

.101 

12618 

12621 

12624 

12627 

12630 

12633 

12636  1  12639 

12642  12644 

1 

0 

.102 

12647 

12650 

12653 

12656 

12659 

12662 

12665 

12668 

12671 ; 12674 

2 

1 

.103 

12677 

12679 

12682 

12685 

12688 

12691 

12694 

12697 

12700 

12703 

3 

1 

.104 

12706 

12709 

12712 

12715 

12717 

12720 

12723 

12726 

12729 

12732 

4 

1 

.105 

12735 

12738 

12741 

12744 

12747 

12750 

12753  12756 

12759 

12761 1  5 

1 

.106 

12764 

12767 

12770 

12773 

12776 

12779 

12782 

12785 

12788  1  12791  6 

2 

.107 

12794 

12797 

12800  i  12803 

12806 

12809 

12812 

12814 

12817112820  7 

2 

.108 

12823 

12826 

12829  i  12832 

12835 

12838 

12841 

12844 

12847 

12850 

8 

2 

'.109 

12853 

12856 

12859  12862 

12865 

12868 

12871 

12874 

12877 

12880 

9 

3 

.110 

12882 

12885 

12888  12891 

12894 

12897 

12900 

12903 

12906 

12909 

.111 

12912 

12915 

12918  12921 

12924 

12927  12930 

12933 

12936 

12939 

1 

0 

.112 

12942 

12945 

12948  12951 

12954 

12957 1 12960 

12963 

12966 

12969 

2 

1 

.113  112972 

12975 

12978  1 12981 

12984 

12987 ; 12990 

12993 

12996 

12999 

3 

1 

.114 

13002 

13005 

13008  i  13011 

13014 

13017 

13020 

13023 

13026 

13029 

4 

1 

.115 

13032 

13035 

13038  1 13041 

13044 

13047 

13050 

13053 

13056 

13059 

5 

2 

.116 

13062 

13065 

13068  '  13071 

13074 

13077 

13080  13083 

13086 

13089 

6 

2 

.117 

13092 

13095 

13098 

13101 

13104 

13107 1 13110  13113 

13116 

13119  7 

2 

.118 

13122 

13125 

13128 

13131 

13134 

13137 

13140  i  13143 

13146 

13149 

8 

2 

.119 

13152 

13155 

13158 

13161 

13164 

13167 

13170  13173 

13176 

13180 

9 

3 

.120 

13183 

13186 

13189 

13192 

13195 

13198 

13201  !  13204 

13207 

13210 

.121 

13213 

13216 

13219 

13222 

13225 

13228 

13231  1  13234 

13237 

13240 

1 

0 

.122 

13243 

13246 

13250 

13253 

13256 

13259 

13262  13265 

13268 

1.3271  2 

1 

.123 

13274 

13277 

13280 

13283 

13286 

13289 

13292  13295 

13298 

13301  3 

1 

.124 

13305 

13308 

13311 

13314 

13317 

13320 

13323  13326 

13329 

13332  4 

1 

.125 

13335 

13338 

13341 

13344 

13348 

13351 

13354  13357 

13360 

13363 

5 

2 

.126 

13366 

13369 

13372 

13375 

13378 

13381 

13384  13388 

13391  13394 

6 

2 

.127 

13397 

13400 

13403 

13406 

13409 

13412 

13415  13418 

13421  13425 

7 

2 

.128 

13428 

13431 

13434 

13437 

13440 

13443 

13446  i  13449 

13452  13456 

8 

2 

.129 

13459 

13462 

13465 

13468 

13471 

13474 

13477 

13480 

13483 1 13487 

9 

3 

.130 

13490 

13493 

13496 

13499 

13502 

13505 

13508 

13511 

13515  13518 

.131 

13521 

13524 

13527 

13530 

13533 

13536 

13539  i 13543 

13546 

13549 

1 

0 

.132 

13552 

13555  13558 

13561 

13564 

13568 

13571 

13574 

13577 

13580 

2 

1 

.133 

13583 

13586  13589 

13593 

13596 

13599 

13602 

13605 

13608 

13611 

3 

1 

.134 

13614  13618  j  13621 

13624 

13627 

13630 

13633 

13636 

13640 

13643 

4 

1 

.135 

13646 

13649 

13652 

13655 

13658 

13662 

13665 

13668 

13671 

13674 

5 

2 

.136 

13677  i  13680 

13684 

13687 

13690 

13693 

13696 

13699  13703 

13706 

6 

2 

.137 

13709 

13712 

13715 

13718 

13721 

13725 

13728 

13731  '  13734 

13737 

7 

2 

.138 

13740 

13744 

13747 

13750 

13753 

13756 

13759 

13763  13766 

13769 

8 

3 

.139 

13772 

13775 

13778 

13782 

13785 

13788 

13791 

13794 

13797 

13801 

9 

3 

.140 

13804 

13807 

13810 

13813 

13817 

13820 

13823 

13826 

13829 

13832 

.141 

13836 

13839 

13842 

13845 

13848 

13852 

13855  !  13858 

13861 

13864 

1 

0 

.142 

13868 

13871 

13874 

13877 

13880 

13884 

13887  1  13890 

13893 

13896 

2 

1 

.143 

13900 

13903 

13906 

13909 

13912 

13916 

13919 

13922 

13925 

13928 

3 

1 

.144 

13932 

13935 

13938 

13941 

13944 

13948 

13951 

13954 

13957 

13960 

4 

1 

.145 

13964 

13967 

13970 

13973 

13977 

13980 

13983 

13986 

13989 

13993 

5 

2 

.146 

13996 

13999 

14002 

14006 

14009 

14012 

14015 

14018 

14022 

14025 

6 

2 

.147 

14028 

14031 

14035 

14038 

14041 

14044 

14048 

14051 

14054 

14057 

7 

2 

.148 

14060 

14064 

14067 

14070 

14073 

14077 

14080- 

14083 

14086 

14090 

8 

3 

.149 

14093 

14096 

14099 

14103 

14106 

14109 

14112 

14116 

14119 

14122 

9 

3 

Loo. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

» 

TABLE    LXXXII. 

ANTI-LOGARITHMS,  OR  NUMBERS  TO  LOGARITHMS. 


♦337 


Log. 

0 

1 

2 

3 

4 

6 

6 

7 

8 

9 

P.P. 

.150 

14125 

14129 

14132 

14135 

14138 

14142 

14145 

14148 

14151 

14155 

.151 

14158 

14161 

14164 

14168 

14171 

14174 

14178 

14181 

14184 

14187 

1 

0 

.152 

14191 

14194 

14197 

14200 

14204 

14207 

14210 

14213 

14217 

14220 

2 

1 

.153 

14223 

14227 

14230 

14233 

14236 

14240 

14243 

14246 

14250 

14253 

3 

1 

.154 

14256 

14259 

14263 

14266 

14269 

14272 

14276 

14279 

14282 

14286 

4 

1 

.155 

14289 

14292 

14296 

14299 

14302 

14305 

14309 

14312 

14315 

14319 

5 

2 

.156 

14322 

14325 

14328 

14332 

14335 

14338 

14342 

14345 

14348 

14352 

6 

2 

.157 

14355 

14358 

14362 

14365 

14368 

14371 

14375 

14378 

14381 

14385 

7 

2 

.158 

14388 

14391 

14395 

14398 

14401 

14405 

14408 

14411 

14415 

14418 

8 

3 

.159 

14421 

14424 

14428 

14431 

14434 

14438 

14441 

14444 

14448 

14451 

9 

3 

.160 

14454  14458 

14461 

14464 

14468 

14471 

14474 

14478 

14481 

14484 

.161 

14488  i  14491 

14494 

14498 

14501 

14504 

14508 

14511 

14514 

14518 

1 

0 

.162 

14521  14524 

14528 

14531 

14534 

14538 

14541 

14545 

14548 

14551 

2 

1 

.163 

14555 

14558 

14561 

14565 

14568 

14571 

14575 

14578 

14581 

14585 

3 

1 

.164 

14588 

14592 

14595 

14598 

14602 

14605 

14608 

14612 

14615 

14618 

4 

1 

.165 

14622 

14625 

14629 

14632 

14635 

14639 

14642 

14645 

14649 

14652 

5 

2 

.166 

14655 

14659 

14662 

14666 

14669 

14672 

14676 

14679 

14682 

14686 

6 

2 

.167 

14689 

14693 

14696 

14699 

14703 

14706 

14710 

14713 

14716 

14720 

7 

2 

.168 

14723 

14727 

14730 

14733 

14737 

14740 

14743 

14747 

14750 

14754 

8 

3 

.169 

14757 

14760 

14764 

14767 

14771 

14774 

14777 

14781 

14784 

14788 

9 

3 

.170 

14791 

14794 

14798 

14801 

14805 

14808 

14812 

14815 

14818 

14822 

.171 

14825 

14829 

14832 

14835 

14839 

14842 

14846 

14849 

14853 

14856 

1 

0 

.172 

14859 

14863 

14866 

14870 

14873 

14876 

14880 

14883 

14887 

14890 

2 

1 

.173 

14894 

14897 

14900 

14904 

14907 

14911 

14914 

14918 

14921 

14925 

3 

1 

.174 

14928 

14931 

14935 

14938 

14942 

14945 

14949 

14952 

14955 

14959 1  4 

1 

.175 

14962 

14966 

14969 

14973 

14976 

14980 

14983 

14986 

14990 

14993 

5 

2 

.176 

14997 

15000 

15004 

15007 

15011 

15014 

15018 

15021 

15024 

15028 

6 

2 

.177 

15031 

15035 

15038 

15042 

15045 

15049 

15052 

15056 

15059 

15063 

7 

2 

.178 

15066 

15070 

15073 

15076 

15080 

15083 

15087 

15090 

15094 

15097 

8 

3 

.179 

15101 

15104 

15108 

15111 

15115 

15118 

15122 

15125 

15129 

15132 

9 

3 

.180 

15136 

15139 

15143 

15146 

15150 

15153 

15157 

15160 

15164 

15167 

.181 

15171 

15174 

15177 

15181 

15184 

15188 

15191 

15195 

15198 

15202 

1 

0 

.182 

15205 

15209 

15212 

15216 

15219 

15223 

15226 

15230 

15234 

15237 

2 

1 

.183 

15241 

15244 

15248 

15251 

15255 

15258 

15262 

15265 

15269 

15272 

3 

1 

.184 

15276 

15279 

15283 

15286 

15290 

15293 

15297 

15300 

15304 

15307 

4 

1 

.185 

15311 

15314 

15318 

15321 

15325 

15329 

15332 

15336 

15339 

15343 

5 

2 

.186 

15346 

15350 

15353 

15357 

15360 

15364 

15367 

15371 

15374 

15378 

6 

2 

.187 

15382 

15385 

15389 

15392 

15396 

15399 

15403 

15406 

15410 

15413  7 

2 

.188 

15417 

15421 

15424 

15428 

15431 

15435 

15438 

15442 

15445 

15449 

8 

3 

.189 

15453 

15456 

15460 

15463 

15467 

15470 

15474 

15477 

15481  j  15485 

9 

3 

.190 

15488 

15492 

15495 

15499 

15502 

15506 

15510 

15513 

15517  '  15520 

.191 

15524 

15527 

15531 

15535 

15538 

15542 

15545 

15549 

15552 

15556 

1 

0 

.192 

15560 

15563 

15567 

15570 

15574 

15578 

15581 

15585 

15588 

15592 

2 

1 

.193 

15596 

15599 

15603 

15606 

15610 

15613 

15617 

15621 

15624 

15628 

3 

1 

.194 

15631 

15635 

15639 

15642 

15646 

15649 

15653 

15657 

15660 

15664 

4 

1 

.195 

15668 

15671 

15675 

15678 

15682 

15686 

15689 

15693 

15696 

15700 

5 

2 

.196 

15704 

15707 

15711 

15714 

15718 

15722 

15725 

15729 

15733 

15736 

6 

2 

.197 

15740 

15743 

15747 

15751 

15754 

15758 

15762 

15765 

15769 

15772 

7 

3 

.198 

15776 

15780 

15783 

15787 

15791 

15794 

15798 

15802 

15805 

15809 

8 

3 

.199 

15812 

15816 

15820 

15823 

15827 

15831 

15834 

15838 

15842 

15845 

9 

3 

Log. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

^338 


TABLE     LXXXII. 


ANTI-LOGARITIBIS,   OR  NUMBERS  TO  LOGARITHMS. 


Log. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.P. 

.200 

15849 

15853 

15856 

15860 

15864  15867 

15871 

15874 

15878 

15882 

t 
1 

.201 

15885 

15889 

15893 

15896 

15900 

15904 

15907  1 

15911  j 

15915 

15918  ll 

0 

.202 

15922 

15926 

15929 

15933 

15937 

15940 

15944 

15948 

15951 

15955 

2 

1  1 

.203 

15959 

15962 

15966 

15970 

15973 

15977 

15981 

15985 

15988 

15992 

3 

1 

.204 

15996 

15999 

16003 

16007 

16010 

16014 

16018 

16021 

16025 

16029 

4 

1 

.205 

16032 

16036 

16040 

16044 

16047 

16051 

16055 

16058  ' 

16062 

16066 

5 

2 

.206 

16069 

16073 

16077 

16081 

16084 

16088 

16092 

16095  i 

16099 

16103 

6j 

2 

.207 

16106 

16110 

16114 

16118 

16121 

16125 

16129 

16132 

16136 

16140 

7 

3 

.208  i  16144 

16147 

16151 

16155 

16158 

16162 

16166 

16170 

16173 

16177 

8 

3 

.209  16181 

16185 

16188 

16192 

16196 

10199 

16203 

16207 

16211 

16214 

9 

3 

.210  16218 

16222 

16226 

16229 

16233 

16237 

16241 

16244 

16248 

16252 

.211  16255 

16259 

16263 

16267 

16270 

16274 

16278 

16282 

16285 

16289 

1 

0 

.212  16293 

16297 

16300 

16304 

16308 

16312 

16315 

16319 

16323 

16327 

2 

1 

.213  I  16331 

16334 

16338 

16342 

16346 

16349 

16353 

16357 

16361 

16364 

3 

1 

.214 

16368 

16372 

16376 

16379 

16383 

10387 

16391 

16395 

16398 

16402 

4 

2 

.215 

16406 

16410 

16413 

16417 

16421 

16425 

16429 

16432 

16436 

16440 

5 

2 

.216 

16444 

16448 

16451 

16455 

16459 

16463 

16466 

16470 

16474 

16478 

6 

2 

.217 

16482 

16485 

16489 

16493 

16497 

16501 

16504 

16508 

16512 

16516 

7 

3 

.218 

16520 

16523 

16527 

16531 

16535 

16539 

16542 

16546 

16550 

16554 

8 

3 

.219 

16558 

16562 

16565 

16569 

16573 

16577 

16581 

16584 

16588 

16592 

9 

3 

.220 

16596 

16600 

16604 

16607 

16611 

16615 

16619 

16623 

16626 

16630 

.221 

16634 

16638 

16642 

16646 

16649 

16653 

16657 

16661 

16665 

16669 

1 

0 

.222 

16672 

16676 

16680 

16684 

16688 

16692 

16696 

16699 

16703 

16707 

2 

1 

.223 

16711 

16715 

16719 

16722 

16726 

16730 

16734 

16738 

16742 

16746 

3 

1 

.224 

16749 

16753 

16757 

16761 

16765 

16769 

16773 

16776 

16780 

16784 

4 

2 

.225 

16788 

16792 

16796 

16800 

16804 

16807 

16811 

16815 

16819 

16823 

5 

2 

.226 

16827 

16831 

16834 

16838 

16842 

16846 

16850 

16854 

16858 

16862 

6 

2 

.227 

16866 

16869 

16873 

16877 

16881 

16885 

16889 

16893 

16897 

16901 

7 

3 

.228 

16904 

16908 

16912 

16918 

16920 

16924 

16928 

16932 

16936 

16939 

8 

3 

.229 

16943 

16947 

16951 

16955 

16959 

16963 

16967 

16971 

16975 

16979 

9 

3 

.230 

16982 

16986 

16990 

16994 

16998 

17002 

17006 

17010 

17014 

17018 

.231 

17022 

17026 

17029 

17033 

17037 

17041 

17045 

17049 

17053 

17057 

1 

0 

.232 

17061 

17065 

17069. 

17073 

17077 

17080 

17084 

17088 

17092 

17096 

2 

1 

.233 

17100 

17104 

17108 

17112 

17116 

17120 

17124 

17128 

17132  1  17136 

3 

1 

.234 

17140 

17144 

17147 

17151 

17155 

17159 

17163 

17167 

17171 

17175^ 

4 

2 

.235  '  17179 

17183 

17187 

17191 

17195 

17199 

17203 

17207 

17211 

17215"^ 

5 

2 

.236  17219 

17223 

17227 

17231 

17235 

17239 

17242 

17246 

17250 

17254 

6 

2 

.237  17258 

17262 

17266 

17270 

17274 

17278 

17282  \  17286 

17290 

17294 

7 

3 

.238  17298 

17302 

17306 

17310 

17314 

17318 

17322  '  17326 

17330 

17334 

8 

3 

.239 

17338 

17342 

17346 

17350 

17354 

17358 

17362 

17366 

17370 

17374 

9 

4 

.240 

17378 

17382 

17386 

17390 

17394 

17398  17402 

17406 

17410 

17414 

.241 

17418 

17422 

17426 

17430 

17434 

17438  17442 

17446 

17450 

17454 

1 

0 

.242 

17458 

17462 

17468 

17470 

17474 

17478  17482 

17486 

17490 

17494 

2 

1 

.243 

17498 

17502 

17507 

17511 

17515 

17519  ^ 17523 

17527 

17531 

17535 

3 

1 

.244 

17539 

17543 

17547 

17551 

17555 

17559  17563 

17567 

17571 

17575 

4 

2 

.245 

17579 

17583 

17587 

17591 

17595 

17599  i  17604 

17608 

17612 

17616 

5 

2 

.246 

17620 

17624 

17628 

17632 

17636 

17640  17644 

17648 

17652 

17656 

6 

2 

.247 

17660 

17664 

17669 

17673 

17677 

17681  17685 

17689 

17693 

17697 

7 

3 

.248 

17701 

17705 

17709 

17713 

17717 

17721  :  17726 

17730 

17734 

17738 

8 

3 

.249 

17742 

17746 

17750 

17754 

17758 

17762  1  17766 

17771 

17775 

17779 

9 

4 

j  Log 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

TABLE    LXXXII. 

ANTI-LOGARITHMS,  OR  NUMBERS  TO  LOGARITHMS. 


*239 


Loa. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.P. 

.250 

17783 

17787 

17791 

17795 

17799 

17803 

17807 

17811 

17816 

17820 

.251 

17824 

17828 

17832 

17836 

17840 

17844 

17848 

17853 

17857 

17861 

1 

0 

.252 

17865 

17869 

17873 

17877 

17881 

17885 

17890 

17894 

17898 

17902 

2 

1 

.253 

17906 

17910 

17914 

17918 

17923 

17927 

17931 

17935 

17939 

17943 

3 

1 

.254 

17947 

17951 

17956 

17960 

17964 

17968 

17972 

17976 

17980 

17985 

4 

2 

.255 

17989 

17993 

17997 

18001 

18005 

18009 

18014 

18018 

18022 

18026 

5 

2 

.256 

18030 

18034 

18038 

18043 

18047 

18051 

18055 

18059 

18063 

18068 

6 

2 

.257 

18072 

18076 

18080 

18084 

18088 

18093 

18097 

18101 

18105 

18109 

7 

3 

.258 

18113 

18118 

18122 

18126 

18130 

18134 

18138 

18143 

18147 

18151 

8 

3 

.259 

18155 

18159 

18164 

18168 

18172 

18176 

18180 

18184 

18189 

18193 

9 

4 

.260 

18197 

18201 

18205 

18210 

18214 

18218 

18222 

18226 

18231 

18235 

.261 

18239 

18243 

18247 

18252  '  18256 

18260 

18264 

18268 

18273 

18277 

1 

0 

.262 

18281 

18285 

18289 

18294  j  18298 

18302 

18306 

18310 

18315 

18319 

2 

1 

.263 

18323 

18327 

18332 

18336  1  18340 

18344 

18348 

18353 

18357 

18361 

3 

1 

.264 

18365 

18370 

18374 

18378  18382 

18387 

18391 

18395 

18399 

18403 

4 

2 

.265 

18408 

18412 

18416 

18420  18425 

18429 

18433 

18437 

18442 

18446 

5 

2 

.266 

18450 

18454 

18459 

18463  18467 

18471 

18476 

18480 

18484 

18488 

6 

3 

.267 

18493 

18497 

18501 

18505  i  18510 

18514 

18518 

18523 

18527 

18531 

7 

3 

.268 

18535 

18540 

18544 

18548  18552 

18557 

18561 

18565 

18569 

18574 

8 

3 

.269 

18578 

18582 

18587 

18591  18595 

18599 

18604 

18608 

18612 

18617 

9 

4 

.270 

18621 

18625 

18629 

18634 

18638 

18642 

18647 

18651 

18655 

18659 

.271 

18664 

18668 

18672 

18677 

18681 

18685 

18690 

18694 

18698 

18703 

1 

0 

.272 

18707 

18711 

18715 

18720 

18724 

18728 

18733 

18737 

18741 

18746 

2 

1 

.273 

18750 

18754 

18759 

18763 

18767 

18772 

18776 

18780 

18785 

18789 

3 

1 

.274 

18793 

18797 

18802 

18806 

18810 

18815 

18819 

18823 

18828  '  18832 

4 

2 

.275 

18836 

18841 

18845 

18850 

18854 

18858 

18863 

18867 

18871  i  18876 

5 

2 

.276 

18880 

18884 

18889 

18893 

18897 

18902 

18906 

18910 

18915 

18919 

6 

3 

.277 

18923 

18928 

18932 

18937 

18941 

18945 

18950 

18954 

18958 

18963 

7 

3 

.278 

18967 

18971 

18976 

18980 

18985 

18989 

18993 

18998 

19002 

19006 

8 

3 

.279 

19011 

19015 

19020 

19024 

19028 

19033 

19037 

19041 

19046 

19050 

9 

4 

.280 

19055 

19059 

19063 

19068 

19072 

19077 

19081 

19085 

19090 

19094 

.281 

19099 

19103 

19107 

19112 

19116 

19121 

19125 

19129 

19134 

19138 

1 

0 

.282 

19143 

19147  19151 

19156 

19160 

19165 

19169 

19173 

19178 

19182 

2 

1 

.283 

19187 

19191 

19196 

19200 

19204 

19209 

19213 

19218 

19222 

19226 

3 

1 

.284 

19231 

19235 

19240 

19244 

19249 

19253 

19258 

19262 

19266 

19271 

4 

2 

.285 

19275 

19280 

19284 

19289 

19293 

19297 

19302 

19306 

19311 

19315 

5 

2 

.286 

19320 

19324 

19329 

19333 

19337 

19342 

19346 

19351 

19355 

19360 

6 

3 

.287 

19364 

19369 

19373 

19378 

19382 

19387 

19391 

19395 

19400 

19404 

7 

3 

.288 

19409 

19413 

19418 

19422 

19427 

19431 

19436 

19440 

19445 

19449 

8 

4 

.289 

19454 

19458 

19463 

19467 

19472 

19476 

19480 

19485 

19489  19494 

9 

4 

.290 

19498 

19503 

19507 

19512 

19516 

19521 

19525 

19530 

19534  19539 

.291 

19543 

19548 

19552 

19557 

19561 

19566 

19570 

19575 

19579 

19584 

1 

0 

.292 

19588 

19593 

19597 

19602 

19606 

19611 

19616 

19620 

19625 

19629 

2 

1 

.293 

19634 

19638 

19643 

19647 

19652 

19656 

19661 

19665 

19670 

19674 

3 

1  ! 

.294 

19679 

19683 

19688 

19692 

19697 

19702 

19706 

19711 

19715 

19720 

4 

2 

.295 

19724 

19729 

19733 

19738 

19742 

19747 

19751 

19756 

19761 

19765 

5 

2 

.296 

19770 

19774 

19779 

19783 

19788 

19792 

19797 

19802 

19806 

19811 

6 

3  i 

.297 

19815 

19820 

19824 

19829 

19834 

19838 

19843 

19847 

19852 

19856 

7 

3 

.298 

19861 

19866 

19870 

19875 

19879 

19884 

19888 

19893 

19898 

19902 

8 

4 

.299 

19907 

19911 

19916 

19920 

19925 

19930 

19934 

19939 

19943 

19948 

9 

4 

Log. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

*240 


TABLE     LXXXII. 

ANTI-LOGARIimfS,  OR  NUMBERS  TO  LOGARITHMS. 


Log. 

0 

1 

2 

3 

4 

5 

6 

7 

1 

8    9 

1 

P.  P. 

.300 

19953 

19957 

19962 

19966 

1997'l 

19976 

19980 

19985 

19989  19994 

i  .301 

19999 

20003 

20008 

'  20012 

20017 

20022 

20026 

20031 

20035  200401  llO 

|.302 

20045 

20049 

20054 

' 20059 

20063 

20068 

20072 

20077  1  20082  !  20086  !  2 1 1 

.303 

20091 

20096 

,  20100 

i  20105 

20109 

20114 

20119 

20123 

2012^  20133^3 jl 

.304 

20137 

20142 

20147 

20151 

20156 

20160 

20165 

20170 

20174:201791  4:2 

.305 

20184 

20188 

20193 

20198 

20202 

20207 

20212 

20216  20221  20226  5  2 

.306 

20230 

20235 

20240 

20244 

20249 

20253 

20258 

20263!  20267  20272  6  3  | 

.307 

20277 

20281 

20286 

20291 

20296 

20300 

20305 

20310  '  20314  20319 

1  7  3 

.308 

20324 

20328 

20333 

1 20338 

20342 

20347 

20352 

20356  i  20361  20366 

8  4 

.309 

20370 

20375 

20380 

20384 

20389 

20394 

20399 

20403  20408  20413 

9  4 

.310 

20417 

20422 

20427 

20431 

20436 

20441 

20446 

20450  :  20455  20460 

.311 

20464 

20469 

20474 

20479 

20483 

20488 

20493 

:  20497  j  20502  20507 

1  0 

.312 

20512 

20516 

20521 

20526 

20531 

20535 

20540 

; 20545 

20549  20554 

2  1 

.313 

20559 

i  20564 

20568 

20573 

20578 

20583 

20587 

20592 

20597.  20602 

31 

.314 

20606 

20611 

20616 

20621 

20625 

20630 

20635 

20640 

20644  20649 

4  2 

.315 

20654 

20659 

20663 

20668 

20673 

20678 

20682 

20687 

20692  20697 

5  2 

.316 

20701 

20706 

20711 

20716 

20720 

20725 

20730 

20735 

20740  20744 

6  3 

.317 

20749 

20754 

20759 

20763 

20768 

20773 

20778 

20783 

20787 \  20792 

7!3 

.318 

20797 

20802 

20807 

20811 

20816 

20821 

20826 

20831 

20835  I  20840 

8  4 

.319 

20845 

20850 

20855 

20859 

20864 

20869 

20874 

20879 

20883 

20888 

9  4 

.320 

20893 

20898 

20903 

20907 

20912 

20917 

20922 

20927 

20931 

20936 

.321 

20941 

20946 

20951 

20956 

20960 

20965 

20970 

20975 

20980 

' 20985 

1  0 

.322 

20989 

20994 

20999 

21004 

21009 

21014 

21018 

21023 

21028 

21C33 

2  1 

.323 

21038 

21043 

,21047 

21052 

21057 

21062 

21067 

21072 

21077 

,  21081 

3  1 

.324 

21086 

21091 

21096 

21101 

21106 

21111 

21115 

21120 

21125 

21130 

4  2 

.325 

21135 

21140 

21145 

21149 

21154 

21159 

21164 

21169 

21174 

21179 

5  2 

.326 

21184 

21188 

21193 

21198 

21203 

21208 

21213 

21218 

21223 

21228 

613 

.327 

21232 

21237 

21242 

21247 

21252 

21257 

21262 

21267 

21272 

21276 

7  3 

.328 

21281 

21286 

21291 

21296 

21301 

21306 

21311 

21316 

21321 

, 21326 

8  4 

.329 

21330 

21335 

21340 

21345 

21350 

21355 

21360 

21365 

21370 

21375 

9  4 

.330 

21380 

21385 

21389 

21394 

21399 

21404 ' 

21409 

21414 

21419 

21424 

.331 

21429 

21434 

21439 

21444 

21449 

21454 

21459 

21463 

21468 

21473 

1  0 

.332 

21478 

21483 

21488 

21493 

21498 

21503 

21508  . 

21513 

21518 

21523 

2  1 

.333  21528 

21533 

21538 

21543 

21548 

21553 

21558 

21563 

21568 

21572 

3  1 

.334  21577 

21582 

21587 

21592 

21597 

21602 

21607 

21612 

21617 

21622 

4  2 

.335  21627 

21632 

21637 

21642 

21647 

21652 

21657 

21662 

21667 

21672 

5  2 

.336 

21677 

21682 

21687 

21692 

21697 

21702 

21707 

21712 

21717 

21722 

6  3 

.337 

21727 

21732 

21737 

21742 

21747 

21752 

21757 

21762 

21767 

21772 

7  3 

.338 

21777 

21782 

21787 

21792 

21797 

21802 

21807 

21812 

21817 

21822 

8  4 

.339 

21827 

21832 

21837 

21842 

21847 

21852 

21857 

21863 

21868 

21873 

9  4 

.340 

21878 

21883 

21888 

21893 

21898 

21903 

21908 

21913 

21918 

21923 

.341 

21928 

21933 

21938 

21943 

21948 

21953 

21958  !  21963 

21968 

21974 

1  1 

.342 

21979 

21984 

21989 

21994 

21999 

22004 

22009  22014 

22019 

22024 

2  1 

.343 

22029 

22034 

22039 

22044 

22050 

22055 

22060  22065 

22070 

22075 

3  2 

.344 

22080 

22085 

22090 

22095 

22100 

22105 

22111  22116 

22121  \ 

22126 

4  2 

.345 

22131 

22136 

22141 

22146 

22151 

22156 

22162  22167 

22172  ' 

22177 

5  3 

.346 

22182 

22187 

22192 

22197 

22202 

22208 

22213  22218 

22223  i 

22228 

6  3 

.347 

22233 

22238 

22243 

22248 

22254 

22259 

22264  !  22269 

22274 

22279 

7  4 

.348 

22284 

22289 

22295 

22300 

22305 

22310  22315  | 

22320 

22325 

22331 

8  4 

.349 

22336 

22341 

22346 

22351 

22356 

22361 

22367 1 

22372 

22377 

22382 

9  5 

Log. 

0 

1 

2 

3 

4 

5    6 

7 

8 

9 

i 

TABLE    LXXXn. 

ANTI-LOGAEITHMS,  OR  NUMBERS   TO  LOGARITHMS. 


♦241 


Log. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.P. 

.350 

22387 

22392 

22398 

22403 

22408 

22413 

22418 

22423 

22428 

22434 

.351 

22439 

22444 

22449 

22454 

22459 

22465 

22470 

22475 

22480 

22485 

1 

1 

.352 

22491 

22496 

22501 

22506 

22511 

22516 

22522 

22527 

22532 

22537 

2 

1 

.353 

22542 

22548 

22553 

22558 

22563 

22568 

22574 

22579 

22584 

22589 

3 

2 

.354 

22594 

22600 

22605 

22610 

22615 

22620 

22626 

22631 

22636 

22641 

4 

2 

.355 

22646 

22652 

22657 

22662 

22667 

22673 

22678 

22683 

22688 

22693 

5 

3 

.356 

g5699 

22704 

22709 

22714 

22720 

22725 

22730 

22735 

22740 

22746 

6 

3 

.357 

22751 

22756 

22761 

22767 

22772 

22777 

22782 

22788 

22793 

22798 

7 

4 

.358 

22803 

22809 

22^4 

22819 

22824 

22830 

22835 

22840 

22845 

22851 

8 

4 

.359 

22856 

22861 

22867 

22872 

22877 

22882 

22888 

22893 

22898 

22903 

9 

5 

.360 

22909 

22914 

22919 

22925 

22930 

22935 

22940 

22946 

22951 

22956 

.361 

22961 

22967 

22972 

22977 

22983 

22988 

22993 

22999 

23004 

23009 

1 

1 

.362 

23014 

23020 

23025 

23030 

23036 

23041 

23046 

23052 

23057 

23062 

2 

1 

.363 

23067 

23073 

23078 

23083 

23089 

23094 

23099 

23105 

23110 

23115 

3 

2 

.364 

23121 

23126 

23131 

23137 

23142 

23147 

23153 

23158 

23163 

23169 

4 

2 

.365 

23174 

23179 

23185 

23190 

23195 

23201 

23206 

23211 

23217 

23222 

5 

3 

.366 

23227 

23233 

23238 

23243 

23249 

23254 

23259 

23265 

23270 

23276 

6 

3 

.367 

23281 

23286 

23292 

23297 

23302 

23308 

23313 

23318 

23324 

23329 

7 

4 

.368 

23335 

23340  23345 

23351 

23356 

23361 

23367 

23372 

23378 

23383 

8 

4 

.369 

23388 

23394  23399 

23405 

23410 

23415 

23421 

23426 

23432 

23437 

9 

5 

.370 

23442 

23448  23453 

23458 

23464 

23469 

23475 

23480 

23486 

23491 

.371 

23496 

23502  23507 

23513 

23518 

23523 

23529 

23534 

23540 

23545 

1 

1 

.372 

23550 

23556 

23561 

23567 

23572 

23578 

23583 

23588 

23594 

23599 

2 

1 

.373 

23605 

23610 

23616 

23621 

23627 

23632 

23637 

23643 

23648 

23654 

3 

2 

.374 

23659 

23665 

23670 

23676 

23681 

23686 

23692 

23697 

23703 

23708 

4 

2 

.375 

23714 

23719 

23725 

23730 

23736 

23741 

23747 

23752 

23757 

23763 

5 

3 

.376 

23768 

23774 

23779 

23785 

23790 

23796 

23801 

23807 

23812 

23818 

6 

3 

.377 

23823 

23829 

23834 

23840 

23845 

23851 

23856 

23862 

23867 

23873 

7 

4 

.378 

23878 

23884 

23889 

23895 

23900 

23906 

23911 

23917 

23922 

23928 

8 

4 

.379 

23933 

23939 

23944 

23950 

23955 

23961 

23966 

23972 

23977 

23983 

9 

5 

.380 

23988 

23994 

23999 

24005 

24010 

24016 

24021 

,24027 

24033 

24038 

.381 

24044 

24049 

24055 

24060 

24066 

24071 

24077 

24082 

24088 

24094 

1 

1 

.382 

24099 

24105 

24110 

24116 

24121 

24127 

24132 

24138 

24143 

24149 

2 

1 

.383 

24155 

24160 

24166 

24171 

24177 

24182 

24188 

24194 

24199 

24205 

3 

2 

.384 

24210 

24216 

24221 

24227 

24233 

24238 

24244 

24249 

24255 

24261 

4 

2 

.385 

24266 

24272 

24277 

24283 

24288 

24294 

24300 

24305 

24311 

24316 

5 

3 

.386 

24322 

24328 

24333 

24339 

24344 

24350 

24356 

24361 

24367 

24373 

6 

3 

.387 

24378 

24384 

24389 

24395 

24401 

24406 

24412 

24417 

24423 

24429 

7 

4 

.388 

24484 

24440 

24446 

24451 

24457 

24462 

24468 

24474 

24479 

24485 

8 

4 

.389 

24491 

24496  i  24502 

24508 

24513 

24519 

24524 

24530 

24536 

24541 

9 

5 

.390 

24547 

24553  24558 

24564 

24570 

24575 

24581 

24587 

24592 

24598 

.391 

24604 

24609  24615 

24621 

24626 

24632 

24638 

24643 

24649 

24655 

1 

1 

.392 

24660 

24666 

24672 

24677 

24683 

24689 

24694 

24700 

24706 

24712 

2 

1 

.393 

24717 

24723 

24729 

24734 

24740 

24746 

24751 

24757 

24763  i  24769 

3 

2 

.394 

24774 

24780 

24786 

24791 

24797 

24803 

24808 

24814 

24820  24826 

4 

2 

.395 

24831 

24837 

24843 

24848 

24854 

24860 

24866 

24871 

24877  24883 

5 

3 

.396 

24889 

24894 

24900 

24906 

24912 

24917 

24923 

24929 

24934  24940 

6 

3 

.397 

24946 

24952 

24957 

24963 

24969 

24975 

24980 

24986 

24992 

24998 

7 

4 

.398 

25003 

25009 

25015 

25021 

25026 

25032 

25038 

25044 

25050 

25055 

8 

5 

.399 

25061 

25067 

25073 

25078 

25084. 

25090 

25096 

25102 

25107  25113 

9 

5 

Loa. 

0 

1 

2 

8 

4 

6 

6 

7 

8    9 

*243 


TABLE     LXXXII. 

ANTI-LOGARITHMS,  OR  NUMBERS  TO  LOGARITHMS. 


!  Log. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

.400 

25119 

25125 

25130 

25136 

25142 

25148 

25154 

25159 

25165 

25171 

.401 

25177 

25183 

25188 

25194 

25200 

25206 

25212 

25217 

25223 

25229 

1  1 

.402 

25235 

25241 

25246 

25252 

25258 

25264 

25270 

25276 

25281 

25287 

2  1 

i.403 

25293 

25299 

25305 

25310 

25316 

25322 

25328 

25334  25340 

25345 

3  2 

.404 

25351 

25357 

25363 

25369 

25375 

25380 

25386 

25392 

25398 

25404 

4  2 

.405 

25410 

25416 

25421 

25427  1  25433 

25439 

25445 

25451 

25457 

25462 

5  3 

.406 

25468 

25474 

25480 

25486 

25492 

25498 

25504 

25509 

25515 

25521 

6  4 

.407 

25527 

25533 

25539 

25545 

25551 

25556 

25562 

25568 

25574 

25580 

7  4 

.408 

25586 

25592 

25598 

25604 

25609 

25615 

25621 

23627 

25633 

25639 

8  5 

.409 

25645 

25651 

25657 

25663 

25668 

25674 

25680 

25686 

25692 

25698 

9  5 

.410 

25704 

25710 

25716 

25722 

25728 

25734 

25739 

25745 

25751 

25757 

.411 

25763 

25769 

25775 

25781 

25787 

25793 

25799 

25805 

25811 

25817 

1  1 

.412 

25823 

25829 

25834 

25840 

25846 

25852 

25858 

25864 

25870 

25876 

2  1 

.413 

25882 

25888 

25894 

25900 

25906 

25912 

25918 

25924 

25930 

25936 

3  2 

.414 

25942 

25948 

25954 

25960 

25966 

25972 

25978 

1  25984 

25990 

25996 

4  2 

.415 

26002 

26008 

26014 

26020 

26026 

26032 

26038 

26044 

26050 

26056 

5  3 

.416 

26062 

26068 

26074 

26080 

26086 

26092 

26098 

i  26104 

26110 

26116 

6  4 

.417 

26122 

26128 

26134 

26140 

26146 

26152 

26158 

26164 

26170 

26176 

7  4 

.418 

26182 

26188 

26194 

26200 

26206 

26212 

26218 

26224 

26230 

26236 

8  5 

.419 

26242 

26248 

26254 

26260 

26266 

26272 

26278 

26285 

26291 

26297 

9  5 

.420 

26303 

26309 

26315 

26321 

26327 

26333 

26339 

'  26345 

26351 

26357 

.421 

26363 

26369 

26375 

26382 

26388 

26394 

26400 

26406 

26412 

26418 

1  1 

.422 

26424 

26430 

26436 

26442 

26448 

26455 

26461 

26467 

26473 

26479 

2  1 

.423 

26485 

26491 

26497 

26503 

26509 

26516 

26522 

26528 

26534 

26540 

3  2 

.424 

26546 

26552 

26558 

26564 

26571 

26577 

26583 

26589 

26595 

26601 

4  2 

.425 

26607 

26613 

26620 

26626 

26632 

26638 

26644 

26650 

26656 

26662 

5i3 

.426 

26669 

26675 

26681 

26687 

26693 

26699 

26705 

26712 

26718 

26724 

64 

.427 

26730 

26736 

26742 

26749 

26755 

26761 

26767 

26773 

26779 

26786 

7,4 

.428 

26792 

26798 

26804 

26810 

26816 

26823 

26829 

26835 

26841 

26847 

8'5 

.429 

26853 

26860 

26866 

26872 

26878 

26884 

26891 

26897 

26903 

26909 

9  6 

.430 

26915 

26922 

26928 

26934 

26940 

26946 

26953 

26959 

26965 

26971 

1 

.431 

26977 

26984 

26990 

26996 

27002 

27008 

27015 

27021 

27027 

27033 

1  1 

.432 

27040 

27046 

27052 

27058 

27064 

27071 

27077 

27083 

27089 

27096 

2  1 

.433 

27102 

27108 

27114 

^7121 

^7127 

27133 

27139 

27146 

27152 

27158 

3  2 

.434 

27164 

27171 

27177 

27183 

27189 

27196 

27202 

27208 

27214 

27221 

4  3 

.435 

27227 

27233 

27240 

27246 

27252 

27258 

27265 

27271 

27277 

27283 

5  3 

.436 

27290 

27296 

27302 

27309 

27315 

27321 

27328 

27334 

27340 

27346 

6  4 

.437 

27353 

27359 

27365 

27372 

27378 

27384 

27391 

27397 

27403 

27409 

7  4 

.438 

27416 

27422 

27428 

27435 

27441 

27447 

27454 

27460 

27466 

27473 

8  5 

.439 

27479 

27485 

27492 

27498 

27504 

27511 

27517 

27523 

27530 

27536 

9  6 

.440 

27542 

27549 

27555 

27561 

27568 

27574 

27580 

27587 

27593 

27599 

.441 

27606 

27612 

27618 

27625 

27631 

27638 

27644 

27650 

27657 

27663 

1  1 

.442 

27669 

27676 

27682 

27689 

27695 

27701 

27708 

27714 

27720 

27727 

2  1 

.443 

27733 

27740 

27746 

27752 

27759 

27765 

27772 

27778 

27784 

27791 

3  2 

.444 

27797 

27804 

27810 

27816 

27823 

27829 

27836 

27842 

27848 

27855 

4  3 

.445 

27861 

27868 

27874 

27880 

27887 

27893 

27900 

27906 

27913 

27919 

5  3 

.446 

27925 

27932 

27938 

27945 

27951 

27958 

27964 

27970 

27977 

27983 

6  4 

.447 

27990 

27996 

28003 

28009 

28016 

28022 

28029 

28035 

28041 

28048 

7  4 

.448 

28054 

28061 

28067 

28074 

28080 

28087 

28093 

28100 

28106 

28113 

8  5 

.449 

28119 

28125 

28132 

28138 

28145 

28151 

28158 

28164 

28171 

28177 

9  6 

Log. 

0 

1 

2 

3 

4 

6 

6 

7 

8    9 

TABLE    LXXXII. 


♦243 


ANTI-LOGARITHMS,  OR  NUMBERS  TO  LOGARITHMS. 


Log. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.P. 

.450 

28184 

28190 

28197 

28203 

28210 

28216 

28223 

28229 

28236 

28242 

1  .451 

28249 

28255 

28262 

28268 

28275 

28281 

28288 

28294 

28301 

28307 

1 

1 

.452 

28314 

28320 

28327 

28333 

28340 

28347 

28353 

28360 

28366 

28373 

2 

1 

.453 

28379 

28386 

28392 

28399 

28405 

28412 

28418 

28425 

28432 

28438 

3 

2 

.454 

28445 

28451 

28458 

28464 

28471 

28477 

28484 

28490 

28497 

28504 

4 

3 

.455 

28510 

28517 

28523 

28530 

28536 

28543 

28550 

28556 

28563 

28569 

5 

3 

.456 

28576 

28582 

28589 

28596 

28602 

28609 

28615 

28622 

28629 

28635 

6 

4 

.457 

28642 

28648 

28655 

28662 

28668 

28675- 

28681 

28688 

28695 

28701 

7 

5 

.458 

28708 

28714 

28721 

28728 

28734 

28741 

28747 

28754 

28761 

28767 

8 

5 

.459 

28774 

28781 

28787 

28794 

28800 

28807 

28814 

28820 

28827 

28834 

9 

6 

.460 

28840 

28847 

28854 

28860 

28867 

28874 

28880 

28887 

28893 

28900 

.461 

28907 

28913 

28920 

28927 

28933 

28940 

28947  i  28953 

28960 

28967 

1 

1 

.462 

28973 

28980 

28987 

28993 

29000 

29007 

29013 

29020 

29027 

29034 

2 

1 

.463 

29040 

29047 

29054 

29060 

29067 

29074 

29080 

29087 

29094 

29100 

3 

2 

.464 

29107 

29114 

29121 

29127 

29134 

29141 

29147 

29154 

29161 

29168 

4 

3 

.465 

29174 

29181 

29188 

29194 

29201 

29208 

29215 

29221 

29228 

29235 

5 

3 

.466 

29242 

29248 

29255 

29262 

29268 

29275 

29282 

29289 

29295 

29302 

6 

4 

.467 

29309 

29316 

29322 

29329 

29336 

29343 

29349 

29356 

29363 

29370 

7 

5 

.468 

29376 

29383 

29390 

29397 

29404 

29410 

29417 

29424 

29431 

29437 

8 

5 

.469 

29444 

29451 

29458 

29465 

29471 

29478 

29485 

29492 

29499 

29505 

9 

6 

.470 

29512 

29519 

29526 

29532 

29539 

29546 

29553 

29560 

29567 

29573 

.471 

29580 

29587 

29594 

29601 

29607 

29614 

29621 

29628 

29635 

29641 

1 

1 

.472 

29648 

29655 

29662 

29669 

29676 

29682 

29689 

29696 

29703 

29710 

2 

1 

.473 

29717 

29724 

29730 

29737 

29744 

29751 

29758 

29765 

29771 

29778 

3 

2 

.474 

29785 

29792 

29799 

29806 

29813 

29819 

29826 

29833 

29840 

29847 

4 

3 

i  .475 

29854 

29861 

29868 

29874 

29881 

29888 

29895 

29902 

29909 

29916 

5 

3 

.476 

29923 

29930 

29936 

29943 

29950 

29957 

29964 

29971 

29978 

29985 

6 

4 

.477 

29992 

29999 

30005 

30012 

30019 

30026 

30033 

30040 

30047 

30054 

7 

5 

.478 

30061 

30068 

30075 

30082 

30088 

30095 

30102 

30109  30116 

30123 

8 

5 

.479 

30130 

30137 

30144 

30151 

30158 

30165 

30172 

30179 

30186 

30193 

9 

6 

.480 

30200 

30206 

30213 

30220 

30227 

30234 

30241 

30248 

30255 

30262 

.481 

30269 

30276 

30283 

30290 

30297 

30304 

30311 

30318  30325 

30332 

1 

1 

.482 

30339 

30346 

30353 

30360 

30367 

30374 

30381 

30388 

30395 

30402 

2 

1 

.483 

30409 

30416 

30423 

30430 

30437 

30444 

30451 

30458 

30465 

30472 

3 

2 

.484 

30479 

30486 

30493 

30500 

30507 

30514 

30521 

30528 

30535 

30542 

4 

3 

.485 

30549 

30556 

30563 

30570 

30577 

30584 

30591 

30598 

30606 

30613 

5 

4 

.486 

30620 

30627 

30634 

30641 

30648 

30655 

30662 

30669 

30676 

30683 

6 

4 

.487 

30690 

30697 

30704 

30711 

30718 

30726 

30733 

30740 

30747 

30754 

7 

5 

.488 

30761 

30768 

30775 

30782 

30789 

30796 

30803 

30811 

30818 

30825 

8 

6 

.489 

30832 

30839 

30846 

30853 

30860 

30867 

30875 

30882 

30889 

30896 

9 

6 

.490 

30903 

30910  30917 

30924 

30931 

30939 

30946 

30953 

30960 

30967 

.491 

30974 

30981  30988 

30996 

31003 

31010 

31017 

31024 

31031 

31038 

1 

1 

.492 

31046 

31053 

31060 

31067 

31074 

31081 

31089 

31096 

31103 

31110 

2 

1 

.493 

31117 

31124 

31131 

31139 

31146 

31153 

31160 

31167 

31175 

31182 

3 

2 

.494 

31189 

31196 

31203 

31210 

31218 

31225 

31232 

31239 

31246 

31254 

4 

3 

.495 

31261 

31268 

31275 

31282 

31290 

31297 

31304 

31311 

31318 

31326 

5 

4 

.496 

31333 

31340 

31347 

31355 

31362 

31369 

31376 

31383 

31391 

31398 

6 

4 

.497 

31405 

31412 

31420 

31427 

31434 

31441 

31449 

31456 

31463 

31470 

7 

5 

.498 

31477 

31485 

31492 

31499 

31506 

31514 

31521 

31528 

31536 

31543 

8 

6 

.499 

31550 

31557 

31565 

31572 

31579 

31586 

31594 

31601 

31608 

31615 

9 

6 

Log. 

0 

1 

2 

3 

4    5 

6 

7 

8 

9 

"^44 


TABLE     LXXXTI. 


ANTI-LOGARITHMS,    OR  NUMBERS  TO  LOGARITHMS. 


Log. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.P. 

.500 

31623 

31630 

31637 

31645 

31652 

31659 

31666 

31674 

31681 

31688 

.501 

31696 

31703  \  31710 

31718 

31725 

31732 

31739 

31747 

31754 

31761 

1 

1 

.502 

31769 

31776  '  31783 

31791 

31798 

31805 

31813 

31820 

31827 

31835 

2 

1 

.503 

31842 

31849 

31857 

31864 

31871 

31879 

31886 

31893 

31901 

31908 

3 

2 

.504 

31915 

31923 

31930 

31937 

31945 

31952 

31960 

31967 

31974 

31982 

4 

3 

.505 

31989 

31996 

32004 

32011 

32018 

32026 

32033 

32041 

32048 

32055 

5 

4 

.506 

32063 

32070 

32077 

32085 

32092 

32100 

32107 

32114 

32122 

32129 

6 

4 

.507 

32137 

32144 

32151 

32159 

32166 

32174 

32181 

32188 

32196 

32203 

7 

5 

.508 

32211 

32218 

32226 

32233 

32240 

32248 

32255 

322e3 

32270 

32278 

8 

6 

.509 

32285 

32292 

32300 

32307 

32315 

32322 

32330 

32337 

32344 

32352 

9 

7 

.510 

32359 

32367 

32374 

32382 

32389 

32397 

32404 

32412 

32419 

32426 

.611 

32434 

32441 

32449 

32456 

32464 

32471 

32479 

32486 

32494 

32501 

1 

1 

.512 

32509 

32516 

32524 

32531 

32539 

32546 

32554 

32561 

32569 

82576 

2 

2 

.513 

32584 

32591 

32599 

32606 

32614 

32621 

32629 

32636 

32644 

32651 

3 

2 

.514 

32659 

32666 

32674 

32681 

32689 

32696 

32704 

^2711 

32719 

32727 

4 

3 

.515 

32734 

32742 

32749 

32757 

32764 

32772 

32779 

32787 

32794 

32802 

5 

4 

.516 

32810 

32817 

32825 

32832 

32840 

32847 

32855 

32862 

32870 

32878 

6 

5 

.517 

32885 

32893 

32900 

32908 

32915 

32923 

32931 

32938 

32946 

32953 

7 

5 

.518 

32961 

32969 

32976 

32984 

32991 

32999 

33007 

33014 

33022 

33029 

8 

6 

.519 

33037 

33045 

33052 

33060 

33067 

33075 

33083 

33090 

33098  1  33105 

9 

7 

.520 

33113 

33121 

33128 

33136 

33144 

33151 

33159 

33167  33174 

33182 

.521  33189 

33197 

33205 

33212 

33220 

33228 

33235 

33243  33251 

83258 

1 

1 

.522 

33266 

33274  33281 

33289 

33297 

33304 

33312 

33320  33327 

33335 

2 

2 

.523 

33343 

33350  33358 

33366 

33373 

33381 

33389 

33396  33404 

33412 

3 

2 

.524 

33420 

33427  33435 

33443 

33450 

33458 

33466 

33473  33481 

33489 

4 

3 

.525 

33497 

33504  :  33512 

33520 

33527 

33535 

33543 

33551  33558 

33566 

5 

4 

.526  33574 

33581  !  33589 

33597 

33605 

33612 

33620 

33628  33636 

33643 

6 

5 

.527 

33651 

33659  1  33667 

33674 

33682 

33690 

33698 

33705  33713 

83721 

7 

5 

.528 

33729 

33736  33744 

33752 

33760 

38768 

33775 

33783  33791 

33799 

8 

6 

.529 

33806 

33814  33822 

33830 

33838 

33845 

33853 

33861  1 33869 

33877 

9 

7 

.530 

33884 

33892  33900 

33908 

33916 

33923 

33931 

33939 

33947 

83955 

.531 

33963 

33970  1  33978 

33986 

33994 

34002 

34009 

34017 

34025 

34033 

1 

1 

.532 

34041 

34049  1  34056 

34064 

34072 

34080 

34088 

34096 

34104 

84111 

2 

2 

.533 

34119 

34127 

34135 

34143 

34151 

34159 

34166 

34174 

34182 

84190 

3 

2 

.534 

34198 

34206 

34214 

34222 

34229 

34237 

34245 

34253 

34261  :  34269 

4 

3 

.535 

34277 

34285 

34293 

34300 

34308 

34316 

34324 

34332 

34340  1  34348 

5 

4 

.536 

34356 

34364 

34372 

34380 

34387 

34395 

34403 

34411 

34419  1  34427 

6 

5 

.537 

34435 

34443 

34451 

34459 

34467 

34475 

34483 

34491 

34498  '  34506 

7 

6 

.538 

34514 

34522 

34530 

34538 

34546 

34554 

34562 

34570 

34578  34586 

8 

6 

.539 

34594 

34602 

34610 

34618 

34626 

34634 

34642 

34650 

34658  34666 

9 

7 

.540 

34674 

34682 

34690 

34698 

34706 

34714 

34722 

34730 

34738 

34746 

.541 

34754 

34762 

34770 

34778 

34786 

34794 

34802 

34810 

34818 

84826 

1 

1 

.542 

34834 

34842 

34850 

34858 

34866 

34874 

34882 

34890 

34898 

84906 

2 

2 

.543 

34914 

34922 

34930 

34938 

34946 

34954 

34962 

34970 

34978 

84986 

3 

2 

.544 

34995 

35003 

35011 

35019 

35027 

35035 

35043 

35051 

35059 

85067 

4 

3 

.545 

35075 

35083  '  35091 

35099 

35108 

35116 

35124 

35132 

35140 

35148 

5 

4 

.546 

35156 

35164 !  35172 

35180  35188 

35197 

35205 

35213 

35221 

35229 

6 

5 

.547 

35237 

35245  :  35253 

35261  35270 

35278 

35286 

35294 

35302 

85310 

7 

6 

.548 

35318 

35326  1  35335 

35343  1  35351 

35359 

35367 

35375 

35383 

85892 

8 

6 

.549 

35400 

35408 

35416 

35424  i  35432 

i 

35441  i  35449 

1 

35457 

35465 

85473 

9 

7 

Log. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

TABLE     LXXXTI. 

ANTI-LOGARITHMS,  OR  NUMBERS  TO  LOGARITHMS. 


*245 


Log. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.P. 

.550 

35481 

35490 

35498 

35506 

35514 

35522 

35530 

35539 

35547 

35555 

.551 

35563 

35571 

35580 

35588 

35596 

35604 

35612 

35620 

35629 

35637 

1 

1 

.552 

35645 

35653 

35662 

35670 

35678 

35686 

35694 

35703 

35711 

35719 

2 

2 

.553 

35727 

35736 

35744 

35752 

35760 

35768 

35777 

35785 

35793 

35801 

3 

2 

.554 

35810 

35818 

35826 

35834 

35843 

35851 

35859 

35867 

35876 

35884 

4 

3 

.555 

35892 

35900 

35909 

35917 

35925 

35934 

35942 

35950 

35958 

35967 

5 

4 

.556 

35975 

35983 

35992 

36000 

36008 

36016 

36025 

36033 

36041 

36050 

6 

5 

.557 

36058 

36066 

36074 

36083 

36091 

36099 

36108 

36116 

36124 

36133 

7 

6 

.558 

36141  36149 

36158 

36166 

36174 

36183 

36191 

36199 

36208 

36216 

8 

7 

.559 

36224  36233 

36241 

36249 

36258 

36266 

36274 

36283 

36291 

36299 

9 

7 

.560 

36308  36316 

36325 

36333 

36341 

36350 

36358 

36366 

36375 

36383 

.561 

36392 

36400 

36408 

36417 

36425 

36433 

36442 

36450 

36459 

36467 

1 

1 

.562 

36475 

36484 

36492 

36501 

36509 

36517 

36526 

36534 

36543 

36551 

2 

2 

.563 

36559 

36568 

36576 

36585 

36593 

36602 

36610 

36618 

36627 

36635 

3 

3 

.564 

36644 

36652 

36661 

36669 

36678 

36686 

36694 

36703 

36711 

36720 

4 

3 

.565 

36728 

36737 

36745 

36754 

36762 

36771 

36779 

36787 

36796 

36804 

5 

4 

.566 

36813 

36821 

36830 

36838 

36847 

36855 

36864 

36872 

36881 

36889 

6 

5 

.567 

36898 

36906 

36915 

36923 

36932 

36940 

36949 

36957 

36966 

36974 

7 

6 

.568 

36983 

36991 

37000 

37008 

37017 

37025 

37034 

37042 

37051 

37060 

8 

7 

.569 

37068 

37077 

37085 

37094 

37102 

37111 

37119 

37128 

37136 

37145 

9 

8 

.570 

37154 

37162 

37171 

37179 

37188 

37196 

37205 

37213 

37222 

37231 

.571 

37239 

37248 

37256 

37265 

37273 

37282 

37291 

37299 

37308 

37316 

1 

1 

.572 

37325 

37334 

37342 

37351 

37359 

37368 

37377 

37385 

37394 

37402 

2 

2 

.573 

37411 

37420 

37428 

37437 

37446 

37454 

37463 

37471 

37480 

37489 

3 

3 

.574 

37497 

37506 

37515 

37523 

37532 

37540 

37549 

37558 

37566 

37575 

4 

3 

.575 

37584 

37592 

37601 

37610 

37618 

37627 

37636 

37644 

37653 

37662 

5 

4 

.576 

37670 

37679 

37688 

37696 

37705 

37714 

37722 

37731 

37740 

37749 

6 

5 

.577 

37757 

37766 

37775 

37783 

37792 

37801 

37809 

37818 

37827 

37836 

7 

6 

.578 

37844 

37853 

37862 

37870 

37879 

37888 

37897 

37905 

37914 

37923 

8 

7 

.579 

37931 

37940 

37949 

37958 

37966 

37975 

37984 

37993 

38001 

38010 

9 

8 

.580 

38019 

38028 

38036 

38045 

38054 

38063 

38072 

38080 

38089 

38098 

.581 

38107 

38115 

38124  38133 

38142 

38150 

38159 

38168 

38177 

38186 

1 

1 

.582 

38194 

38203 

38212 

38221 

38230 

38238 

38247 

38256 

38265 

38274 

2 

2 

.583 

38282 

38291 

38300 

38309 

38318 

38327 

38335 

38344 

38353 

38362 

3 

3 

.584 

38371 

38380 

38388 

38397 

38406 

38415 

38424 

38433 

38441 

38450 

4 

4 

.585 

38459 

38468 

38477 

38486 

38495 

38503 

38512 

38521 

38530 

38539 

5 

4 

.586 

38548 

38557 

38566 

38574 

38583 

38592 

38601 

38610 

38619 

38628 

6 

5 

.587 

38637 

38646 

38654 

38663 

38672 

38681 

38690 

38699 

38708 

38717 

7 

6 

.588 

38726 

38735 

38744 

38753 

38761 

38770 

38779 

38788 

38797 

38806 

8 

7 

.589 

38815 

38824 

38833 

38842 

38851 

38860 

38869  1  38878 

38887 

38896 

9 

8 

.590 

38905 

38913 

38922 

38931 

38940 

38949 

38958  38967 

38976 

38985 

.591 

38994 

39003 

39012 

39021 

39030 

39039 

39048 

39057 

39066 

39075 

1 

1 

.592 

39084 

39093 

39102 

39111 

39120 

39129 

39138 

39147 

39156 

39165 

2 

2 

.593 

39174 

39183 

39192 

39201 

39210 

39219 

39228 

39237 

39246 

39255 

3 

3 

.594 

39264 

39274 

39283 

39292 

39301 

39310 

39319 

39328 

39337 

39346 

4 

4 

.595 

39355 

39364 

39373 

39382 

39391 

39400 

39409 

39418 

39428 

39437 

5 

5 

.596 

39446 

39455 

39464 

39473 

39482 

39491 

39500 

39509 

39518 

39528 

6 

5 

.597 

39537 

39546 

39555 

39564 

39573 

39582 

39591 

39600 

39610 

39619 

7 

6 

.598 

39628 

39637 

39646 

39655 

39664 

39673 

39683 

39692 

39701 

39710 

8 

7  . 

.599 

39T19 

39728 

39737 

39747 

39756 

39765 

39774 

39783 

39792 

39802 

9 

8 

Loo 

0 

1 

2 

3 

4 

6 

6 

7 

8 

9 

*246 


TABLE     LXXXII. 


ANTI-LOGARITHMS,  OR  NUMBERS  TO  LOGARITHMS. 


Log. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.P. 

.600 

39811 

,39820 

39829 

39838 

39847 

39857 

39866 

39875 

39884 

39893 

1  .601 

39902 

39912 

39921 

39930 

39939 

39948 

39958 

39967 ; 39976 

39985 

1 

1 

.602 

39994 

40004 

40013 

40022 

40031 

40041 

40050 

40059 

40068 

40077 

2 

2 

.603 

40087 

40096 

40105 

40114 

40124 

40133 

40142 

40151 

40161 

40170 

3 

3 

.604 

40179 

40188 

40198 

40207 

40216 

40225 

40235 

40244 

40253  40262 

4 

4 

.605 

40272 

40281 

40290 

40300 

40309 

40318 

40327 

40337 

40346  40355 

5 

5 

.606 

40365  !  40374 

40383 

40392 

40402 

40411 

40420 

40430 

40439  40448 

6 

6 

.607 

40458  5  40467 

40476 

40486 

40495 

40504 

40514 

40523  1  40532  !  40542 

7 

6 

.608 

40551  !  40560 

40570 

40579 

40588 

40598 

40607 

40616 

40626  1  40635 

8 

7 

.609 

40644  40654 

40663 

40672 

40682 

40691 

40701 

40710 

40719  40729 

9 

8 

.610 

40738  40747 

40757 

40766 

40776 

40785 

40794 

40804 

40813  40823 

.611 

40832 

40841 

40851 

40860 

40870 

40879 

40888 

4C898 

40907  40917 

1 

1 

.612 

40926 

40935 

40945 

40954 

40964 

40973 

40983 

40992 

41002  41011 

2 

2 

.613 

41020 

41030 

41039 

41049 

41058 

41068 

41077 

41087 

41096  1  41106 

3 

3 

.614 

41115 

41124 

41134 

41143 

41153 

41162 

41172 

41181 

41191 

41200 

4 

4 

.615 

41210 

41219 

41229 

41238 

41248 

41257 

41267 

41276 

41286 

41295 

5 

5 

.616 

41305  ;  41314 

41324 

41333 

41343 

41352 

41362 

41371 

41381 

41390 

6 

6 

.617 

41400 

41410 

41419 

41429 

41438 

41448 

41457 

41467 

41476  1  41486 

7 

7 

.618 

41495 

41505 

41515 

41524 

41534 

41543 

41553 

41562 

41572  i  41581 

8 

8 

.619 

41591 

41601 

41610 

41620 

41629 

41639 

41649 

41658 

41668 

41677 

9 

9 

.620 

41687 

41697 

41706 

41716 

41725 

41735 

41745 

41754 

41764 

41773 

.621 

41783 

41793 

41802 

41812 

41822 

41831 

41841 

41850 

41860  1  41870 

1 

1 

.622 

41879 

41889 

41899 

41908 

41918 

41928 

41937 

41947 

41957 

41966 

2 

2 

.623 

41976 

41986 

41995 

42005 

42015 

42024 

42034 

42044 

42053 

42063 

3 

3 

.624 

42073 

42082 

42092 

42102 

42111 

42121 

42131 

42141 

42150  42160 

4 

4 

.625 

42170 

42179 

42189 

42199 

42209 

42218 

42228 

42238 

42247  42257 

5 

5 

.626 

42267 

42277 

42286 

42296 

42306 

42316 

42325 

42335 

42345  !  42355 

6 

6 

.627 

42364 

42374 

42384 

42394 

42403 

42413 

42423 

42433 

42442  !  42452 

7 

7 

.628 

42462 

42472 

42482 

42491 

42501 

42511 

42521 

42530  I  42540  ;  42550 

8 

8 

.629 

42560  42570 

42579 

42589 

42599 

42609 

42619 

42628 

42638 

42648 

9 

9 

.630 

42658  42668 

42678 

4^687 
42786 

42697 

42707 

42717 !  42727 

42737 

42746 

.631 

42756  !  42766  42776  ! 

42796 

42806 

42815 

42825  !  42835 

42845 

1 

1 

.632 

42855  42865 

42875 

42884 

42894 

42904 

42914 

42924  42934  42944 

2 

2 

.633 

42954  42964. 

42973 

42983 

42993 

43003 

43013 

43023  !  43033  43043 

3 

3 

.634 

43053 

43063 

43072 

43082 

43092 

43102 

43112  43122  ;  43132  43142 

4 

4 

.635 

43152 

43162 

43172 

43182 

43192 

43202  43212  43222 

43231  43241 

5 

5 

.636 

43251 

43261 

43271 

43281 

43291 

43301  43311  43321 

43331  •  43341 

6 

6 

.637 

43351 

43361 

43371 

43381 

43391 

43401  43411  43421 

43431  '  43441 

7 

7 

.638 

43451 

43461 

43471 

43481 

43491 

43501  43511  43521 

43531  43541 

8 

8 

.639 

43551 

43561 

43571 

43581 

43591 

43601  43611 

43621 

43631 

43642 

9 

9 

.640 

43652 

43662 

43672 

43682 

43692 

43702  43712 

43722 

43732 

43742 

.641 

43752 

43762 

43772 

43782 

43793 

43803  43813  43823 

43833  43843 

1 

1 

.642 

43853 

43863 

43873 

43883 

43893 

43904  43914  43924 

43934  43944 

2 

2 

.643 

43954  43964 

43974 

43985 

43995 

44005  44015 

44025 

44035  '  44045 

3 

3 

.644 

44055 

44066  44076  1 

44086 

44096 

44106  44116 

44127 

44137 

44147 

4 

4 

.645 

44157 

44167 

44177 

44188 

44198 

44208 

44218 

44228 

44238 

44249 

5 

5 

.646 

44259 

44269 

44279 

44289 

44300 

44310 

44320 

44330 

44340 

44351 

6 

6 

.647 

44361 

44371 

44381 

44392 

44402 

44412 

44422 

44432 

44443 

44453 

7 

7 

.648 

44463 

44473 

44484 

44494 

44504 

44514 

44525 

44535 

44545 

44555 

8 

8 

.649 

44566 

44576 

44586 

44596 

44607 

44617 

44627 

44638 

44648 

44658 

9| 

9 

Log, 

0 

1 

2 

3 

4    5 

6 

7 

8 

9 

- 

TABLE     LXXXII. 


^247 


ANTI-LOQARITHMS,  OR  NUMBERS  TO  LOGARITHMS. 


Loo. 

0 

1 

2 

3 

4 

6 

6 

7 

8 

9 

P.  P. 

.850 

44668 

44679 

44689 

44699 

44710 

44720 

44730 

44740 

44751 

44761 

.651 

44771 

44782 

44792 

44802 

44813 

44823 

44833 

44844 

44854 

44864 

1 

1 

.652 

44875 

44885 

44895 

44906 

44916 

44926 

44937 

44947 

44957 

44968 

2 

2 

.653 

44978 

44988 

44999 

45009 

45019 

45030 

45040 

45051 

45061 

45071 

3 

3 

.654 

45082 

45092 

45102 

45113 

45123 

45134 

45144 

45154 

45165 

45175 

4 

4 

.655 

45186 

45196 

45206 

45217 

45227 

45238 

45248 

45258 

45269 

45279 

5 

5 

.656 

45290 

45300 

45311 

45321 

45331 

45342 

45352 

45363 

45373 

45384 

6 

6 

.657 

45394 

45405 

45415 

45426 

45436 

45446 

45457 

45467 

45478 

45488 

7 

7 

.658 

45499 

45509 

45520 

45530 

45541 

45551 

45562 

45572 

45583 

45593 

8 

8 

.659 

45604 

45614 

45625 

45635 

45646 

45656 

45667 

45677 

45688 

45698 

9 

9 

.660 

45709 

45719 

45730 

45740 

45751 

45761 

45772 

45783 

45793 

45804 

.661 

45814 

45825 

45835 

45846 

45856 

45867 

45878 

45888 

45899 

45909 

1 

1 

.662 

45920 

45930 

45941 

45952 

45962 

45973 

45983 

45994 

46004 

46015 

2 

2 

.663 

46026 

46036 

46047 

46057 

46068 

46079 

46089 

46100 

46111 

46121 

3 

3 

.664 

46132 

46142 

46153 

46164 

46174 

46185 

46196 

46206 

46217 

46227 

4 

4 

.665 

46238 

46249 

46259 

46270 

46281 

46291 

46302 

46313 

46323 

46334 

5 

5 

.666 

46345 

46355 

46366 

46377 

46387 

46398 

46409 

46419 

46430 

46441 

6 

6 

.687 

46452 

46462 

46473 

46484 

46494 

46505 

46516 

46526 

46537 

46548 

7 

7 

.688 

46559 

46569 

46580 

46591 

46602 

46612 

46623 

46634 

46644 

46655 

8 

9 

.669 

46666 

46677 

46687 

46698 

46709 

46720 

46730 

46741 

46752 

46763 

9 

10 

.670 

46774 

46784 

46795 

46806 

46817 

46827 

46838 

46849 

46860 

46871 

.671 

46881 

46892 

46903 

46914 

46925 

46935 

46946 

46957 

46968 

46979 

1 

1 

.872 

46989 

47000 

47011 

47022 

47033 

47044 

47054 

47065 

47076 

47087 

2 

2 

.673 

47098 

47109 

47119 

47130 

47141 

47152 

47163 

47174- 

47185 

47195 

3 

3 

.674 

47206 

47217 

47228 

47239 

47250 

47261 

47272 

47282 

47293 

47304 

4 

4 

.675 

47315 

47326 

47337 

47348 

47359 

47370 

47381 

47391 

47402 

47413 

6 

5 

.878 

47424 

47435 

47446 

47457 

47468 

47479 

47490 

47501 

47512 

47523 

6 

7 

.677 

47534 

47544 

47555 

47566 

47577 

47588 

47599 

47610 

47621 

47632 

7 

8 

.878 

47643 

47654 

47665 

47676 

47687 

47698 

47709 

47720 

47731 

47742 

8 

9 

,879 

47753 

47764 

47775 

47786 

47797 

47808 

47819 

47830 

47841 

47852 

9 

10 

.880 

47863 

47874 

47885 

47896 

47907 

47918 

47929 

47940 

47951 

47962 

.881 

47973 

47984 

47995 

48006 

48018 

48029 

48040 

48051 

48062 

48073 

1 

1 

.682 

48084 

48095 

48106 

48117 

48128 

48139 

48150 

48161 

48173 

48184 

2 

2 

.883  48195 

48206 

48217 

48228 

48239 

48250 

48261 

48273 

48284 

48295 

3 

3 

.884 

48306 

48317 

48328 

48339 

48350 

48362 

48373 

48384 

48395 

48406 

4 

4 

.685 

48417 

48428 

48440 

48451 

48462 

48473 

48484 

48495 

48507 

48518 

5 

6 

.688 

48529 

48540 

48551 

48562 

48574 

48585 

48596 

48607 

48618 

48630 

8 

7 

.687 

48641 

48652 

48663 

48674 

48686 

48697 

48708 

48719 

48730 

48742 

7 

8 

.888 

48753 

48764 

48775 

48787 

48798 

48809 

48820 

48831 

48843 

48854 

8 

9 

.889 

48865 

48876 

48888 

48899 

48910 

48922 

48933 

48944 

48955 

48967 

9 

10 

.690 

48978 

48989 

49000 

49012 

49023 

49034 

49046 

49057 

49068 

49079 

.891 

49091 

49102 

49113 

49125 

49136 

49147 

49159 

49170 

49181 

49193 

1 

1 

.692 

49204 

49215 

49227 

49238 

49249 

49261 

49272 

49283 

49295 

49306 

2 

2 

.693 

49317 

49329 

49340 

49351 

49363 

49374 

49386 

49397 

49408 

49420 

3 

3 

.694 

49431 

49442 

49454 

49465 

49477 

49488 

49499 

49511 

49522 

49534 

4 

5 

.695 

49545 

49556 

49568 

49579 

49591 

49602 

49614 

49625 

49636 

49648 

5 

6 

.696 

49659 

49671 

49682 

49694 

49705 

49716 

49728 

49739 

49751 

49762 

6 

7 

.697 

49774 

49785 

49797 

49808 

49820 

49831 

49843 

49854 

49865 

49877 

7 

8 

.898 

49888 

49900 

49911 

49923 

49934 

49946 

49957 

49969 

49980 

49992 

8 

9 

.899 

50003 

50015 

50026 

50038 

50050 

50061 

50073 

50084 

50096 

50107 

9 

1 

10 

Loo. 

0 

1 

2 

3 

4 

6 

6 

7 

8 

9 

, 

248 


TABLE     LXXXII. 


ANTI-LOGARITHMS,  OR  NUMBERS  TO  LOGARITHMS. 


Loa. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

.700 

50119 

50130 

50142 

50153 

50165 

50176 

50188 

50200 

50211 

50223 

.701 

50234 

50246 

50257 

50269  :  50281 

50292 

50304 

50315 

50327 

50338 

1 

1 

.702 

50350 

50362 

50373 

50385  50396 

50408 

50420 

50431 

50443 

50455 

2 

2 

.703 

50466 

50478 

50489 

50501  50513 

50524 

50536 

50548 

50559 

50571 

3 

4 

.704 

50582 

50594 

50606 

50617  50629 

50641 

50652 

50664 

50676 

50687 

4 

6 

.705 

50699 

50711 

50722 

50734  50746 

50757 

50769 

50781 

50793 

50804 

5 

6 

.706 

50816 

50828 

50839 

50851 

50863 

50874 

50886 

50898 

50910 

50921 

6 

7 

.707 

50933 

50945 

50957 

50968 

50980 

50992 

51004 

51015 

51027 

51039 

7 

8 

.708 

51050 

51062 

51074 

51086 

51098 

51109 

51121 

511.33 

51145 

51156 

8 

9 

.709 

51168 

51180 

51192 

51204 

51215 

51227 

51239 

51251 

51263 

51274 

9 

11 

.710 

51286 

51298 

51310 

51322 

51333 

51345 

51357 

51369 

51381 

51393 

.711 

51404 

51416 

51428 

51440  51452 

51464 

51475 

51487 

51499 

51511 

1 

1 

.712 

51523 

51535 

51547 

51558  j  51570 

51582 

51594 

51606 

51618 

51630 

2 

2 

.713 

51642 

51654 

51665 

51677  1  51689 

51701 

51713 

51725 

51737 

51749 

3 

4 

.714 

51761 

51773 

51785 

51796  51808 

51820 

51832 

51844 

51856 

51868 

4 

6 

.715 

51880 

51892 

51904 

51916  51928 

51940 

51952 

51964 

51976 

51988 

5 

6 

.716 

52000 

52012 

52024 

52036  52048 

52060 

52071 

52083 

52095 

52107 

6 

7 

.717 

52119 

52131 

52143 

52155  52167 

52180 

52192 

52204 

52216 

52228 

7 

8 

.718 

52240 

52252 

52264 

52276 

52288 

52300 

52312 

52324 

52336 

52348 

8 

10 

.719 

52360 

52372 

52384 

52396 

52408 

52420 

52432 

52445 

52457 

62469 

9 

11 

.720 

52481* 

52493 

52505 

52S17 

52529 

52541 

52553 

52565 

52578 

52590 

.721 

52602 

52614 

52626 

52638 

52650 

52662 

52674 

52687 

52699 

52711 

1 

1 

.722 

52723 

52735 

52747 

52759 

52772 

52784 

52796 

52808 

52820 

52832 

2 

2 

.723 

52845 

52857 

52869 

52881 

52893 

52905 

52918 

52930 

52942 

52954 

3 

4 

.724 

52966 

52979 

52991 

53003 

53015 

53027 

53040 

53052 

53064 

53076 

4 

6 

.725 

53088 

53101 

53113 

53125 

53137 

53150 

53162 

53174 

53186 

53199 

5 

6 

.726 

53211 

53223 

53235 

53248 

53260 

532  >2 

53284 

53297 

53309 

53321 

6 

7 

.727 

53333 

53346 

53358 

53370 

53383 

53395 

53407 

53420 

53432 

53444 

7 

9 

.728 

53456 

53469 

53481 

53493 

53506 

53518 

53530 

53543 

53555 

53567 

8 

10 

.729 

53580 

53592 

53604 

53617 

53629 

53641 

53654 

53666 

53678 

53691 

9 

11 

.730 

53703 

53716 

53728 

53740 

53753 

53765 

53777 

53790 

53802 

53815 

.731 

53827 

53839 

53852 

53864 

53877 

53889 

5390] 

53914 

53926 

53939 

1 

1 

.732 

53951 

53963 

53976 

53988 

54001 

54013 

54026 

54038 

54051 

54063 

2 

3 

.733 

54075 

54088 

54100 

54113 

54125 

54138 

54150 

54163 

54175 

54188 

3 

4 

.734 

54200 

54213 

54225 

54238 

54250 

54263 

54275 

54288 

54300 

54313 

4 

6 

.735 

54325 

54338 

54350 

54363 

54375 

54388 

54400 

54413 

54425 

54438 

5 

6 

.736 

54450 

54463 

54475 

54488 

54500 

54513 

54526 

54538 

54551 

54563 

6 

8 

.737 

54576 

54588 

54601 

54613 

54626 

54639 

54651 

54664 

54676 

64689 

7 

9 

.738 

54702 

54714 

54727 

54739 

54752 

54765 

54777 

54790 

54802 

54815 

8 

10 

.739 

54828 

54840 

54853 

54866 

54878 

54891 

54903 

54916 

54929 

64941 

9 

11 

.740 

54954 

54967 

54979 

54992 

55005 

55017 

55030 

55043 

55055 

55068 

.741 

55081 

55093 

55106 

55119 

55132 

55144 

55157 

55170 

55182 

55195 

1 

1 

.742 

55208 

55220 

55233 

55246 

55259 

55271 

55284 

55297 

55310  55322 

2 

3 

.743 

55335 

55348 

55360 

55373 

55386 

55399 

55412 

55424 

55437 

55450 

3 

4 

.744 

55463 

55475 

55488 

55501 

55514 

55526 

55539 

55552 

55565 

55678 

4 

5 

.745 

55590 

55603 

55616 

55629 

55642 

55654 

55667 

55680 

55693  55706 

5 

6 

.746 

55719 

55731 

55744 

55757 

55770 

55783  1  55796 

55808 

55821  55834 

6 

8 

.747 

55847 

55860 

55873 

55886 

55898 

55911  1  55924 

55937 

55950  i  55963 

7 

9 

.748 

55976 

55989 

56002 

56014 

56027 

56040 

56053 

56066 

56079 

56092 

8 

10 

.749 

56105 

56118 

56131 

56144 

56156 

56169 

56182 

56195 

56208 

56221 

9 

12 

Log. 

0 

1 

2 

3 

4 

5 

6 

7    8 

9 

TABLE     LXXXII. 

ANTI-LOGARITHMS,  OR  NUMBERS  TO  LOGARITHMS. 


*249 


Log. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.P. 

.750 

56234 

56247 

56260 

56273 

56286 

56299 

56312 

56325 

56338 

56351 

.751 

56364 

56377 

56390 

56403 

56416 

56429 

56442 

56455 

56468 

56481 

1  1 

.752 

56494 

56507 

56520 

56533 

56546 

56559 

56572 

56585 

56598 

66611 

2  3 

.753 

56624 

56637 

56650 

56663 

56676 

56689 

56702 

56715 

56728 

66741 

3  4 

.754 

56754 

56768 

56781 

56794 

56807 

56820 

56833 

56846 

56859 

66872 

4  5 

.755 

56885 

56898 

56911 

56925 

56938 

56951 

56964 

56977 

56990 

67003 

5  7 

.756 

57016 

57030 

57043 

57056 

57069 

57082 

57095 

57108 

57122 

57135 

6  8 

.757 

57148 

57161 

57174 

57187 

57201 

57214 

57227 

57240 

67253 

67266 

7  9 

.758 

57280 

57293 

57306 

57319 

57332 

57346 

57359 

57372 

57385 

67398 

8  10 

.759 

57412 

57425 

57438 

57451 

57465 

57478 

57491 

57504 

57517 

67531 

9  12 

.760 

57544 

57557 

57570 

57584 

57597 

57610 

57624 

57637 

57650 

57663 

.761 

57677 

57690 

57703 

57717 

57730 

57743 

57756 

57770 

67783 

57796 

1  1 

.762 

57810 

57823 

57836 

57850 

57863 

57876 

57890 

57903 

57916 

57930 

2  3 

.763 

57943 

57956 

57970 

57983 

57996 

58010 

5S023 

58036 

58050 

58063 

3  4 

.764 

58076 

58090 

58103 

58117 

58130 

58143 

58157 

58170 

58184 

68197 

4  5 

.765 

58210 

58224 

58237 

58251 

58264 

58277 

58291 

58304 

58318 

58331 

5  7 

.766 

58345 

58358 

58371 

58385 

58398 

58412 

58425 

58439 

68452 

58466 

6  8 

.767 

58479 

58492 

58506 

58519 

58533 

58546 

58560 

58573 

58587 

58600 

7  9 

.768 

58614 

58627 

58641 

58654 

58668 

58681 

58695 

58708 

58722 

68735 

8  11 

.769 

58749 

58762 

58776 

58790 

58803 

58817 

58830 

58844 

58857 

58871 

9  12 

.770 

58884 

58898 

58911 

58925 

58939 

58952 

58966 

58979 

58993 

69007 

.771 

59020 

59034 

59047 

59061 

59074 

59088 

59102 

59115 

59129 

69143 

1  1 

.772 

59156 

59170 

59183 

59197 

59211 

59224 

59238 

59252 

59265 

69279 

2  3 

.773 

59293 

59306 

59320 

59334 

59347 

59361 

59375 

59388 

59402 

59416 

3  4 

.774 

59429 

59443 

59457 

59470 

59484 

59498 

59511 

59525 

59539 

69553 

4  6 

.775 

59566 

59580 

59594 

59607 

59621 

59635 

59649 

59662 

59676 

69690 

5  7 

.776 

59704 

59717 

59731 

59745 

59759 

59772 

59786 

59800 

69814 

59827 

6  8 

.777 

59841 

59855 

59869 

59883 

59896 

59910 

59924 

59938 

69951 

69965 

7   10 

.778 

59979 

59993 

60007 

60021 

60034 

60048 

60062 

60076 

60090 

60104 

B  11 

.779 

60U7 

60131 

60145 

60159 

60173 

60187 

60200 

60214 

60228 

60242  < 

9  12 

.780 

60256 

60270 

60284 

60298 

60311 

60325 

60339 

60353 

60367 

60381 

.781 

60395 

60409 

60423 

60437 

60451 

60464 

60478 

60492 

60506 

60520  ] 

I  1 

.782 

60534 

60548 

60562 

60576 

60590 

60604 

60618 

60632 

60646 

60660  i 

I    3 

.783 

60674 

60688 

60702 

60716 

p0730 

60744 

60758 

60772 

60786 

60799  { 

J  4 

.784 

60814 

60828 

60842 

60856 

60870 

60884 

60898 

60912 

60926 

60940  ^ 

L  6 

.785 

60954 

60968 

60982 

60996 

61010 

61024 

61038 

61052 

61066 

61080  t 

)  7 

.786 

61094 

61108 

61122 

61136 

61150 

61165 

61179 

61193 

61207 

61221  i 

J  8 

.787 

61235 

61249 

61263 

61277 

61291 

61306 

61320 

61334 

61348 

61362  : 

f   10 

.788 

61376 

61390 

61404 

61419 

61433 

61447 

61461 

61475 

61489 

61504  i 

1  11 

.789 

61518 

61532 

61546 

61560 

61574 

61589 

61603 

61617 

61631 

61645  i 

1  13 

.790 

61660 

61674 

61688 

61702 

61716 

61731 

61745 

61759 

61773 

61787 

.791 

61802 

61816 

61830 

61844 

61859 

61873 

61887 

61901 

61916 

61930  1 

1 

.792 

61944 

61958 

61973 

61987 

62001 

62015 

62030 

62044 

62058 

62073  2 

3 

.793 

62087 

62101 

62116 

62130 

62144 

62158 

62173 

62187 

62201 

62216  a 

4 

.794 

62230 

62244 

62259 

62273 

62287 

62302 

62316 

62330 

62345 

62359  4 

6 

.795 

62373 

62388 

62402 

62417 

62431 

62445 

62460 

62474 

62488 

62503  6 

7 

.796 

62517 

62532 

62546 

62560 

62575 

62589 

62604 

62618 

62633 

62647  6 

9 

.797 

62661 

62676 

62690 

62705 

62719 

62734 

62748 

62762 

62777 

62791  7 

10 

.798 

62806 

62820 

62835 

62849 

62864 

62878 

62893 

62907 

62922 

62936  8 

11 

.799 

62951 

62965 

62980 

62994 

63009 

63023 

63038 

63052 

63067 

63081  9 

13 

Loo. 

0 

1 

2    3 

4 

5 

6 

7 

8 

9 

-  I 

*250 


TABLE     LXXXII. 


ANTI-LOGARITHMS,  OR  NUMBERS  TO  LOGARITHMS. 


Log. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.P. 

.800 

63096 

63110 

63125 

63139 

63154 

63168 

63183 

63198 

63212 

63227 

.801 

63241 

63256 

63270 

63285 

63299 

63314 

63329 

63343 

63358 

63372 

1  1 

.802 

63387 

63402 

63416 

63431 

' 63445 

63460 

63475 

63489 

63504 

63518 

2  3 

.803 

63533 

63548 

63562  1  63577 

63592 

63606 

63621  i  63636 

63650 

63665 

3  4 

.804 

63680 

63694 

63709  63724 

63738 

63753 

63768 

63782 

63797 

63812 

4  6 

.805 

63826 

63841 

63856  63870 

63885 

63900 

63915 

63929 

63944 

63959 

5  7 

.806 

63973 

63988 

64003  64018 

64032 

64047 

64062 

64077 

64091 

64106 

6  9 

.807 

64121 

64136 

64150  64165 

64180 

64195 

64210 

64224 

64239 

64254 

7  10 

.808 

64269 

64284 

64298  64313 

64328 

64343 

64358 

64372 

64387 

64402 

8  12 

.809 

64417 

64432 

64447 

64461 

64476 

64491 

64506 

64521 

64536 

64551 

9  13 

.810 

64565 

64580 

64595 

64610 

64625 

64640 

64655 

64670 

64684 

64699 

.811 

64714 

64729 

64744 

64759 

64774 

64789 

64804 

64819' 

64834 

64849 

1  2 

.812 

64863 

64878 

64893  i  64908 

64923 

64938 

64953 

64968 

64983 

64998 

2  3 

.813 

65013 

65028 

65043 

65058 

65073 

65088 

65103 

65118 

65133 

65148 

3  5 

.814 

65163 

65178 

65193 

65208 

65223 

65238 

65253 

65268 

65283 

65298 

4  6 

.815 

65313 

65328 

65343 

65358 

65373 

65388 

65403 

65418 

65433 

65449 

5  8 

.816 

65464 

65479 

65494 

65509 

65524 

65539 

65554 

! 65569 

65584 

65599 

6  9 

.817 

65615 

65630 

65645 

65660 

65675 

65690 

65705 

65720 

65736 

65751 

7  11 

.818 

65766 

65781 

65796 

65811 

65826 

65842 

65857 

-65872 

65887 

65902 

B  12 

.819 

65917 

65933 

65948 

65963 

65978 

65993 

66009 

66024 

66039 

66054 

9  14 

.820 

66069 

66085 

66100 

66115 

66130 

66145 

66161 

66176 

66191 

66206 

.821 

'66222 

66237 

66252 

66267 

66283 

66298 

66313 

66328 

66344 

66359 

1  2 

.822 

66374 

66390 

66405 

66420 

66435 

66451 

66466 

66481 

66497 

66512 

2    3 

.823 

66527 

66543 

66558 

66573 

66589 

66604 

66619 

66635 

66650 

66665 

3  5 

.824 

66681 

66696 

66711 

66727 

66742 

66757 

66773 

66788 

66804 

66819  ' 

1  6 

.825 

66834 

66850 

66865 

66881 

66896 

66911 

66927 

66942 

66958 

66973 

5  8 

.826 

66988 

67004 

67019 

67035 

67050 

67066 

67081 

67097 

67112 

67127  < 

5  9 

.827 

67143 

67158 

67174 

67189 

67205 

67220 

67236 

67251 

67267 

67282  • 

7   11 

.828 

67298 

67313 

67329 

67344 

67360 

67375 

67391 

67406 

67422 

67437  J 

3  12 

.829 

67453 

67468 

67484 

67499 

67515 

67531 

67546 

67562 

67577 

67593  1 

J  14 

.830 

67608 

67624 

67639 

67655 

67671 

67686 

67702 

67717 

67733 

67749 

.831 

67764 

67780 

67795 

67811 

67827 

67842 

67858 

67873 

67889 

67905  ] 

I  2 

.832 

67920 

67936 

67952 

67967 

67983 

67999 

68014 

68030 

68046 

68061  i 

I     3 

.833 

68077 

68093 

68108 

68124 

68140 

68155 

68171 

68187 

68202 

68218  i 

)      0 

.834 

68234  68250  | 

68265 

68281 

68297 

68312 

68328 

68344 

68360 

68375  4 

L  6 

.835 

68391 

68407 

68423 

68438 

68454 

68470 

68486 

68501 

68517  68533  I  t 

)  8 

.836 

68549 

68565 

68580 

68596 

68612 

68628 

68644 

68659 

68675  68691  |  ( 

}  9 

.837 

68707 

68723 

68738 

68754 

68770 

68786 

68802 

68818 

68834  j  68849  !1 

r  11 

.838 

68865 

68881 

68897 

68913 

68929 

68945 

68960 

68976 

68992  !  69008  i 

1  13 

.839 

69024 

69040 

69056 

69072 

69088 

69103 

69119 

69135 

69151  69167  £ 

)  14 

.840 

69183 

69199 

69215  69231 

69247 

69263 

69279 

69295 

69311 

69327 

.841 

69343 

69359 

69375  !  69390 

69406 

69422 

69438 

69454 

69470 

69486  1 

2 

.842  69502  !  69518 

69534  69550 

69566 

69582 

69599 

69615 

69631 

69647  2 

1  3 

.843  69663  |  69679 

69695 

69711 

69727 

69743 

69759 

69775 

69791 

69807  a 

5 

.844 

69823  69839 

69855 

69871 

69888 

69904 

69920 

69936 

69952 

69968  4 

6 

.845 

69984  70000 

70016 

70033 

70049 

70065 

70081 

70097 

70113 

70129  5 

8 

.846 

70146 

70162 

70178 

70194 

70210 

70226 

70243 

70259 

70275 

70291  6 

10 

.847 

70307 

70323 

70340  1  70356 

70372 

70388 

70404 

70421 

70437 

70453  7 

11 

.848 

70469 

70486 

70502  1  70518 

70534 

70550 

70567 

70583 

70599 

70615  8 

113 

.849 

70632 

70648 

70664 

70681 

70697 

70713 

70729 

70746 

70762  70778  9 

14 

Loo. 

0 

1 

2 

3 

4 

6 

6 

7 

8 

9 

TABLE     LXXXII. 


♦251 


ANTI-LOGARITHMS,  OR  NUMBERS  TO  LOGARITHMS. 


Log. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

.850 

70795  70811 

70827 

70843 

70860 

70876 

70892 

70909 

70925 

70941 

.851 

70958  :  70974 

70990  71007 

71023 

71040 

71056 

71072 

71089 

71105 

1  2 

.852 

71121 

71138 

71154  71170 

71187 

71203 

71220 

71236 

71252 

71269 

2  3 

.853 

71285 

71302 

71318  71335 

71351 

71367 

71384 

71400 

71417 

71433 

3  5 

.854 

71450 

71466 

71483  71499 

71515 

71532 

71548 

71565 

71581 

71598 

4  7 

.855 

71614 

71631 

71647  71664 

71680 

71697 

71713 

71730 

71746 

71763 

5  8 

.856 

71779 

71796 

71812  '  71829 

71846 

71862 

71879 

71895 

71912 

71928 

6  10 

.857 

71945 

71961 

71978 

71995 

72011 

72028 

72044 

72061 

72078 

72094 

7  12 

.858 

72111 

72127 

72144 

; 72161 

72177 

72194 

72210 

72227 

72244 

72260 

8  13 

.859 

72277 

72294 

72310 

72327 

72344 

72360 

72377 

72394 

72410 

72427 

9  15 

.860 

72444 

72460 

72477 

72494 

72510 

72527 

72544 

72560 

72577 

72594 

.861 

72611 

72627 

72644 

72661 

72678 

72694 

72711 

72728 

72744 

72761 

1  2 

.862 

72778 

72795 

72812 

1 72828 

72845 

72862 

72879 

72895 

72912 

72929 

2  3 

.863 

72946 

72963 

72979 

: 72996 

73013 

73030 

73047 

73063 

73080 

73097 

3  6 

.864 

73114 

73131 

73148 

73164 

73181 

73198 

73215 

73232 

73249 

73266 

4  7 

.865 

73282 

73299 

73316 

73333 

73350 

73367 

73384 

73401 

73418 

73434 

5  8 

.866 

73451 

73468 

73485 

73502 

73519 

73536 

73553 

73570 

73587 

73604 

6  10 

.867 

73621 

73638 

73655 

73672 

73689 

73706 

73722 

73739 

73756 

73773 

7  12 

.868 

73790 

73807 

73824 

73841 

73858 

73875 

73892 

73909 

73926 

73943 

8  13 

.869 

73961 

73978 

73995 

74012 

74029 

74046 

74063 

74080 

74097 

74114 

9  15 

.870 

74131 

74148 

74165 

74182 

74199 

74216 

74234 

74251 

74268 

74285 

.871 

74302 

74319 

74336 

74353 

74370 

74388 

74405 

74422 

74439 

74456 

1  2 

.872 

74473 

74490 

74508 

74525 

74542 

74559 

74576 

74593 

74611 

74628 

2  3 

.873 

74645 

74662 

74679 

74696 

74714 

74731 

74748 

74765 

74783 

74800 

3  5 

.874 

74817 

74834 

74851 

74869 

74886 

74903 

74920 

74938 

74955 

74972  - 

4  7 

.875 

74989 

75007 

75024 

75041 

75059 

75076 

75093 

75110 

75128 

75145  j  . 

5  9 

.876 

75162 

75180 

75197 

75214 

75232 

75249 

75266 

75284 

75301 

75318  i  ( 

5  10 

.877 

75336 

75353 

75370 

75388 

75405 

75422 

75440 

75457 

75474 

75492  ' 

7   12 

.878 

75509 

75527 

75544 

75561 

75579 

75596 

75614 

75631 

75648 

75666  i 

J  14 

.879 

75688 

75701 

75718 

75736 

75753 

75770 

75788 

75805 

75823 

75840  i 

)  16 

.880 

75858 

75875 

75893 

75910 

75928 

75945 

75963 

75980 

75998 

76015 

.881 

76033 

76050 

76068 

76085 

76103 

76120 

76138 

76155 

76173 

76190  ] 

L  2 

.882 

76208 

76225 

76243 

76261 

76278 

76296 

76313 

76331 

76348 

76366  S 

I    4 

.883 

76384 

76401 

76419 

76436 

76454 

76472 

76489 

76507 

76524 

76542  I  2 

t  5 

.884 

76560 

76577 

76595 

76613 

76630 

76648 

76666 

76683 

76701 

76718  4 

I  7 

.885  1 

76736 

76754 

76771 

76789 

76807 

76825 

76842 

76860 

76878 

76895  S 

»  9 

.886 

76913 

76931 

76948 

76966 

76984 

77002 

77019 

77037 

77055 

77073  € 

»  11 

.887 

77090 

77108 

77126 

77144 

77161 

77179 

77197 

77215 

77232 

77250  7 

12 

.888 

77268 

77286 

77304 

77321 

77339 

77357 

77375 

77393 

77411 

77428  8 

14 

.889  1  77446 

77464 

77482 

77500 

77518 

77535 

77553 

77571 

77589 

77607  9 

16 

.890  !  77625 

77643 

77660 

77678 

77696 

77714 

77732 

77750 

77768 

77786 

.891  1  77804 

77822 

77839  1 

77857 

77875 

77893 

77911 

77929 

77947 

77965  1 

2 

.892  77983 

78001 

78019 

78037 

78055 

78073 

78091 

78109 

78127 

78145  2 

4 

.893 

78163 

78181 

78199 

78217 

78235 

78253 

78271 

78289 

78307 

78325  3 

5 

.894 

78343 

78361 

78379 

78397 

78415 

78433 

78451 

78469 

78487 

78505  4 

7 

.895 

78524 

78542 

78560 

78578 

78596 

78614 

78632 

78650 

78668 

78686  5 

9 

.896 

78705 

78723 

78741  1  78759 

78777 

78795 

78813 

78832 

78850 

78868  6 

11 

.897 

78886 

78904 

78922  :  78941 

78959 

78977 

78995 

79013 

79031 

79050  7 

13 

.898 

79068 

79086 

79104  1  79122 

79141 

79159 

79177 

79195 

79214 

79232  8 

14 

.899 

79250 

79268 

79287 

79305 

79323 

79341 

79360 

79378 

79396 

79415  9 

16 

Log. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

i 

♦262 


TABLE    LXXXII. 

ANTI-LOGARITHMS,  OR  NUMBERS  TO  LOGARITHMS. 


Log. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.P. 

.900 

79433 

79451 

79469 

79488 

79506 

79524 

79543 

79561 

79579 

79598 

1.901 

79616 

79634 

79653 

79671 

79689 

79708 

79726 

79744 

79763 

79781 

1 

2 

.902 

79799 

79818 

79836 

79855 

79873 

79891 

79910 

79928 

79947 

79965 

2 

4 

.903 

79983 

80002 

80020 

80039 

80057 

80076 

80094 

80112 

80131 

80149 

3 

6 

.904 

80168 

80186 

80205 

80223 

80242 

80260 

80279 

80297 

80316 

80334 

4 

7 

.905 

80353 

80371 

80390 

80408 

80427 

80445 

80464 

80482 

80501 

80519 

5 

9 

.906 

80538 

80556 

80575 

80593 

80612 

80631 

80649 

\  80668 

80686 

80705 

6 

11 

.907 

80724 

80742 

80761 

80779 

80798 

80816 

80835 

80854 

80872 

80891 

7 

13 

.908 

80910 

80928 

80947 

80965 

80984 

81003 

81021 

81040 

81059 

81077 

8 

15 

.909 

81096 

81115 

81133 

81152 

81171 

81190 

81208 

81227 

81246 

81264 

9 

17 

.910 

81283 

81302 

81320 

81339 

81358 

81377 

81395 

81414. 

81433  81452 

.911 

81470 

81489 

81508 

81527 

81546 

81564 

81583 

81602 

81621  81639 

1 

2 

.912 

81658 

81677 

81696 

81715 

81733 

81752 

81771 

81790 

81809  81828 

2 

4 

.913 

81846 

81865 

81884 

81903 

81922 

81941 

81960 

81979 

81997  1  82016 

3 

6 

.914 

82035 

82054 

82073 

82092 

82111 

82130 

82149 

82167 

82186 

82205 

4 

8 

.915 

82224 

82243 

82262 

82281 

82300 

82319 

82338 

82357 

82376 

82395 

5 

9 

.916 

82414 

82433 

82452 

82471 

82490 

82509 

82528 

82547 

82566 

82585 

6 

11 

.917 

82604 

82623 

82642 

82661 

82680 

82699 

82718 

82737 

82756 

82775 

7 

13 

.918 

82794 

82813 

82832 

82851 

82871 

82890 

82909 

82928 

82947 

82966 

8 

15 

.919 

82985 

83004 

83023 

83042 

83062 

83081 

83100 

83119 

83138 

83157 

9 

17 

.920 

83176 

83196 

83215 

83234 

83253 

83272 

83291 

83311 

83330 

83349 

.921 

83368 

83387 

83407 

83426 

83445 

83464 

83483 

83503 

83522  83541 

1 

2 

.922 

83560 

83580 

83599 

83618 

83637 

83657 

83676 

83695 

83714  83734 

2 

4 

.923 

83753 

83772 

83792 

83811 

83830 

83849 

83869 

83888 

83907  i  83927 

3 

6 

.924 

83946 

83965 

83985 

84004 

84023 

84043 

84062 

84081 

84101 

84120 

4 

8 

.925 

84140 

84159 

84178 

84198 

84217 

84236 

84256 

84275 

84295 

84314 

5 

10 

.926 

84333 

84353 

84372 

84392 

84411 

84431 

84450 

84470 

84489 

84508 

6 

12 

.927 

84528 

84547 

84567 

84586 

84606 

84625 

84645 

84664 

84684 

84703 

7 

14 

.928 

84723 

84742 

84762 

84781 

84801 

84820 

•84840 

84859 

84879 

84898 

8 

16 

.929 

84918 

84938 

84957 

84977 

84996 

85016 

85035 

85055 

85075 

85094 

9 

17 

.930 

85114 

85133 

85153 

85173 

85192 

85212 

85231 

85251 

85271 

85290 

.931 

85310 

85330 

85349 

85369 

85389 

85408 

85428 

85448 

85467 

85487 

1 

2 

.932 

85507 

85526 

85546 

85566 

85585 

85605 

85625 

85645 

85664 

85684 

2 

4 

.933 

85704 

85724 

85743 

85763 

85783 

85803 

85822 

85842 

85862 

86882 

3 

6 

.934 

85901 

85921 

85941 

85961 

85981 

86000 

86020 

86040 

86060 

86080 

4 

8 

.935 

86099 

86119 

86139 

86159 

86179 

86199 

86218 

86238 

86258 

86278 

5 

10 

.936 

86298 

86318 

86338 

86357 

86377 

86397 

86417 

86437 

86457 

86477 

6 

12 

.937 

86497 

86517 

86537 

86557 

86576 

86596 

86616 

86636 

86656 

86676 

7 

14 

.938 

86696 

86716 

86736 

86756 

86776 

86796 

86816 

86836 

86856 

86876 

8 

16 

.939 

86896 

86916 

86936 

86956 

86976 

86996 

87016 

87036 

87056 

87076 

9 

18 

.940 

87096 

87116 

87136 

87157 

87177 

87197 

87217 

87237 

87257 

87277 

.941 

87297 

87317 

87337 

87357 

87378 

87398  i  87418  | 

87438 

87458 

87478 

1 

2 

.942  s 

87498 

87519  87539  1 

87559 

87579 

87599 

87619 

87640 

87660 

87680 

2 

4 

.943! 

87700  87720 

87740 

87761 

87781 

87801 

87821 

87842 

87862 

87882 

3 

6 

.944  J 

87902  87922 

87943 

87963 

87983 

88004 

88024 

88044 

88064 

88085 

4 

8 

.945^ 

88105 

88125 

88145 

88166 

88186 

88206 

88227 

88247 

88267 

88288 

5 

10 

.946 

88308 

88328 

88349 

88369 

88389 

88410 

88430 

88450 

88471 

88491 

6 

12 

.947 

88512 

88532 

88552 

88573 

88593 

88614 

88634 

88654 

88675 

88695 

7 

14 

.948 

88716  88736 

88756 

88777 

88797 

88818 

88838 

88859 

88879 

88900 

8 

16 

.949 

Log. 

88920 

88941 

88961 

88982 

89002 

89023 

89043 

89064 

89084 

89105 

9 

18 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

TABLE     LXXXII. 

ANTI-LOGARITHMS,   OR  NUMBERS  TO  LOGARITHMS. 


*^53 


Log. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.P. 

.950 

89125 

89146 

89166 

89187 

89207 

89228 

89248 

89269 

89289 

89310 

.951 

89331 

89351 

89372 

89392 

89413 

89433 

89454 

89475 

89495 

89516 

1 

2 

.952 

89536 

89557 

89578 

89598 

89619 

89640 

89660 

89681 

89702 

89722 

2 

4 

.953 

89743 

89764 

89784 

89805 

89826 

89846 

89867 

89888 

89908 

89929 

3 

6 

.954 

89950 

89970 

.89991 

90012 

90033 

90053 

90074 

90095 

90116 

90136 

4 

8 

.955 

90157 

90178 

90199 

90219 

90240 

90261 

90282 

90303 

90323 

90344 

5 

10 

.956 

90365 

90386 

904:07 

90427 

90448 

90469 

90490 

90511 

90532 

90552 

6 

12 

.957 

90573 

90594 

90615 

90636 

90657 

90678 

90698 

90719 

90740 

90761 

7 

15 

.958 

90782 

90803 

90824 

90845 

90866 

90887 

90908 

90928 

90949 

90970 

8 

17 

.959 

90991 

91012 

91033 

91054 

91075 

91096 

91117 

91138 

91159 

91180 

9 

19 

.960 

91201 

91222 

91243 

91264 

91285 

91306 

91327 

91348 

91369 

91390 

.961 

91411 

91432 

91453 

91474 

91496 

91517 

91538 

91559 

91580 

91601 

1 

2 

.962 

91622 

91643 

91664 

91685 

91706 

91728 

91749 

91770 

91791 

91812 

2 

4 

.963 

91833 

91854 

91876 

91897 

91918 

91939 

91960 

91981 

92003 

92024 

3 

6 

.964 

92045 

92066 

92087 

92109 

92130 

92151 

92172 

92193 

92215 

92236 

4 

8 

.965 

92257 

92278 

92300 

92321 

92342 

92363 

92385 

92406 

92427 

92449 

5 

11 

.966 

92470 

92491 

92512 

92534 

92555 

92576 

92598 

92619 

92640 

92662 

6 

13 

.967 

92683 

92704 

92726 

92747 

92768 

92790 

92811 

92832 

92854 

92875 

7 

15 

.968 

92897 

92918 

92939 

92961 

92982 

93004 

93025 

93046 

93068 

93089 

8 

17 

.969 

93111 

93132 

93154 

93175 

93197 

93218 

93240 

93261 

93282 

93304 

9 

19 

.970 

93325 

93347 

93368 

93390 

93411 

93433 

93454 

93476 

93498 

93519 

.971 

93541 

93562 

93584 

93605 

93627 

93648 

93670 

93691 

93713 

93735 

1 

2 

.972 

93756 

93778 

93799 

93821 

93843 

93864 

93886 

93907 

93929 

93951 

2 

4 

.973 

93972 

93994 

94016 

94037 

94059 

94081 

94102 

94124 

94146 

94167 

3 

7 

.974 

94189 

94211 

94232 

94254 

94276 

94297 

94319 

94341 

94363 

94384 

4 

9 

.975 

94406 

94428 

94450 

94471 

94493 

94515 

94537 

94558 

94580 

94602 

5 

11 

.976 

94624 

94646 

94667 

94689 

94711 

94733 

94755 

94776 

94798 

94820 

6 

13 

.977 

94842 

94864 

94886 

94907 

94929 

94951 

94973 

94995 

95017 

95039 

7 

15 

.978 

95060 

95082 

95104 

95126 

95148 

95170 

95192 

95214 

95236 

95258 

8 

17 

.979 

95280 

95302 

95324 

95345 

95367 

95389 

95411 

95433 

95455 

95477 

9 

20 

.980 

95499 

95521 

95543 

95565 

95587 

95609 

95631 

95653 

95675 

95697 

.981 

95719 

95741 

95763 

95786 

95808 

95830 

95852 

95874 

95896 

95918 

1 

2 

.982 

95940 

95962 

95984 

96006 

96028 

96051 

96073 

96095 

96117 

96139 

2 

4 

.983 

96161 

96183 

96206 

96228 

96250 

96272 

96294 

96316 

96339 

96361 

3 

7 

.984 

96383 

96405 

96427 

96450 

96472 

96494 

96516 

96538 

96561 

96583 

4 

9 

.985 

96605 

96627 

96650 

96672 

96694 

96716 

96739 

96761 

96783 

96805 

5 

11 

.986 

96828 

96850 

96872 

96895 

96917 

96939 

96962 

96984 

97006 

97029 

6 

13 

.987 

97051 

97073 

97096 

97118 

97140 

97163 

97185 

97208 

97230 

97252 

7 

16 

.988 

97275 

97297 

97320 

97342 

97364 

97387 

97409 

97432 

97454 

97477 

8 

18 

.989 

97499 

97521 

97544 

97566 

97589 

97611 

97634 

97656 

97679 

97701 

9 

20 

.990 

97724 

97746 

97769 

97791 

97814 

97836 

97859 

97881 

97904 

97926 

.991 

97949 

97972 

97994 

98017 

98039 

980G2 

98084 

98107 

98130 

98152 

1 

2 

.992 

98175 

98197 

98220 

98243 

98265 

98288 

98311 

98333 

98356 

98378 

2 

5 

.993 

98401 

98424  98446 

98469 

98492 

98514 

98537 

98560 

98583 

98605 

3 

7 

.994 

98628  : 

j 

98651  98673 

1 

98696 

98719 

98742 

98764 

98787 

98810 

98833 

4 

9 

.995 

98855 

98878  98901 

98924 

98946 

98969 

98992 

99015 

99038 

99060 

5 

11 

.996 

99083 

99106 

99129 

99152 

99174 

99197 

99220 

99243 

99266 

99289 

6 

14 

.997 

99312 

99334 

99357 

99380 

99403 

99426 

99449 

99472 

99495 

99518 

7 

16 

.998 

99541 

99563 

99586 

99609 

99632 

99655 

99678 

99701 

99724 

99747 

8 

18 

.999 

99770 

99793 

99816 

99839 

99862 

99885 

99908 

99931 

99954 

99977 

9 

20 

Log. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

ADDITION   TO   SECTION   VII. 

Tontines.  Dividends  of  Annual  Interest  may  be  made  to  survivors  of  all 
ages,  proportional  to  their  deposits.  Dividends  from  Mortality  can  be  appor- 
tioned to  the  products  of  each  Deposit  X  g:t+n-^px  +  n  from  Table  XXYI;  the 
shares  being  as  if  the  Tontines  were  separate  for  each  age. 

ADDITION  TO  THE  FIRST  FORM,  Page  *256. 

The  Method  of  Least  Squares  and  of  Least  Product. 

To  explain  the  fundamental  principle  of  Least-  Squares,  let  j)  denote  the 
probability  of  the  error  e,  regarded  as  the  radius  of  a  circle.  Then  as  the 
probability  changes  by — dp,  the  mathematical  expection  of  error  increases  by 
the  ring  p.2nede.  Among  the  possible  hypotheses,  the  theory  of  least  squares 
assumes  these  increments  to  be  in  a  constant  ratio,  as  in  the  equation  integra- 
ted below.  The  maximum  probability  po  is  evidently  attained  when  e  =  0,  as 
at  the  center  of  the  circle.  For  the  rest,  including  weights  and  probable  error, 
reference  may  be  made  to  ivoi^lcs  on  Least  Squares. 

-dp=kp.2^ede,        p=poe-*^'^,         pjj  j9  3=^0' e— *"■('>' +'^2" +'3'.) 

Method  of  Least  Product.  In  either  of  the  forms  of  equations  from 
the  Census,  although  positive  and  negative  errors  are  equally  likely,  as  re- 
quired by  least  squares,  yet  the  square  roots  of  the  weights  are  unequal,  and 
difficult  of  estimation.  Therefore  to  diminish  the  large  errors  in  these  and 
other  Examples,  let  the  square  of  each  error  be  replaced  by  its  logarithm, 
before  differentiating  for  the  minimum ;  thus, 

^  aiX-{-h^y+ ...+k^v+l^  =6^,  ....  a„x-\-h^y+...+l\v+In^  e^.  (1) 

IT  =  i  (log  61'  +log  e,"  +  ...  -f-  log  e„*)  =  Log  {e^e^...e^)  (2) 

(3) 


d\J      a,     a- 

ttn           ^ 

dU 

= —  _| j- 

..  +  — =0,    ., 



'Zdx     e.      e. 

Cn 

Mv 

1  /A    A  \ 
For  two  equations  of  condition,  x  =  —  -I — •""^l'     i^^*  i^  is  only  m  these 

limiting  cases,  where  the  n  equations  have  n — 1  unknown  quantities,  that  the 
true  value  of  x,  y, ...  is  the  mean  of  the  n  particular  values,  found  by  omitting 
one  equation  at  a  time  and  solving  the  others.  In  all  other  cases,  the  true  roots 
are  different,  and  must  be  approximately  known  in  advance.  For  example,  in 
the  eight  equations  from  the  Census,  making  x=  1.431  +  x'  and  y  =  0.703  +  y', 
we  first  take  x'  and  i/'=0,  0.001,  .002,  ...  and  so  compute  U=  common  log 
{e^e^...e^)  to  represent  a,  a',  b,  h',  c,  c',  on  page  304  text.  Then  differentiating 
U  on  page  304,  for  the  minimum,  we  find  x'  and  y'  from  the  resulting  equations, 
by  common  elimination. 

g=  ^+y'  (A'_A)  +  (y  _i)  A«  =0.     6+x'  (A'_A)  +  (y'_i)  J*=0=f . 


AMERIOAIsr    LIFE    TABLES. 
From  Combinations  of  the  Census. 

The  American  Life  Tables  on  the  following  pages,  being  derived  from  the  general  census  of  the 
United  States,  will  be  the  proper  standard  for  civil  purposes,  especially  for  the  youthful  ages,  and  the 
valuation  of  Legacies,  Reversions  and  widows*  right  of  Dower.  They  diflfer  to  some  extent  from  Life 
Insurance  Tables,  which  are  modified  by  selection,  and  from  which  a  considerable  number  of 
unhealthy  or  diseased  lives  have  been  rejected  by  "the  medical  examination." 

For  greater  accuracy,  separate  Tables  have  been  constructed  for  Males  and  for  Females  of  the 
White  Population.  In  regard  to  other  classes,  the  census  of  1880  gives  the  relative  Deaths  per  cent, 
of  Whites  1.474  to  1.728  of  Colored.  Further  comparisons  indicate  the  average  mortality  of  the 
Colored  to  be  nearly  that  of  the  Northampton  Table.  Hence,  as  shown  by  the  text  page  49,  the 
Annuity  for  the  Colored  at  5  per  cent,  interest  may  be  taken  from  the  following  Table  at  G  per  cent, 
by  accounting  in  this  and  in  other  cases,  the  difference  or  excess  of  1  per  cent,  interest  as  an  offset 
against  the  extra  mortality.  A  similar  difference  of  1  or  2  per  cent,  interest  evidently  appertains  to 
the  Irish  popidation  ;  for  by  the  census  of  1870,  the  relative  Deaths  per  cent,  were  for  total  foreign  as 
1.474,  Irish  1.813,  German  1.371.  A  similar  correction  has  been  applied  in  the  preceding  Climatic 
Tables. 

Since  1850,  a  series  of  systematic  trials  have  shown  that  in  the  present  state  of  the  national 
statistics,  the  average  rates  of  Mortality  are  most  correctly  determined  from  repeated  enumerations  of 
the  people,  by  the  survivorships  from  one  census  to  another.  For  this  object,  the  following  mode  of 
analysis  was  found  superior  to  all  others  in  precision,  and  is  entirely  similar  to  that  which  astronomers 
have  proved  to  be  the  most  advantageous  in  similar  cases.  During  a  tour  in  Europe  in  1869,  the 
whole  process  was  submitted  to  the  highest  authority.  Prof.  De  Morgan  of  London,  and  fully  endorsed 
by  him,  repeating  "  it  is  a  very  fine  method  indeed."  In  order  to  obtain  permanent  results  between 
fluctuations  of  high  or  low  mortality,  the  present  Tables  are  based  on  four  enumerations  from  1830  to 
1860,  including  thirty  years'  experience  and  more  than  seventy  millions  of  observations.  Compared 
with  the  experience  twenty  years  later  by  the  census  of  1880,  the  one  series  verifies  the  other,  without 
either  increase  or  decrease  of  mortality.  Thus,  omitting  certain  States  in  which  the  census  of  1870 
was  deficient,  the  number  of  annual  survivors  calculated  by  the  Life  Table,  for  males  between  the 
ages  of  20  and  75,  was  to  the  survivors  found  from  the  census  of  1870  and  1880,  as  1  to  1.00014.  And 
the  corresponding  ratio  for  surviving  females  was  as  1  to  1.00005.  Had  the  census  of  1870  been  com- 
plete, the  ratios  in  verification  would  have  approached  stUl  nearer  to  equality. 

Equations  of  Condition.  In  any  large  population,  let  Dx  denote  the  Deaths  and  ly  the  Immi- 
gration registered  during  twelve  months  at  any  specified  age  or  ages,  as  from  ten  to  fifteen.  If  the 
registry  of  Deaths  be  complete,  the  value  of  a;  is  1.  But  if  incomplete,  and  still  D  and  I  are  proved 
to  be  proportional  to  the  true  numbers  by  ages,  let  D'  denote  the  true  result  found  from  correct  cen- 
suses of  the  living  ;  and  let  P  denote  the  population  thus  exposed,  in  the  middle  of  the  same  twelve 
months.  Also  admitting  averages,  let  L  denote  the  value  of  P  exposed  in  the  death  registry.  By 
the  common  method,  the  correlative  values  in  the  equation  will  be  : 

Mrst  Form,    = J^  =  tT-  Second  Form,    — ly  =  D'. 

\t         r        r  L 

D' 
In  order  to  determine  ^ ,  let  a;  denote  any  age  specified  above,  at  the  calendar  time  t,  between 

two  censuses ;  then  by  Taylor's  Theorem,  if  La;,<  —  L, 

_dL_dL_ 
La;-i,  <-}— La;  +  i,/  +  i  _       dx      dt 


(p-) 


La;,< 


Here  the  second  derivatives  have  disappeared  by  opposite  signs,  and  the  third  by  their  smallness. 
For  if  we  assume  L  =  a6*c<,  observing  that  c  is  nearly  1.03,  we  find  by  the  next  data  that  the  third 

Copyright,  1886,  by  Lbvi  W.  Mbbch. 

♦255 


♦256 


AMERICAN  LIFE    TABLES, 


derivatives  could  only  augment  the  numerator  in  the  fifth  decimal  place,  which  is  here  insensible. 
Therefore  summing  the  numerator  and  the  denominator  by  double  integration  between  the  proper 
limits  of  X  and  t,  we  obtain  the  mean  ratio : 


D[  _  f(U -U')dt-f(Jj^-lj^)dx  _  F-F^ -(I860) +  (1830) 
P  ~  SS\.dxdt  ~  P 

P  =  ^ U  (1830)  +  (1840)  + (1850) +  i  (1860) +  2  V(1830  '40  '50)  (1840  '50  '60)}. 

Those  versed  in  the  Integral  Calculus  will  observe  that  the  second  member  corresponds  to  a  gen- 
eral Theorem,  the  denominator  representing  the  contents  of  a  solid  P,  of  which  the  terms  of  the 
numerator  are  the  four  lateral  surfaces,  comparable  to  the  walls  of  a  four  square  city.  For  example,  if 
the  specified  ages  are  from  10  to  15,  as  before,  the  difference  of  two  opposite  walls  may  be  denoted  by 
—(I860) +  (1830),  being  the  difference  of  population  at  those  ages  by  the  census  of  1830  and  of  1860. 
While  P—P"  denotes  the  difference  of  the  other  two  walls.  Thus  if  we  suppose  intermediate  cen- 
suses to  fill  the  spaces  between  (1830),  (1840),  (1850),  and  (1860),  this  continuous  solid  will  represent  P 
the  denominator,  here  found  by  Legendre's  quadratures;  the  last  term  denoting  twice  the  sum  of 
population  in  1835,  '45,  '55.  And  if  A,  B,  C  denote  three  continuous  five-year  values  of  P,  then  P'  will 
denote  the  boundary  between  A  and  B,  and  P"  that  between  B  and  C.  Hence  by  parabolic  inter- 
polation, 

F  -P"  r=  =^ :    P"  =  Z°     — .    D'  =  P'  -P''  -(I860)  +  (1830). 


10 


90 


In  this  manner  the  fallowing  equations  were  derived  from  the  U.  S.  Census  of  White  Males  in 
1830,  1840,  1850,  and  1860 ;  and  another  parallel  solution  for  Females,  not  here  inserted.  The  Deaths 
of  Whites  are  those  given  by  the  census  of  1860,  adjusted  by  weights  to  one  aggregate  of  P  above  the 
age  of  40  ;  and  the  Immigration  returns  are  those  of  the  State  Department,  of  which  a  full  summary 
down  to  1855  was  given  in  Bromwell's  History  of  Immigration.  The  proportionality  by  ages  was 
proved  by  comparing  the  statistics  of  different  decades  or  periods,  excluding  those  imder  five  years 
of  age : 

lOOD'-^P.      S€C<md  Form.  PDxh-L.  ly.  jy . 

+  0.0861  240,700ar  -  199,704y  =  +  31,516 

-0.0769  98,487x  -  194,580^  =  -  24,736 

-0.8294  127,410a;  -  404,338y  =  -229,418 

-1.1374  .                171,520x  -  669,853y  =  -297,798 

+  0.1387  150,990a;  -  576,822y  =  +  31,417 

+  0.4114  135,320a;  -  352,619y  =  +  75,904 

+  0.3591  120,410x  -  239,468y  =  +  53,958 

40  and  over.l.8213x  -  0.7579y  =   +2.0742  821,940x  -  342,022y  =  +936,101 


irat  Form. 

lOODxH-L 

lOOIy-HP. 

5-10 

0.6572a; 

-  0.5453y  = 

10-15 

.3062a; 

-  O.eOoQy  = 

15-20 

.4606a; 

-  1.4617y  = 

20-25 

.6551a; 

-  2.5584y  = 

25-30 

.6668X- 

-  2.5474y  = 

30-35 

.7334a; 

-  l.Ollly  = 

35-40 

.8013a;  - 

-  1.5936^  = 

Second  ^orm.— Adding  now  the  seven  equations  under  40  years,  the  local  errors  so  nearly  cancel 
each  other,  that  by  eliminating  between  the  sum,  and  the  last  equation  above  40,  we  find  for  the  first 
approximation,  y  —  0.7033  and  x  =  1.4315. 

First  Form. — In  the  distribution  of  ages,  the  immigration  differs  widely  from  the  mortality ; 
which  would  be  highly  conducive  to  an  accurate  solution,  if  we  knew  the  weights  of  the  several 
equations  for  "  least  squares."  But  the  larger  errors  will  certainly  be  attenuated  by  "  the  method  of 
replacing  the  square  of  each  error  by  its  logarithm  ; "  which  gives  3"=  1.4314.  This  value  was  slightly 
corrected  for  the  order  of  arrival  of  immigrants  ;  whence  finally  x  =  1.43323. 

Multiplying  this  factor  into  the  proportional,  we  obtain  the  corrected  Deaths  per  cent,  shown  in 
column  second,  next  page,  for  White  Males.  And  the  percentages  for  White  Females  were  wrought 
out  independently  in  the  same  manner.  In  taking  the  census,  "  the  ages  at  last  birthday "  have 
always  been  specified.  A  comparison  with  other  tables  required  the  results  "  under  5  "  to  be  multi- 
plied by  1|,  and  the  result  for  Females  "5-10,"  by  1.038,  to  correct  for  extra  omissions  of  death  at 
those  ages.  From  these  percentages,  the  Life  Tables  following  were  constructed  chiefly  by  "  the 
graphic  method  "  of  page  38,  to  represent  the  percentages  without  subsequent  graduation.  Only  the 
Life  Table  for  Males  was  graduated  by  Makeham's  law  (page  237)  above  the  age  of  21,  with  slight 
amendment  above  90  ;  the  four  values  of  I  at  the  ages  21,  43^,  66,  88^,  gave  g  —  0.9991671, 
«  =  0.99114498,  q  =  1.095671.  Also,  U.  =  4.895404,  Xg  =  -0.00036193,  /^  =  -0.003862807, 
Aj  =  0.039680044, 


AMERICAN  LIFE    TABLES. 


*%b1 


On  the  Mathematical  Law   of  Mortality. 

The  genera]  fonnula  for  the  whole  life,  on  page  239,  is  at  present  an  interpolation  formula, 
whose  three  sets  of  constants  are  determined  from  three  separate  portions  of  the  life  table,  requiring 
the  full  experience  to  be  known  in  advance.  A  different  expression  of  the  law  of  mortality  is 
required,  as  in  life  insurance  and  the  vital  statistics  of  large  cities,  for  determining  one  part  of  the 
life  table  from  another.  While  awaiting  the  progress  of  its  discovery,  we  may  employ  the  formulas 
below,  to  pass  from  the  adult,  to  at  least  a  large  portion  of  the  youthful  ages  :  From  four  equi-dis- 
tant  ages  above  21,  the  constants  g,  k,  q,  s  are  first  determined  by  Makeham's  formula  for  I' ,  as  on 
page  237  ;  with  these,  the  tabular  values  of  I  are  computed  for  all  ages  above  21  or  22,  with  M  =  0. 
For  the  ages  under  21,  the  calculation  of  V  is  continued,  and  the  values  of  V  when  corrected  by  the 
Last  Terms  M  below,  give  &  first  series  for  4.  It  is  remarkable  that  the  present  sum  of  all  the  Last 
Terms  M  is  0  ;  and  the  sum  of  R  from  10  to  22  inclusive  is  nearly  0.  Secondly,  applying  the  cognate 
formula  for  I"  as  equal  to  I'  at  the  three  special  ages  22,  44,  and  66,  and  dividing  one  difference  of 
equations  by  the  other,  to  determine  C,  then  finding  B  and  A,  the  values  of  I"  under  21  are  next  com- 
puted. These  being  corrected  by  the  Last  Terms  R  below  give  a  second  series  for  Ig  ;  from  which  to 
conclude  the  true  values  of  4- 

M  =  U  +  x?is  +  q^^g,  4  =:  V  +  M.  V  =  A-BC.  4  =  I"  +  R. 

In  the  present  Table,        A  =  92,979.73,        ?.B  =  4.3915244,        ;iC  =  0.0075972^ 


AMERICAN    LIFE    TABLE.      MALES. 


Deaths  Per  Cent. 

Last  Tbbms. 

AGES. 

lOOD 
L 

AGES. 

M. 

R. 

AGES. 

M. 

R. 

0-5 

5.6889 

0 

+  21,469 

+  26,587 

12 

-1,970 

-348 

5-10 

0.9419 

1 

+  5,975 

+ 10,738 

13 

-1,620 

-213 

10-15 

.4389 

2 

+  1,297 

+  5,715 

14 

-1,266 

-  62 

15-20 

.6601 

3 

-     824 

+  3,261 

1    15 

-    924 

+  89 

20-30 

.9469 

4 

-  1,919 

+  1,845 

16 

-    616 

+  217 

30-40 

1.0958 

5 

-  2,547 

+      908 

17 

-    357 

+  309 

40-50 

1.3904 

6 

-  2,853 

+      305 

18 

-    164 

+  346 

50-60 

2.0380 

7 

-  2,957 

-       85 

i    19 

-     53 

+  312 

60-70 

3.5130 

8 

-  2,941 

-     343 

i    20 

-      13 

+  219 

70-80 

7.5370 

9 

-  2.818 

-     481 

1    21 

0 

+  110 

80-90 

16.086 

10 

-  2,599 

-     512 

22 

0 

0 

90,  etc. 

27.369 

11 

-  2,301 

-     453 

23 

0 

-100 

Total, 

1.890 

0 

48,364 

The  researches  during  the  past  century  to  discover  the  law  of  mortality  by  induction  from 
imperfect  life  tables,  may  be  aided  by  comparisons  from  physical  science.  Making  ^  =  1,  or  log  ^  =  0, 
to  define  the  oldest  year  of  age  of  Makeham's  formula,  the  resulting  form  of  equatio'n  0  =  «  +  6a;  +  ccP, 
which  defines  the  span  of  the  life  table,  also  defines  the  range  of  a  projectile  in  a  resisting  medium, 
and  the  rise-and-fall  of  the  centres  of  motion  of  particles  in  deep  sea  waves,  according  to  Rankine. 
The  most  complete  computations  of  Log  4  mentioned  at  the  foot  of  page  239,  with  slight  allowance 
for  imperfect  data,  are  identical  with  the  integral  of  the  equations  of  heat  in  Poisson's  Them'ie  de  la 
Chaleur,  page  514.  Omitting  the  periodic  terms,  the  compound  effect  of  one  negative  and  two  posi- 
tive sources  of  heat  has  the  same  expression  as  for  three  corresponding  sources  of  vitality  found  by 
Makeham,  page  239.  The  negative  one  of  these  is  evidently  the  growth  of  the  reproductive  function; 
and  the  other  two  are  explained  by  animal  chemistry.  Possibly  another  integral  may  be  found  from 
Dulong  and  Petit's  law  of  cooling  of  a  heated  body  in  air.  Or  the  derivative  equations  of  heat 
may  be  combined  with  the  formula  of  page  239,  to  determine  laws  of  relation  between  its  constants  ; 
which  will  define  the  mathematical  law  of  mortality. 

It  will  be  proper  to  mention  that  the  magical  properties  of  the  double  exponential  introduced  by 
Gompertz  and  Makeham,  are  applicable  to  any  life  table  or  law  of  mortality,  as  illustrated  on  page 
*268,  where  "  relative  ages"  admit  of  the  further  co-ordinate  of  a  relative  joint  rate  of  interest.  The 
present  limits  do  not  permit  further  discussion  of  the  new  expedient,  page  *268,  of  a  "  companion  life 
table/'  and  the  extraordinary  advantages  it  offers  in  tabulating  Joint  Lives  and  Survivorships. 


♦258 


AMERICAN  LIFE  TABLE.      FROM  THIRTY  YEARS'  EXPERIENCE. 


MALES.  WHITE  POPULATION. 

1 

.FEMALES.  WHITE  POPULATION. 

AGE. 
X. 

Number 
Living. 

I. 

Annual 
Deaths. 

Proportion 
Dying. 

Expect'n 
of  Life. 
Years. 

Logarithm 

of  Number 

Living. 

AGE. 

X. 

Number 
Living. 

Annual 
Deaths. 

Proportion 
Dying. 

Expect'n 
of  Life. 

Years. 

Logarithm 

of  Number 

Living. 

0 

100,000 

16,195 

0.161950 

41.01 

5.000000 

0 

100,000 

13,430 

0.134300 

42.91 

5.000000 

1 

83,805 

5,374 

.064125 

47.83 

4.923270 

1 

86,570 

5,322 

.061476 

48.49 

4.937367 

2 

78,431 

2,812 

.035854 

50.08 

.894488 

2 

81,248 

2,838 

.034930 

50.64 

.909813 

3 

75,619 

1,779 

.023525 

50.93 

.878631 

3 

78,410 

1,859 

.023709 

51.45 

.894372 

4 

73,840 

1,308 

.017714 

51.14 

.868292 

4 

76,551 

1,320 

.017244 

51.69 

.883951 

5 

72,532 

980 

0.013512 

51.05 

4.860530 

5 

75,231 

675 

0.008972 

51.59 

4.876397 

6 

71,552 

773 

.010805 

50.74 

.854622 

6 

74,556 

656 

.008799 

51.05 

.872483 

7 

70,779 

648 

.009154 

50.29 

.849904 

7 

73,900 

652 

.008823 

50.50 

.868644 

8 

70,131 

536 

.007643 

49.75 

.845910 

8 

73,248 

634 

.008656 

49.94 

.864796 

9 

69,595 

435 

.006250 

49.13 

.842578 

9 

72,614 

616 

.008483 

49.37 

.861020 

10 

69,160 

352 

0.005090 

48.44 

4.839855 

10 

71,998 

564 

0.007833 

48.79 

4.857320 

11 

68,808 

314 

.004563 

47.68 

.837639 

11 

71,434 

449 

.006286 

48.17 

.853905 

12 

68,494 

291 

.004242 

46.90 

.835653 

12 

70,985 

284 

.004001 

47.47 

.851167 

13 

68,203 

282 

.004136 

46.10 

.833804 

13 

70,701 

203 

.002871 

46.66 

.849426 

14 

67,921 

290 

.004269 

45.28 

.832004 

14 

70,498 

204 

.002894 

45.80 

.848177 

16 

67,631 

321 

0.004746 

44.48 

4.830146 

15 

70,294 

318 

0.004524 

44.93 

4.846918 

16 

67,310 

365 

.005424 

43.69 

.828080 

16 

69,976 

397 

.005673 

44.13 

.844949 

17 

66,945 

428 

.006392 

42.92 

.825718 

17 

69,579 

556 

.007991 

43.38 

.842478 

18 

66,517 

507 

.007622 

42.20 

.822938 

18 

69,023 

568 

.008229 

42.72 

.838994 

19 

66,010 

574 

.008696 

41.52 

.819610 

19 

68,455 

591 

.008633 

42.07 

.835405 

20 

65,436 

599 

0.009154 

40.87 

4.815817 

20 

67,864 

597 

0.008797 

41.44 

4.831640 

21 

64,837 

609 

.009394 

40.25 

.811823 

21 

67,267 

617 

.009172 

40.80 

.827802 

22 

64,228 

607 

.009449 

39.63 

.807724 

22 

66,650 

636 

.009543 

40.17 

.823800 

23 

63,621 

604 

.009494 

39.00 

.803601 

23 

66,014 

694 

.010513 

39.55 

.819636 

24 

63,017 

603 

.009570 

38.37 

.799458 

24 

65,320 

697 

.010671 

38.97 

.815046 

25 

62,414 

601 

0.009629 

37.73 

4.795282 

25 

64,623 

696 

0.010770 

38.38 

4.810387 

26 

61,813 

600 

.009706 

37.09 

.791080 

26 

63,927 

695 

.010872 

37.80 

.805684 

27 

61,213 

599 

.009786 

36.46 

.786844 

27 

63,232 

681 

.010770 

37.21 

.800937 

28 

60,614 

599 

.009882 

35.81 

.782573 

28 

62,551 

677 

.010823 

36.61 

.796234 

29 

60,015 

598 

.009964 

35.16 

.778260 

29 

61,874 

670 

.010829 

36.00 

.791508 

30 

59,417 

599 

0.010083 

34.51 

4.773911 

30 

61,204 

669 

0.010931 

35.39 

4.786780 

31 

58,818 

600  0.010201 

33.86 

.769510 

31 

60,535 

670 

.011068 

34.78 

.782007 

32 

58,218 

601 

.010322 

33.20 

.765057 

32 

59,865 

670 

.011192 

34.16 

.777173 

33 

57,617 

603 

.010465 

32.54 

.760551 

33 

59,195 

672 

.011352 

33.54 

.772285 

34 

57,014 

605 

.010613 

31.88 

.755982 

34 

58,523 

682 

.011654 

32.92 

.767327 

35 

56,409 

609 

0.010796 

31.22 

4.751348 

35 

57,841 

697 

0.012050 

32.30 

4.762236 

36 

55,800 

612 

.010967 

30.55 

.746634 

36 

57,144 

698 

.012215 

31.69 

.756971 

37 

55,188 

617 

.011181 

29.88 

.741845 

37 

56,446 

698 

.012366 

31.08 

.751633 

38 

54,571 

622 

.011399 

29.22 

.736962 

38 

55,748 

699 

.012539 

30.46 

.746229 

39 

53,949 

628 

.011640 

28.55 

.731983 

39 

55,049 

699 

.012698 

29.84 

.740749 

40 

53,321 

634 

0.011888 

27.88 

4.726898 

40 

54,350 

664  0.012217 

29.22 

4.735200 

41 

52,687 

•643 

.012205 

27.21 

.721704 

41 

53,686 

645  .012014 

28.57 

.729861 

42 

52,044 

651 

.012509 

26.54 

.716371 

42 

53,041 

640  .012066 

27.91 

.724612 

43 

51,393 

661 

.012862 

25.87 

.710904 

43 

52,401 

629i  .012004 

27.25 

.719340 

44 

50,732 

672 

.013246 

25.20 

.705282 

44 

51,772 

628 

.012130 

26.57 

.714095 

45 

50,060 

685 

0.013684 

24.53 

4.699491 

45 

51,144 

624 

0.012201 

25.89 

4.708795 

46 

49,375 

697 

.014116 

23.86 

.693507 

46 

50,520 

630 

.012470 

25.21 

.703463 

47 

48,678 

712 

.014626 

23.20 

.687333 

47 

49,890 

632 

.012668 

24.52 

.698014 

48 

47,966 

728 

.015177 

22.53 

.680934 

48 

49,258 

634 

.012871 

23.83 

.692477 

49 

47,238 

746 

.015794 

21.87 

.674292 

49 

48,624 

640 

.013162 

23.13 

.686851 

50 

46,492 

764 

0.016433 

21.22 

4.667378 

50 

47,984 

658 

0.013713 

22.43 

4.681096 

51 

45,728 

785 

.017166 

20.56  1  .660182 

51 

47,326 

664 

.014031 

21.74 

.675100 

*259 


AMERICAN  LIFE  TABLE.      FROM  THIRTY  YEARS'  EXPERIENCE. 


MALES.  WHITE  POPULATION. 

FEMALES.  WHITE  POPULATION. 

AGE. 

X. 

Number 
Living. 

I, 

Annual 
Deaths. 

Proportion 
Dying. 

Expect'n 
of  Life. 

Years. 

Logarithm 

of  Number 

Living. 

AGE. 

X. 

Number 
Living. 

6. 

Annual 
Deaths. 

Proportion 
Dying. 

Expect'n 
ofLife. 
Years. 

Logarithm 

of  Number 

Living. 

52 

44,943 

807 

0.017956 

19.92 

4.652662 

52 

46,662 

689 

0.014766 

21.04 

4.668963 

53 

44,136 

831 

.018828 

19.27 

.644793 

53 

45,973 

715 

.015552 

20.35 

.662503 

54 

43,305 

856 

.019766 

18.63 

.636538 

54 

45,258 

739 

.016329 

19.66 

.655695 

55 

42,449 

883 

0.020803 

18.00 

4.627868 

55 

44,519 

763 

0.017139 

18.98 

4.648545 

56 

41,566 

913 

.021964 

17.37 

.618738 

56 

43,756 

790 

.018055 

18.30 

.641038 

57 

40,653 

942 

.023172 

16.75 

.609093 

57 

42,966 

824 

.019178 

17.63 

.633125 

58 

39,711 

975 

.024552 

16.13 

.598911 

58 

42,142 

862 

.020455 

16.96 

,624715 

59 

38,736 

1,009 

.026049 

15.53 

.588115 

59 

41,280 

891 

.021584 

16.31 

.615740 

60 

37,727 

1,044 

0.027672 

14.93 

4.576652 

60 

40.389 

929 

0.023001 

15.66 

4.606268 

61 

36,683 

1,080 

.029441 

14.34 

.564465 

61 

39,460 

965 

.024455 

15.01 

.596157 

62 

35,603 

1,117 

.031374 

13.76 

.551487 

62 

38,495 

978 

.025406 

14.38 

.585404 

63 

34,486 

1,157 

.033551 

13.19 

.537643 

63 

37,517 

1,046 

.027881 

13.74 

.574228 

64 

33,329 

1,194 

.035825 

12.63 

.522822 

64 

36,471 

1,104 

.030271 

13.12 

.561948 

65 

32,135 

1,234 

0.038399 

12.08 

4.506978 

65 

35,367 

1,166 

0.032969 

12.51 

4.548598 

66 

30,901 

1,273 

.041198 

11.54 

.489973 

66 

34,201 

1,209 

.035350 

11.92 

.534039 

67 

29,628 

1,309 

.044180 

11.01 

.471702 

67 

32,992 

1,270 

.038494 

11.34 

.518409 

68 

28,319 

1,346 

.047531 

10.50 

.452078 

68 

31,722 

1,326 

.041801 

10.77 

.501361 

69 

26,973 

1,380 

.051162 

10.00 

.430929 

69 

30,396 

1,378 

.045335 

10.22 

.482816 

70 

25,593 

1,410 

0.055093 

9.51 

4.408121 

70 

29.018 

1,433 

0.049383 

9.68 

4.462668 

71 

24,183 

1,436 

.059381 

9.04 

.383510 

71 

27.585 

1,462 

.053000 

9.16 

.440673 

72 

22,747 

1,459 

.064140 

8.58 

.356924 

72 

26,123 

1,504 

.057574 

8.65 

.417023 

73 

21,288 

1.473 

.069194 

8.13 

.328135 

73 

24,619 

1,551 

.063000 

8.14 

.391270 

74 

19,815 

1,483 

.074842 

7.70 

.296994 

74 

23,068 

1,616 

.070054 

7.66 

.363010 

75 

18,332 

1,482 

0.080842 

7.28 

.263210 

75 

21,452 

1,666 

0.077662 

7.20 

4.331468 

76 

16,850 

1,474 

.087479 

6.88 

.226600 

76 

19,786 

1,682 

.085010 

6.76 

.296358 

77 

15,376 

1,456 

.094693 

6.49 

•186843 

77 

18,104 

1,695 

.093626 

6.34 

.257775 

78 

13,920 

1,427 

.102513 

6.11 

.143639 

78 

16,409 

1,684 

.102627 

5.95 

.215082 

79 

12,493 

1,386 

.110942 

5.75 

.096667 

79 

14,725 

1,715 

.116469 

5.57 

.168055 

80 

11,107 

1,335 

0.120194 

5.41 

4.045597 

80 

13,010 

1,646 

0.126518 

5.24 

4.114277 

81 

9,772 

1,272 

.130169 

5.08 

3.989984 

81 

11,364 

1,591 

.140003 

4.92 

.055531 

82 

8,500 

1,198 

.140941 

4.77 

.929419 

82 

9,773 

1,445 

.147856 

4.64 

3.990028 

83 

7,302 

1,114 

.152562 

4.47 

.863442 

83 

8,328 

1,318 

.158261 

4.36 

.920541 

84 

6,188 

1,022 

.165159 

4.18 

.791550 

84 

7,010 

1,200 

.171184 

4.09 

.845718 

85 

5,166 

924 

0.178860 

3.91 

3.713154 

85 

5,810 

1,084 

0.186575 

3.83 

3.764176 

86 

4,242 

821 

.193542 

3.65 

.627571 

86 

4,726 

953 

.201650 

3.59 

.674494 

87 

3,421 

715 

.209003 

3.41 

.534153 

87 

3,773 

816 

.216274 

3.37 

.576687 

88 

2,706 

612 

.226163 

3.18 

.432328 

88 

2,957 

686 

.231992 

3.16 

.470851 

89 

2,094 

512 

.244508 

2.96 

.320977 

89 

2,271 

563 

.247908 

2.97 

.356217 

90 

1,582 

417 

0.263591 

2.76 

3.199207 

90 

1,708 

454 

0.265808 

2.78 

3.232488 

91 

1,165 

331 

.284120 

2.56 

.066326 

91 

1,254 

356 

.283892 

2.61 

.098298 

92 

834 

255 

.305755 

2.38 

2.921166 

92 

898 

272 

.302895 

2.44 

2.953^76 

93 

579 

191 

.329879 

2.21 

.762679 

93 

626 

203 

.324281 

2.29 

.796574 

94 

388 

137 

.353093 

2.06 

.588832 

94 

423 

146 

.345154 

2.14 

.626340 

95 

251 

96 

0.382470 

1.91 

.399674 

95 

277 

101 

0.364621 

2.01 

2.442480 

96 

155 

63 

.406452 

1.78 

2.190332 

96 

176 

.  69 

.392046 

1.88 

.245513 

97 

92 

40 

.434783 

1.65 

1.963788 

97 

107 

44 

.411215 

1.76 

.029384 

98 

52 

24 

.461538 

1.54 

.716003 

98 

63 

28 

.444444 

1.64 

1.799341 

99 

28 

14 

.500000 

1.42 

.447158 

99 

35 

16 

.457143 

1.55 

.544068 

100 

14 

7 

.500000 

1.35 

1.146128 

100 

19 

9 

0.473684 

1.44 

1.278754 

101 

7 

4 

.571429 

1.19 

0.845098 

101 

10 

5 

.500000 

1.30 

.000000 

102 

3 

2 

.666666 

1.11 

.477121 

102 

5 

3 

.600000 

1.10 

0.698970 

Beyond  102  Ybars:  Male  Life,  Ix,  1.19,  0.44,  0.15,  0.05,  0.01,     Female  Life,  l^,  2, 1, 


*260 


AMERICAN  LIFE  TABLE.      COMMUTATION   COLUMNS.      3  PER  CENT. 


AGE. 

X. 


0 

1 
2 
3 

4 

5 
6 
7 
8 
9 

10 

11 
12 
13 
14 

15 
16 
17 
18 
19 

20 
21 
22 
23 
24 

25 
26 
27 
28 
29 

30 
31 
32 
33 
84 

35 
36 
37 
38 
39 

40 
41 
42 
43 
44 

45 
46 
47 
48 
49 


HALES. 


Dx. 


100,000.0 
81,364.07 
73,928.76 
69,202.09 
65,605.88 

62,566.75 
59,923.68 
57,549.80 
55,362.05 
53,338.77 

51,461.54 
49,708.35 
48,040.31 
46,442.93 
44,903.79 

43,409.76 
41,945.37 
40,502.82 
39,071.73 
37,644.58 

32 
09 
11 
23 

19 


36,230. 
34,853. 
33,520. 
32,236. 
31,000. 

29,809. 
28,662. 
27,557. 
26,492. 
25,467. 

24,479. 
23,526. 

22,608. 
21,723. 
20,869. 

'20,046. 
19,252. 

18,487. 
17,747. 
17,034. 

16,345. 

15,681. 
15,038. 
14,417. 
13,817. 

13,237. 
12,676. 
12,133. 
11,607. 
11,098. 


Na 


FEMALES. 


D. 


1,931,877|100,000.0 
1,831,877  84,048.55 
1,750,513|76,584.04 
1,676,584  71,756.26 
1,607,382;68,014.57 

1,541,776  64,894.92 
1,479,209  62,439.48 
1,419,285  60,087,45 
1,361,736  57,822.65 
1,306,374  55,652.59 

1,253,035'53,573.28 
1,201,573  51,605.44 

1,151,865  49,787.45 
1,103,825  48,143.95 
1,057,38246,607.49 

1,012,477  45,119.05 
969,068.143,606.73 

927.122.8  42,096.44 

886.619.9  40,543.74 
847,548.2  39,038.93 


809,903. 
773,673. 

738,820. 
705,300. 
673,063. 

642,063. 
612,254. 
583,592. 
556,034. 
529,541. 

504,074. 
479,595. 
456,069. 
433,460. 
411,737. 

390,868. 
370,821. 
351,568. 
333,081. 
315,333. 

298,298. 
281,953. 
266,271. 
251,233. 
236,815. 

222,997. 
209,759. 
197,083. 
184,949. 
173,342. 


637,574. 
3  36,159. 
2  34,784. 
133,448. 


66 
32 
14 
74 
932,133.12 


7:30,864. 
4  29,642. 


28,466. 
27,339. 
26,256. 


25,215.24 
24,213.22 
23,247.80 
22,318.07 
21,422.05 


N^. 


2,003,261 
1,903,261 
1,819,213 
1,742,629 
1,670,873 

1,602,858 
1,537,963 
1,475,524 
1,415,436 
1,357,613 

1,301,961 

1,248,388 
1,196,782 
1,146,995 
1,098,851 

1,052,243 
1,007,124 
963,517.6 
921,421.1 

880,877.4 

841,838.5 
804,263.8 
768,104.5 
733,320.3 
699,871.6 

667,738.5 
636,874.2 
607,231.6 
578,765.2 
551,425.6 

525,169.6 
499,954.4 
475,741.2 
452,493.4 
430,175.3 


20,555.73  408,753.2 
19,716.53|388,197.5 
18,908.45|368,481.0 


418,130.71 
417,381.91 

916,661.36 
015,978.46 
8115,326.69 


349,572.5 
331,441.8 

314,059.9 
297,398.6 
281,420.1 


2114,700.73  266,093.4 
314,101.23  251,392.7 

313,524.45  237,291.4 


12,970.33 


12,435.52  210,796.7 


11,920.38 
11,424.23 


223,767.0 


198,361.1 
186,440.8 


AGE, 

X. 


50 
51 
52 
53 
54 

55 
56 
57 
58 
59 

60 
61 
62 
63 
64 

65 
66 
67 
68 
69 

70 
71 
72 
73 

74 

75 
76 

77 
78 
79 

80 
81 
82 
83 
84 

85 
86 
87 
88 
89 

90 
91 
92 
93 
94 

95 
96 
97 
98 
99 


MALES. 


D,.. 


Xo:. 


FEMALES. 


D. 


N. 


10,605.15162,243.410,945.49175,016.5 

10,127.06151,638.3 

9,663.321141,511.2 

213.404131,847.9 

776.633  122,634.5  9,172.449133,960.3 


10,480.96164,071.0 
10,032.92153,590.1 
9,596.877143,557.2 


352.570 

940.605 
539.991 
150.753 
772.025 

403.520 
044.969 
696.114 
356.703 
026.202 


113,857.9  8,759.877  124,787.8 
105,505.3  8,358.975  116,028.0 

97.564.70  7,968.987  107,669.0 

90.024.71  7,588.503  99,700.00 
82,873.96  7,216.779,92,111.49 


6,855. 
6,502. 


76,101.93 
69,698.41 
63,653.446,158 
57,957.33;5,827 
52,600. 62|5,500 


350184,894.71 
590178,039.36 
80471,536.77 
508  65,377.97 
033  59,550.46 


704.991:47,574.42  5,178.197  54,050.43 

392.539  42,869.43  4,861.63148,872.23 

088.916,38,476.89  4,553.176j44,010. 60 

794.430,34,387.98  4,250.395  39,457.43 

508.817  30,593.55  3,954.102  35,207.03 

I  i 

232.329  27,084.73  3,664.897^31,252.93 

965.290:23,852.40  3,382.439,27,588.03 

707.970  20,887.113,109.875  24,205.59 

460.467  18,179. 14  2,845. 464i21,095. 72 

223.51215,718.67  2,588.543118,250.25 


997.18313,495.16 
782.259:11,497.98 
578.9829,715.718 
387.828  8,136.736 
209.278  6,748.908 


1,043.804 
891.5964 
752.9506 
627.9891 
516.6820 

418.7842 
333.8638 
261.4055 
200.7483 
150.8217 

110.6258 
79.09309 
54.97198 
37.05243 
24.10641 

15.14040 
9.077329 
5.230907 
2.870485 
1.500627 


5,539.630 

4,495.82 

3,604.230 

2,851.280 

2,223.291 

1,706.609 

1,287.824 

953.9605 

692.5550 

491.8067 

340.9850 
230.3592 
151.26611 
96.29413 
59.24170 

35.13530 
19.99491 
10.91758 
5.086671 
2.816186 


2,337.09315,661.71 
2,092.806  13,324.62 
1,859.12311,231.81 
1,635.983  9,372.688 
1,425.327  7,736.705 

1,222.642  6,311.378 
1,036.850  5,088.736 
865.71614,051.887 
716.2276  3.186.171 
585.3169  2,469.943 

470.99041,884.626 
371.95671,413.636 
288.3025:1,041.679 
219.3691  753.3765 


163.5702 

119.4367 
85.13538 
59.19045 
40.06013 
26.28097 

16.70873 

10.30716 

6.08377 

3.47770 

1.87578 


534.0074 

370.4372 
251.0006 
165.8652 
106.6747 
66.61459 

40.33362 

23.62489 

13.31773 

7.23396 

3.75626 


Formulas,  V^^^vf^i^-^       N^,  =  D^,  +Dx  + 1  + 


M^  =  D;,-(l-l')N;,. 


*261 


AMERICAN   LIFE   TABLE.      COMMUTATION   COLUMNS.      4  PER  CENT. 


AGE 

X. 

0 

1 
2 
3 

4 

5 
6 
7 
8 
9 

10 
11 
12 
13 

14 

15 
16 
17 
18 
19 

20 
21 
22 
23 
24 

25 
26 
27 
28 
29 

30 
31 
32 
33 

34 

35 
36 
37 
38 
39 

40 
41 
42 
43 
44 

45 
46 
47 
48 
49 


MALES. 


FEMALES. 


D.. 


100,000.0 
80,581.72 
73,513.86 
67,335.01 
63,118.73 

59,616.00 
56,548.57 
53,786.31 
51,244.05 

48,896.54 

46,733.03 
44,696.38 
42,781.16 
40,960.96 
39,232.70 

37,553.10 
35,937.37 
34,367.78 
32,834.67 
31,331.15 

14 

66 
36 
73 
30 


29,864. 
38,452. 
37,101. 
35,813. 
34,584. 

33,413. 

33,295. 
21,229. 
20,213. 
19,343. 


18,319.38 
17,437.31 
16,595.51 
15,793.49 
15,026.17 

14,294.92 
13,596.72 
12,930.38 
12,294.06 
11,686.47 

11,106.18 
10,552.05 
10,022.37 
9,516.354 
9,032.652 

8,570.197 
8,137.815 
7,704.884 
7,300.180 
6,912.867 


N. 


D. 


1,609,551 
1,509,551 
1,428,969 
1,356,456 
1,289,231 

1,226,112 
1,166,496 
1.109,947 
1,056,161 
1,004,917 

956,020.4 
909,298.4 
864,603.0 
831,830.9 
780,859.9 

741,637.2 
704,084.1 
668,146.7 
633,778.9 
600,944.3 

569,613.1 
539,749.0 
511,296.3 
484,195.0 
458,382.2 

433,797.9 
410,385.4 
388,090.1 
366,860.4 
346,647.0 

337,403.1 
309,083.7 
391,646.5 
275,051.0 
259,258.5 

244,232.3 
229,937.4 
216,340.7 
203,410.3 
191,116.3 

179,429.8 
168,323.6 
157,771.6 
147,749.3 
138,332.8 

129,200.2 
120,630.0 
112,502.2 
104,797.3 
97,497.10 


100,000.0 
83,240.39 
75,118.34 
69,706.31 
65,436.11 

61,834.39 
58,932.69 
56,157.92 
53,521.60 
51,017.64 

48,639.36 
46,402.17 
44,337.02 
42,461.19 
40,710.83 

39,031.77 
37,360.76 
35,719.99 
34,071.69 
32,491.65 

24 
03 
33 

61 

74 

17 
78 
90 
35 
98 


30,972. 
29,519, 
28,123. 
26,783. 
35,483. 

34,241. 
33,057. 
21,929. 
20,859. 
19,839. 


18,870.33 
17,946.22 
17,064.99 
16,225.00 
15,423.86 

14,657.80 
13,924.20 
13,225.12 
12,559.31 
11,934.75 

11,330.50 
10,752.13 
10,214.36 
9,702.999 
9,217.815 

8,755.771 
8,316.291 
7,896.717 
7,496.810 
7,115.691 


^x. 


1,667,023 
1,567,023 

1,483,782 
1,408,664 
1,338,958 

1,273,533 
1,311,687 
1,152,765 
1,096,607 
1,043,085 

993,067.6 
943,428.3 
897,026.2 
852,689.1 
810,227.9 

769,517.1 
730,485.3 
693,134.6 
657,404.6 
623,332.9 

590,841.3 
559,869.0 
530,350.0 
502,336.7 
475,443.0 

449,960.3 
435,719.1 
402,661.4 
380,731.5 
359,872.1 

340,033.1 
331,161.8 
303,215.6 
286,150.6 
269,925.6 

354,501.7 
239,843.9 
225,919.7 
212,694.6 
200,135.4 

188,210.6 
176,890.1 
166,138.0 
155,923.7 
146,220.7 

137,002.9 
128,247.1 
119,930.8 
112,034.1 
104,537.3 


AGE. 

X. 


50 
51 
52 
53 
54 

55 
56 
57 
58 
59 

60 
61 
62 
63 
64 

65 
66 
67 
68 
69 

70 
71 
72 
73 

74 

75 
76 
77 
78 
79 

80 

81 

82' 

83 

84 

85 
86 
87 
88 
89 

90 
91 
92 
93 
94 

95 
96 
97 
98 
99 


MALES. 


D. 


6,543.016 
6,187.030 
5,846.942 
5,521.109 
5,208.805 

4,909.465 
4,632.442 
4,347.029 
4,082.982 
3,829.553 

3,586.346 
3,352.984 
3,129.103 
2,914.357 
2,708.251 

2,510.797 
2,321.520 
2,140.371 
1,967.031 
1,801.479 

1,643.568 
1,493.387 
1,350.592 
1,215.350 
1,087.746 

967.6311 
855.1973 
750.3717 
653.1892 
563.6807 

481.8698 
407.6459 
340.9457 
281.6273 

229.4827 

184.2132 
145.4466 
112.7853 

85.78157 
63.82775 

46.36668 
32.83161 
22.59951 
15.08614 
9.720714 

6.046534 
3.590303 
2.049056 
1.113618 

.576577 


^x. 


90,584.23 
84,042.21 

77,855.18 
72,008.24 
66,487.13 

61,278.33 

56,368.86 
51,746.42 
47,399.39 
43,316.41 

39,486.86 
35,900:51 
33,547.53 
29,418.42 
26,504.07 

23,795.81 
21,285.02 
18,963.50 
16,823.23 
14,856.20 

13,054.72 
11,411.15 

9,917.861 
8,567.270 
7,351.920 

6,264.174 
5,296.543 
4,441.345 
3,690.974 
3,037.784 

3,474.104 
1,993.334 
1,584.588 
1,243.642 
962.0150 

732.5323 
548.3191 
402.8725 
290.0872 
204.3057 

140.4779 
94.11122 
61.27961 
38.68010 
23.59396 

13.87325 
7.82671 
4.23641 
2.18735 
1.07373 


FEMALES. 


D. 


2,763. 
2,569. 
2,383. 
2,203. 
3,030. 

1,863. 
1.703. 
1,551. 
1,405. 
1,366. 


6,751.953 
6,403.236 
6,070.573 
5,750.900 
5,443.712 

5,148.867 
4,865.983 
4,594.356 
4,332.927 
4,081.057 

3,839.394 
3,606.811 
3,383.275 
3,170.499 
2,963.562 

319 
440 
279 
401 
093 

518 
358 
039 
519 
318 

1,132.315 
1,004.209 
883.5017 
769,9838 
664.3876 

564.4302 
474.0572 
392.0072 
321.1985 
259.9666 

307.1774 
162.0416 
124.3902 
93.73837 
69.23292 

50.05960 
35.33976 
24.33375 
16.31074 
10.59758 

6.67287 
4.07673 
2.38314 
1.34919 

.72072 


N, 


97,421.57 
90,669.62 
84,266.38 
78,195.81 
73,449.91 

67,001.30 
61,853.33 
56,986.35 
52,391.99 
48,059.06 

43,978.01 
40,138.61 
36,531.80 
33,148.53 

29,978.03 

27,014.47 
34,351.15 
21,681.71 
19,298.43 
17,095.03 

15,064.93 
13,301,42 
11,498.06 
9,947.018 
8,541.499 

7,275.181 
6,142.866 
5,138.658 
4,255,156 
3,485.172 

2,820,785 
2,256.354 
1,782.297 
1,390.390 
1,069.091 

809.1348 
601.9474 
439.9058 
315.5156 

331.7772 

153.5543 

103.4947 
67.15495 
43.83120 
26.51046 

15.91288 
9.24001 
5.16328 
2.78014 
1.43095 


♦263 


AMERICAN  LIFE  TABLE.     COMMUTATION  COLUMNS.     5  PER  CENT. 


AGE. 

X. 


0 
1 
2 
3 

4 

5 
6 
7 
8 
9 

10 
11 
12 
13 
14 

15 
16 
17 
18 
19 

20 
21 
22 
23 
24 

25 
26 
27 
28 
29 

30 
31 
32 
33 
34 

35 
36 
37 
38 
39 

40 

41 
42 
43 

44 

45 
46 
47 
48 
49 


MALES. 


Da-. 


100,000.0 
79,814.28 
71,139.22 
65,322.53 
60,748.35 

56,830.72 
53,393.20 
50,301.31 
47,467.41 
44,861.55 

42,458.23 
40,230.60 
38,140.01 
36,169.50 
34,304.71 

32,531.66 
30,835.48 
29,207.88 
27,639.18 
26,122.39 

24,662.14 
23,272.74 
21,956.33 
20,713.17 
19,539.55 

18,431.02 
17,384.33 
16,395.80 
15,462.24 
14,580.42 

13,747.75 
12,961.10 
12,217.99 
11,516.05 
10,852.89 

10,226.40 
9,634.282 
9,074.872 
8,546.109 
8,046.382 

016 
580 
328 
148 
610 


7,574. 
7,127. 
6,705. 
6,306. 
5,928. 

5,571. 
5,233. 
4,914. 
4,611. 
4,325. 


504 

587 
007 


Na 


FEMALES. 


Dx. 


1,376,220100,000.0 
1,276,220  82,447.62 
1,196,405173,694.34 
1,125,266  67,733.51 
1,059,944  62,978.70 

999,195.4  58,945.45 
942,364.7  55,634.83 
888,971.5|52.519.35 
838,670.2|49,577.13 
791,202.7146,807.63 

746,341.2  44,200.52 
703,883.0|41,765.98 
663,652.4|39,527.11 
625,512.4  37,494.25 
589,342.9  35,606.27 


555,038.1 
522,506.5 
491,671.0 
462,463.1 
434,823.9 

408,701.6 
384,039.4 
360,766.7 
338,810.3 
318,097.2 

298,557.6 
280,126.6 
262,742.3 
246,346.5 
230,884.2 

216,303.8 
202,556.1 
189,595.0 
177,377.0 
165,861.0 

155,008.0 
144,781.6 
135,147.4 
126,072.5 
117,526.4 

109,480.0 
101,906.0 
94,778.39 
88,073.06 
81,766.92 


75,838.31 
70,266.80 
65,033.22 
553160,119.21 
29755,507.66 


33,812.61 
32,056.81 
30,357.09 
28,680.48 
27,089.97 

25,577.23 
24,144.98 
22,784.30 
21,492.26 
20,253.64 

19,083.35 
17,978.87 
16,936.59 
15,956.36 
15,032.06 

14,161.23 
13,339.46 
12,563.64 
11,831.46 
11,140.13 

10,486.01 
9,866.334 
9,281.734 
8,730.436 
8,210.445 

7,720.182 
7,262.727 
6,833.781 
6,429.834 
6,050.144 

5,692.148 
5,354.951 
5,036.356 
4,735.767 
4,452.205 


^x. 


1,424,240 
1,324,240 
1,241.792 
1,168,098 
1,100,364 

1,037,386 
978,440.1 
922,805.2 
870,285.9 
820,708.7 

773,901.1 
729,700.6 
687,934.6 
648,407.5 
610,913.3 

575,307.0 
541,494.4 
509,437.6 
479,080.5 
450,400.0 

423,310.0 
397,732.8 
373,587.8 
350,803.5 
329,311.3 

309,057.6 
289,974.3 
271,995.4 
255,058.8 
239,102.4 

224,070.4 
209,909.2 
196,569.7 
184,006.1 
172,174.6 

161,034.5 
150,548.5 
140,682.1 
131,400.4 
122,670.0 

114,459.5 
106,739.3 
99,476.60 
92,642.82 
86,212.98 

80,162.84 
74,470.69 
69,115.74 
64,079.38 
59,343.62 


AGE, 

X. 


50 
51 
52 
53 

54 

55 
56 
57 
58 
59 

60 
61 
62 
63 
64 

65 
66 
67 
68 
69 

70 

71 
72 
73 

74 

75 
76 
77 
78 
79 

80 
81 
82 
83 
84 

85 
86 
87 
88 
89 

90 
91 
92 
93 
94 

95 
96 
97 
98 
99 


MALES. 


^z. 


N. 


FEMALES. 


D. 


N, 


4,054.276'51,182.36  4,184.383  54,891.41 

3,797.765  47,128.08  3,930.479  50,707.03 
3,554.828  43,330.323,690. 793  46,776.55 
3,324.759  39,775.4913,463.139  43,085.76 
3,106.819  36,450.73  3,246.933  39,622.62 

2,900.388  33,343.913,041.823  36,375.69 
2,704.815:30,443.52  2,847.324  33,333.86 


2,519.432 
2,343.859 
2,177.440 

2,019.735 
1,870.327 
1,728.821 
1,594.840 
1,467.936 


27, 738. 71 !  2, 662. 778  30, 486. 54 
25,219.28:2,487.344  27,823.76 
22,875.4212,320.443  25,336.42 

20.697.98 


18,678.24 
16,807.92 
15,079.09 
13,484.25 


2,162.247  23,015.97 
2,011.917120,853.73 
1,869.25218,841.81 
1,735.011 16,972.56 
1,606.32215,237.55 


1,347.950  12,016.32  1,483.521 13,631.22 
1,234.465  10,668.37ll,366.297'12,147. 70 
1,127.248  9,433. 903|l, 255.237  10,781.41 
1,026.138  8,306.655:1,149.445  9,526.169 
930.824117,280.5171,048.950  8,376.724 


841.1439 

756.9548 
678,1014 


6,349.692 
5,508.549 
4,751.594 


604.3883  4,073.492 
535.7794:3,469.104 

472.0766  2,933.325 
413.2499  2,461.248 
359.142612,047.998 
309.65161,688.856 
264.67421,379.204 


224.1053 

187.7801 
155.5591 
127.2709 
102.7183 

81.67000 
63.85503 
49.04166 
36.94190 
27.22293 

19.58450 
13.73253 
9.370235 
6.195462 
3.954001 

2.436073 

1.432712 

.809889 

.435965 

.223572 


1,114.530 
890.4245 
702.6444 
547.0853 
419.8144 

317.0961 
235.4261 
171.5711 
122.5294 
85.58752 

58.36459 
38.78009 
25.04756 
15.67733 
9.481866 

5.527865 

3.091792 

1.659080 

.849191 

.413226 


953.7105 
863.4413 


7,327.775 
6,374.064 


778.74205,510.623 
698.9589  4,731.881 
623.7374  4,032.922 

552.421313,409.185 
485.25652,856.763 
422.8618  2,371.507 


365.0201 
311.9613 

262.5025 
218.3725 
178.8568 
145.1539 
116.3636 

91.85138 
71.15641 
54.10256 
40.38248 
29.53722 

21.15685 

14.79351 

10.08930 

6.69838 

4.31068 

2.68842 

1.62682 

.94194 

.52819 

.27947 


1,948.645 
1,583.625 

1,271.664 

1,009.161 

790.78 

611.9319 

466.7780 

350.4144 
258.5630 
187.4066 
133.3041 
92.92157 

63.38435 
42.22750 
27.43399 
17.34469 
10.64631 

6.33563 
3.64721 
2.02039 
1.07845 
.55026 


♦263 


AMERICAN  LIFE  TABLE.      COMMUTATION   COLUMNS.     6  PER  CENT. 


A6K 

X. 


0 
1 
2 
3 

4 

5 
6 

7 
8 
9 

10 
11 
12 
13 
14 

15 
16 
17 
18 
19 

20 

21 
22 
23 
24 

25 
26 
27 
28 
29 

30 
31 
32 
33 
34 

35 
36 
37 
38 
39 

40 

41 
42 
43 
44 

45 
46 
47 
48 
49 


100,000.0 
79,061.32 
69,803.31 
63,491.17 

58,488.19 

54,200.13 
50,441.33 
47,072.08 
44,001.05 
41,193.17 

38,618.58 
36,247.19 
34,039.42 
31,976.23 
30,041.52 

28,220.05 
26,496.33 
24,860.99 
23,303.82 
21,817.16 


MALES. 


D... 


20,403. 
19,072. 
17,823. 
16,655. 
15,563. 

14,542. 

13,587. 
12,693. 
11,857. 
11,076. 

10,345.10 

9,-661.141 

021.309 

422.811 

862.888 


339.105 
848.935 
390.394 
961.273 
559.742 

183.984 
832.401 
503.232 
195.190 
906.823 

636.862 
384.053 
147.436 
925.848 
718.341 


N. 


1,201,740 
1,101,740 
1.022,679 

952,875.8 
889,384.6 

830,896.5 
776,696.3 
726,255.0 
679,182.9 
635,181.9 

593,988.7 
555,370.1 
519,122.9 
485,083.5 
453,107.3 

423,065.8 
394,845.7 
368,349.4 
343,488.4 
320,184.6 

298,367.-4 
277,964.2 
258,892.0 
241,068.4 
224,412.6 

208,848.8 
194,306.4 
180,719.3 
168,025.6 
156,167.7 

145,091.6 
134,746.4 
125,085.3 
116,064.0 
107,641.2 

99,778.30 
92,439.19 
85,590.26 
79,199.87 
73,238.59 

67,678.85 
62,494.87 
57,662.47 
53,159.23 
48,964.04 

45,057.22 
41,420.36 
38,036.31 

34,888.87 
31,963.02 


FEMALES. 


Dx. 


100,000.0 
81,669.80 
72,310.44 
65,834.55 
60,635.56 

56,216.98 
52,559.03 
49,147.71 
45,956.70 
42,980.13 

40,203.30 
37,630.54 
35,277.37 
33,147.39 
31,181.34 

29,331.23 

27,545.79 
25,839.17 
24,181.78 
22,625.27 

21,160.32 
19,786.95 
18,495.72 
17,282.28 
16,132.64 

15,057.07 
14,051.80 
13,112.29 
12,236.86 
11,419.26 

10,656.24 
9,943.167 
9,276.524 
8,653.492 
8,070.997 

7,525.416 
7,013.899 
6,536.062 
6,089.848 
5,673.103 

5,284.025 
4,924.028 
4,589.500 

4,277.474 
3,986.913 

3,715.616 
3,462.530 
3,225.803 
3,004.660 
2,798.100 


N;.. 


1,242,999 
1,142,999 
1,061,329 
989,018.9 
923,184.3 

862,548.8 
806,331.8 
753,772.8 
704,625.1 
658,668.4 

615,688.2 
575,484.9 
537,854.4 
502,577.0 
469,429.6 

438,248.3 
408,917.1 
381,371.3 
355,532.1 
331,350.3 

308,725.0 
287,564.7 
267,777.8 
249,282.1 
231,999.8 

215,867.1 
200,810.1 
186,758.3 
173,646.0 
161,409.1 

149,989.9 
139,333.6 
129,390.4 
120,113.9 
111,460.4 

103,389.4 
95,864.02 
88,850.12 
82,314.06 
76,224.21 

70,551.10 
65,267.08 
60,343.05 
55,753.55 
51,476.08 

47,489.16 
43,773.55 
40,311.02 
37,085.22 
34,080.56 


AGE. 

X. 


50 
51 
52 
53 
54 

55 
56 
57 
58 
59 

60 
61 
62 
63 
64 

65 
66 
67 
68 
69 

70 

71 
72 
73 

74 

75 
76 

77 
78 
79 

80 
81 
82 
83 

84 

85 
86 
87 
88 
89 

90 
91 
92 
93 
94 

95 
96 
97 
98 
99 


MALES. 


FEMALES. 


D^. 


2,523.974 
2,341.979 
2,171.485 
2,011.787 
1,862.178 

1,722.046 
1,590.778 
1,467.769 
1,352.602 
1,244.710 

1,143.669 

1,049.076 

960.5562 

877.7547 
800.2888 

727.9422 
660.3668 
597.3229 
538.6155 
483.9766 

433.2219 
386.1833 
342.6901 
302.5565 
265.6806 

231.8834 
201.0731 
173.0978 
147.8365 
125.1709 

104.985] 
87.13815 
71.50525 
57.95021 
46.32950 

36.48848 
28.26612 
21.50517 
16.04766 
11.71533 

8.349850 
5.800857 
3.917657 
2.565860 
1.622109 

0.989957 
.576724 
.322938 
.172198 
.087474 


N. 


29,244.68 
26,720.71 
24,378.73 
22,207.24 
20,195.46 

18,333.28 
16,611.23 
15,020.45 
13,552.68 
12,200.08 

10,955.37 
9,811.703 
8,762.627 
7,802.071 
6,924.317 

6,124.028 
5,396.086 
4,735.719 
4,138.396 
3,599.780 

3,115.804 

2,682.582 
2,296.399 
1,953.708 
1,651.152 

1,385.471 

1,153.588 

952.5148 

779.4170 

631.5805 

506.4096 
401.4245 
314.2864 
242.7811 
.184.8309 

138.5014 
102.0129 
73.74680 
52.24163 
36.19397 

24.47864 
16.12879 
10.32794 
6.410279 
3.844419 

2.222310 

1.232353 

0.655629 

.332691 

.160493 


D. 


2,604.973 
2,423.822 
2,254.542 
2,095.520 
1,946.161 

1,806.021 
1,674.593 
1,551.281 
1,435.406 
1,326.458 

1,224.365 

1,128.494 

1,038.582 

954.9015 

875.7341 

801.1559 
730.8895 
665.1439 
603.3396 
545.3957 

491.1984 
440.5108 
393.5508 
349.8986 
309.2971 

271.3488 
236.1088 
203.8088 
174.2708 
147.5339 

122.9725 
101.3342 
82.21421 
66.09276 
52.48380 

41.03719 
31.49121 
23.71792 
17.53619 
12.70560 

9.01488 
6.24401 
4.21829 
2.77414 
1.76844 

1.09250 

0.65486 

.37559 

.20863 

.10934 


N, 


31,282.46 

28,677.48 
26,253.66 
23,999.12 
21,903.60 

19,957.44 
18,151.42 
16,476.82 
14,925.54 
13,490.14 

12,163.68 
10,939.31 
9,810.819 

8,772.237 
7,817.336 

6,941.602 
6,140.446 
5,409.556 
4,744.413 
4,141.073 

3,595.677 
3,104.479 
2,663.968 
2,270.417 
1,920.519 

1,611.222 
1,339.873 
1,103.764 
899.9551 
725.6843 

578.1504 
455.1779 
353.^8438 
271.6295 
205.5368 

153.0530 
112.0158 
80.52459 
56.80667 
39.27048 

26.56488 

17.55000 

11.30599 

7.08770 

4.31356 

2.54512 

1.45262 

0.79776 

.42217 

.21354 


*264 

AMERICAN  LIFE  TABLE. 


PRESENT  VALUE  (ax)  OF  |1  ANNUITY,  PAYABLE  AT  THE  END 
OF  EACH  YEAR  DURING  LIFE. 


AOE. 

X. 

Interest  3  Per  Cent. 

4  Per  Cent.       5  Per  Cent.    !   6  Per  Cent.       7  Per  Cent. 

1 

AGE. 

X. 

0 

Hale. 

Female. 

Male. 

Female.   Male,  j  Female.   Male.   Female,  j  Male. 

Female. 

0 

18.319 

19.033 

15.096 

15.670  12.762 

13.242  11.017  11.430 

9.675 

10.037 

1 

21.515 

21.645 

17.733 

17.825  1 14.990 

15.062  12.935:12.995 

11.353 

11.405 

1 

a 

22.678 

22.754 

18.706 

18.753  15.818  ;  15.851  13.651  !  13.677 

11.979 

12.003 

2 

3 

23.227 

23.285 

19.178 

19.209  16.226  1 16.245  i  14.008  ;  14.023 

12.295 

12.308 

3 

4 

23.501 

23.566 

19.425 

19.462 

16.448 

16.472  j  14.206  ;  14.225 

12.472 

12.490 

4 

5 

23.642 

23.699 

19.567 

19.596 

16.582 

16.599  14.330  1 14.343 

12.586 

12.598 

5 

6 

23.685 

23.631 

19.628 

19.564 

16.650 

16.587 

14.398  14.341  i  12.651 

12.602 

6 

7 

23.662 

23.556 

19.636 

19.527 

16.673 

16.571 

14.429  14.337:12.685 

12.604 

7 

8 

23.597 

23.479 

19.610 

19.489 

16.668 

16.554  ,  14.436  14.332 

12.698 

12.607 

8 

9 

23.492 

23.394 

19.552 

19.446 

16.637 

16.534  1 14.420  14.325 

12.692 

12.607 

9 

10 

23.349 

23.302 

19.462 

19.396 

16.578 

16.509 

14.381  14.314 

12.666 

12.605 

10 

11 

23.172 

23.191 

19.344 

19.332 

16.496 

16.471 

14.322  14.293 

12.621 

12.593 

11 

12 

22.977 

23.038 

19.210 

19.232 

16.400 

16.404 

14.251  14.246 

12.567 

12.560 

12 

13 

22.767 

22.824 

19.064 

19.082 

16.294 

16.294 

14.170  14.162 

12.504 

12.493 

13 

14 

22.548 

22.577 

18.908 

18.902 

16.180 

16.157 

14.083  :  14.055 

12.435 

12.406 

14 

15 

22.324 

22.321 

18.749 

18.715 

16.061 

16.015 

13.992  13.941 

12.362 

12.313 

15 

16 

22.103 

22.096 

18.592 

18.552 

15.945 

15.892 

13.902  13.845 

12.291 

12.235 

16 

17 

21.890 

21.888 

18.441 

18.404 

15.834 

15.782 

13.816  1  13.759 

12.223 

12.166 

17 

18 

21.692 

21.727 

18.302 

18.295 

15.732 

15.704 

13.740  13.702 

12.163  ;  12.123 

18 

19 

21.514 

21.564 

18.180 

18.184 

15.646 

15.626 

13.676 

13.645 

12.114  112.079 

19 

20 

21.354 

21.404 

18.073 

]8.076 

15.572 

15.550 

13.624 

13.590 

12.076  12.037 

20 

21 

21.198 

21.242 

17.970 

17.966 

15.502  15.473 

13.574 

13.533 

12.040  11.994 

21 

22 

21.041 

21.082 

17.866 

17.858 

15.431  1 15.397 

13.525  1  13.478 

12.005  ;  11.953 

22 

23 

20.884 

20.924 

17.758 

17.751 

15.357 

15.322 

13.474 '  13.424 

11.968  111.913 

23 

24 

20.712 

20.780 

17.645 

17.657 

15.280 

15.259 

13.419  :  13.381 

11.929 '11.882 

24 

25 

20.539 

20.635 

17.528 

17.562 

15.199 

15.195 

13.361  !  13.337 

11.887  11.851 

25 

26 

20.361 

20.485 

17.407 

17.463 

15.114 

15.129 

13.301  !  13.291 

11.843  i  11.818 

26 

27 

20.177 

20.332 

17.281 

17.361 

15.025 

15.060 

13.237  j  13.243 

11.796 

11.785 

27 

28 

19.988 

20.169 

17.149 

17.252 

14.932 

14.985 

13.170  13.190 

11.747 

11.746 

28 

29 

19.793 

20.002 

17.013 

17.139 

14.835 

14.906 

13.099  1  13.135 

11.694 

11.707 

29 

30 

19.592 

19.827 

16.872 

17.019 

14.734 

14.823 

13.025  13.075 

11.639 

11.663 

30 

31 

19.385 

19.648 

16.726 

16.896 

14.628 

14.736 

12.947 

13.013 

11.580 

11.617 

31 

32 

19.173 

19.464 

16.574 

16.768 

14.518 

14.646 

12.866 

12.948 

11.519 

11.570 

32 

33 

18.954 

19.275 

16.417 

16.636 

14.403 

14.552 

12.780 

12.880 

11.454 

11.520 

33 

34 

18.729 

19.081 

16.254 

16.501 

14.283 

14.455 

12.690 

12.810 

11.385 

11.468 

34 

35 

18.498 

18.885 

16.085 

16.363 

14.158 

14.357 

12.595 

12.739 

11.313 

11.415 

35 

36  18.361 

18.689 

15.911 

16.225 

14.028 

14.259 

12.497 

12.668 

11.236 

11.363 

36 

37  1 18.017 

18.488 

15.731 

16.083 

13.892 

14.157 

12.394 

12.594 

11.156 

11.309 

37 

38  !  17.767 

18.281 

15.545 

15.935 

13.752 

14.051 

12.286 

12.517 

11.072 

11.252 

38 

39  17.511 

18.068 

15.353 

15.783 

13.606 

13.941 

12.173 

12.436 

10.984 

11.193 

39 

40  17.249 

17.850 

15.156 

15.626 

13.455 

13.826 

12.055 

12.352 

10.891 

11.130 

40 

41  i  16.980 

17.612 

14.952 

15.452 

13.298  113.697 

11.933 

12.255 

10.794 

11.056 

41 

42  '  16.706 

17.361 

14.742 

15.265 

13.135  i  13.557 

11.805 

12.148 

10.692 

10.974 

42 

43  16.425 

17.101 

14.526 

15.070 

12.966 

13.408 

11.672 

12.034 

10.585 

10.886 

43 

44 

16.138 

16.828 

14.304 

14.863 

12.792 

13.250 

11.533 

11.911 

10.474 

10.789 

44 

45 

15.846 

16.545 

14.076 

14.647 

12.612 

13.083 

11.389 

11.781 

10.358 

10.686 

45 

46 

15.547 

16.252 

13.841 

14.421 

12.426 

12.907 

11.240 

11.642 

10.236 

10.576 

46 

47  15.243 

15.951 

13.601 

14.187 

12.234 

12.723 

11.085 

11.496 

10.110 

10.459 

47 

48  1  14.933 

15.641 

13.355 

13.944 

12.037 

12.531 

10.924 

11.343 

9.978 

10.335 

48 

49  14.618 

15.320 

13.104 

13.691 

11.833 

12.329 

10.758 

11.180 

9.841 

10.202 

49 

FOEMULA,       fix  = 


Da: 


*265 


AMERICAN  LIFE  TABLE. 


PRESENT  VALUE  (ox)  OF  $1  ANNUITY,  PAYABLE  AT  THE  END 
OF  EACH  YEAR  DURING  LIFE. 


AGE. 

X. 

Interest  8  Per  Cent. 

4  Per  Cent. 

5  Per  Cent. 

6  Per  Cent. 

7  Per  Cent. 

AGE. 

1 
X. 

Hale. 

Female. 

Hale. 

Female. 

Male.      Female. 

1 

Male.    ' 

Female. 

Male. 

Female. 

50 

14.299 

14.990 

12.847 

13.429 

11.624 

12.118 

10.587 

11.009 

9.699 

10.062 

50 

51 

13.974 

14  o54 

12.584 

13.160 

11.410 

11.901 

10.410 

10.832 

9.551 

9.916 

51 

52 

13.644 

I':         09 

12.316 

12.881 

11.189 

11.674 

10.227 

10.645 

9.398 

9.761 

52 

53 

13.310 

11.959 

12.042 

12.597 

10.963 

11.441 

10.039 

10.453 

9.240 

9.601 

53 

54 

12.973 

13.605 

11.764 

12.308 

10.733 

11.203 

9.845 

10.255 

9.077 

9.435 

54 

55 

12.631 

13.245 

11.482 

12.013 

10.496 

10.959 

9.646 

10.051 

8.908 

9.263 

55 

56 

12.387 

12.881 

11.195 

11.711 

10.255 

10.707 

9.442 

9.839 

8.734 

9.085 

56 

57 

11.940 

12.511 

10.904 

11.404 

10.010 

10.449 

9.234 

9.621 

8.555 

8.899 

57 

58 

11.590 

12.138 

10.609 

11.092 

9.760 

10.186 

9.020 

9.398 

8.371 

8.708 

58 

59 

11.238 

11.764 

10.311 

10.776 

9.506 

9.919 

8.802 

9.170 

8.183 

8.513 

59 

60 

10.884 

11.384 

10.010 

10.454 

9.248 

9.644 

8.579 

8.935 

7.989 

8.309 

60 

61 

10.530 

11.001 

9.707 

10.129 

8.987 

9.365 

8.353 

8.694 

7.792 

8.100 

61 

62 

10.175 

10.615 

9.401 

9.798 

8.722 

9.080 

8.123 

8.446 

7.590 

7.885 

62 

63 

9.820 

10.219 

9.094 

9.455 

8.455 

8.782 

7.889 

8.187 

7.385 

7.657 

63 

64 

9.465 

9.827 

8.786 

9.116 

8.186 

8.486 

7.652 

7.927 

7.176 

7.427 

64 

65 

9.111 

9.438 

8.477 

8.776 

7.915 

8.188 

7.413 

7.664 

6.964 

7.195 

65 

66 

8.760 

9.053 

8.169 

8.438 

7.642 

7.891 

7.171 

7.401 

6.749 

6.962 

66 

67 

•  8.410 

8.666 

7.860 

8.097 

7.369 

7.589 

6.928 

7.133 

6.531 

6.722 

67 

68 

8.063 

8.283 

7.553 

7.758 

7.095 

7.288 

6.683 

6.864 

6.312 

6.480 

68 

69 

7.719 

7.904 

7.247 

7.421 

6.822 

6.986 

a.  438 

6.593 

6.090 

6.236 

69 

70 

7.379 

7.528 

6.943 

7.084 

6.549 

6.683 

6.192 

6.320 

5.868 

5.990 

70 

71 

7.044 

7.156 

6.642 

6.750 

6.277 

6.382 

5.946 

6.047 

5.645 

5.742 

71 

72 

6.713 

6.783 

6.344 

6.413 

6.007 

6.076 

5.701 

5.769 

5.421 

5.488 

72 

73 

6.388 

6.414 

6.049 

6.077 

5.740 

5.770 

5.457 

5.489 

5.198 

5.231 

73 

74 

.  6.069 

6.050 

5.759 

5.745 

5.475 

5.466 

5.215 

5.209 

4.976 

4.973 

74 

75 

5.757 

5.701 

5.473 

5.425 

5.213 

5.171 

4.975 

4.938 

4.754 

4.722 

75 

76 

5.451 

5.367 

5.194 

5.117 

4.956 

4.887 

4.737 

4.675 

4.535 

4.478 

76 

77 

5.153 

5.041 

4.919 

4.816 

4.702 

4.608 

4.503 

4.416 

4.317 

4.237 

77 

78 

4.863 

4.729 

4.651 

4.526 

4.454 

4.338 

4.272 

4.164 

4.103 

4.002 

78 

79 

4.581 

4.428 

4.389 

4.246 

4.211 

4.076 

4.046 

3.919 

3.891 

3.772 

79 

80 

4.307 

4.162 

4.134 

3.998 

3.973 

3.844 

3.824 

3.701 

3.684 

3.568 

80 

81 

4.042 

3.908 

3.887 

3.760 

3:742 

3.621 

3.607 

3.492 

3.480 

3.371 

81 

82 

3.787 

3.680 

3.647 

3.547 

3.516 

3.421 

3.395 

3.304 

3.280 

3.194  i  82  1 

83 

3.540 

3.449 

3.416 

3.328 

3.298 

3.216 

3.190 

3.110 

3.086 

3.010 

83 

84 

3.303 

3.220 

3.192 

3.112 

3.087 

3.011 

2.990 

2.916 

2.897 

2.826 

84 

85 

3.075 

3.001 

2.977 

2.905 

2.883 

2.815 

2.796 

2.730 

2.713 

2.649 

85 

86  '    2.857 

2.801 

2.770 

2.715 

2.687 

2.634 

2.609 

2.557 

2.535 

2.485 

86 

87      2.649 

2.613 

2.572 

2.536 

2.498 

2.464 

2.429 

2.895 

2.363 

2.330 

87 

88 

2.450 

2.434 

2.382 

2.366 

2.317 

2.301 

2.255 

2.239 

2.197 

2.181 

88 

89 

2.261 

2.265 

2.201 

2.204 

2.144 

2.146 

2.090 

2.091 

2.038 

2.038 

89 

90 

2.082 

2.102 

2.030 

2.047 

1.980 

1.996 

1.932 

1.947 

1.886 

1.900 

90 

91 

1.913 

1.948 

1.867 

1.900 

1.824 

1.854 

1.780 

1.811 

1.740 

1.769 

91 

92 

1.752 

1  802 

1.712 

1.760 

1.673 

1.719 

1.636 

1.680 

1.601 

1.643 

92 

93 

1.599 

1.663 

1.564 

L619 

1.530 

1.589 

1.498 

L555 

1.467 

1.522 

93 

94 

1.458 

1.535 

1.427 

1.502 

1.398 

1.470 

1.370 

1.439 

1.343 

1.410 

94 

95 

1.321 

1.414 

1.295 

1.385 

1.269 

1.357 

1.245 

1.330 

1.222 

1.304 

95 

96 

1.202 

1.292 

1.180 

1.267 

1.158 

1.242 

1.137 

1.218 

1.116 

1.195 

96 

97 

1.087 

1.189 

1.067 

1.167 

1.049 

1.145 

1.030 

1.124 

1.013 

1.104 

97 

98 

0.981 

1.080 

0.964 

1.061 

0.948 

1.042 

0.932 

1.024 

0.917 

1.006 

98 

99 

0.877 

1.003 

0.862 

,0.985 

0.848 

0.969 

0.835 

0.953 

0.822 

0.937 

99 

♦266 

AMERICAN  LIFE  TABLE.     SINGLE  PREMIUM  (Ar)  OR  PRESENT  VALUE  OP    $100,  PAYABLE   AT 
THE  END  OF  THE  YEAR  IN  WHICH  THE  LIFE  FAILS. 


AOE  ^^^^®8t  "^  ^^^  Cent, 
^'        Male.    I  Female. 


0 

1 

2 
3 

4 

5 
6 
7 
8 
9 

10 
11 
12 
13 
14 

15 
16 
17 
18 
19 

20 
21 
22 
23 
24 

25 
26 
27 
28 
29 

30 
31 
32 
33 
34 

35 
36 
37 
38 
39 

40 
41 
42 
43 
44 

45 
46 
47 
48 
49 


38.094 
27.949 
24.208 
22.393 
21.441 

20.897 
20.660 
20.630 
20.729 
20.955 

21.301 
21.753 
22.270 
22.832 
23.430 

24.042 
24.646 
25.227 
25.761 
26.229 

26.640 
27.038 
27.439 
27.854 
28.288 

28.737 
29.205 
29.691 
30.195 
30.719 

31.262 
31.826 
32.409 
33.014 
33.640 

34.288 
34.958 
35.650 
36.365 
37.102 

37.864 
38.647 
39.455 
40.286 
41.139 

42.017 
42.917 
43.841 

44.788 
45.754 


35.884 
27.595 
24.029 
22.275 
21.300 

20.786 
20.908 
21.049 
21.196 
21.363 

21.552 
21.802 
22.185 
22.763 
23.454 

24.173 

24.799 
25.368 
25.789 
26.214 

26.629 
27.052 
27.469 
27.880 
28.241 

28.608 
28.988 
29.380 
29.799 
30.236 

30.695 
31.170 
31.660 
32.168 
32.690 

33.220 
33.750 
34.298 
34.864 
35.449 

36.055 
36.724 
37.442 
38.194 
38.989 

39.819 
40.688 
41.587 
42.522 
43.496 


5  Per  Cent. 


6  Per  Cent. 


Male.    Female.    Male.     Female. 


34.465 
23.858 
19.915 
17.970 
16.914 

16.277 
15.955 
15.843 
15.866 
16.017 

16.294 
16.684 
17.141 
17.649 
18.192 

18.755 
19.309 
19.841 


32.179:31.977  29.642 


23.516 
19.759 
17.879 
16.800 

16.195 
16.253 
16.330 
16.409 
16.506 

16.624 
16.804 
17.123 
17.650 
18.298 

18.978 
19.563 
20.088 


20.32220.457 
20.^35j20.828 

21.08521.189 
21.421i21.559 
21.75621.920 
22.11022.275 
22.478122.574 

22.864'22.880 
23.26823.197 
23.69323.526 
24.132  23.882 
24.59524.256 

25.07724.653 
25.581i25.067 
26.107  25.496 
26.654125.942 
27.225:26.403 

27.82l'26.871 
28.440^27.339 
29.08327.824 
29.753j28.329 
30.448128.854 

31.169'29.400 
31.91830.015 
32.692  30.683 


33.495 
34.324 

35.181 
36.067 
36.980 


31.389 
32.144 

32.938 
33.777 
34.651 


37.92035.567 
38.890  36.528 


21.12020.781 


16.920 
14.965 
13.820 

13.152 
13.162 
13.187 
13.213 
13.255 

13.315 
13.436 
13.699 
14.178 
14.784 


17.070 
15.049 
13.927 

13.225 
12.842 
12.669 
12.629 
12.720 

12.938 
13.273 
13.676 
14.132 
14.627 

15.141  15.426 
15.649  15.972 
16. 134!  16.456 
16.569:16.778 
16.929|l7.103 

17.225  17.416 
17.503  17.737 
17.782  18.050 
18.074  18.354 
18.384|  18.599 

18.709  18.849 
19.052  19.109 
19.413119.379 
19.793  19.677 
20.192!  19.992 

20.61320.328 
21.052  20.681 
21.516:21.048 
22.002;  21.432 
22.51021.830 


23.045 
23.603 


22.234 
22.636 


24.188j23.054 
24. 798123.491 
25.43623.947 

26. 102!  24.424 
26.79724.973 
27.520i  25.577 


28.274 
29.058 

29.874 
30.718 
31.595 
32.503 
33.4:44 


26.221 
26.917 

27.655 
28.441 
29.266 
30.136 
31.057 


A6£ 

X. 


50 
51 
52 
53 
54 

55 
56 
57 
58 
59 

60 
61 
62 
63 
64 

65 
66 
67 
68 
69 

70 
71 
72 
73 

74 

75 
76 

77 
78 
79 

80 
81 
82 
83 
84 

85 
86 
87 
88 
89 

90 
91 
92 
93 
94 

95 
96 
97 
98 
99 


4  Per  Cent. 


5  Per  Cent. 


Male,    Female.;  Male.    Female.    Male,  i Female 


46.744  44.505  39.885 


47.754  45.539 
48.787  46.611 
49.837  47.703 
50.907  48.815 

51.993  49.951 
53.097  51.111 


54.216 
55.350 
56.495 

57.653 
58.820 
59.994 
61.176 
62.361 

63.548 
64.736 
65.922 
67.104 
68.282 

69.450 
70.609 
71.755 

72.888 
74.004 

75.101 
76.179 
77.234 
78.266 
79.273 

80.253 
81.204 
82.126 
83.017 

83.877 

84.706 
85.500 
86.261 
86.993 

87.688 

88.347 
88.975 
89.572 
90.139 
90.664 

91.175 
91.615 
92.048 
92.446 
92.837 


52.294 
53.494 
54.707 

55.945 
57.198 
58.470 

59.787 
61.094 

62.400 
63.699 
65.010 
66.314 
67.612 

68.907 
70.191 
71.488 
72.780 
74.05 

75.288 
76.473 
77.630 
78.745 
79.824 

80.779 
81.694 
82.513 
83.352 
84.183 

84.979 
85.712 
86.398 
87.054 
87.678 

88.279 
88.845 
89.386 
89.926 
90.379 

90.828 
91.283 
91.667 
92.075 
92.364 


6  Per  Cent. 


37.532 

38.567 
39.648 
40.756 
41.890 


43.055j39.739i37.450 
44.252  40. 894J38. 645 
45.480  42.074139.879 


46.733;43.285 
48.006144.519 


49.312 
50.642 
52.001 
53.417 
54.829 

56.246 
57.662 
59.099 


45.778 
47.060 
48.363 
49.687 
51.025 


40.907 
41.956 
43.032 
44.131 

45.255 
46.403 

47.572 
48.763 
49.973 

51.201 
52.445 
53.704 
54.976 
56.258 

57.549 

58.846 

60.148 

61.45160.535 

62.754J61.972 

64.052'63.412 
65.34764.847 
66.632  66.303 
67.905  67.762 
69.166:69.211 

70.413  70.613  66.180 
71.639:71.966!67.525 
72.844  73.294  68.852 
70.158 
71.440 


34.414=32. 026 
35. 418:33.029 
;^6. 452134.086 
37.518j35.174 
38.61336.294 


74.029174.579 
186  75.827 

76.932 
77.994 
78.946 
79.925 
80.898 


76.318 
77.421 
78.492 
79.534 
80.539 

81.511 
82.443 
83.341 
84.205 
85.030 

85.809 
86.552 
87.271 


81.833 
82.697 
83.505 
84.281 
85.019 

85.734 
86.407 
87.052 


87.950  87.670 
88.579  88.239 

89.194  88.778 
89.725  89.324 
90.246  89.786 
90.725  90.277 
91.19990.624 


41.143 
42.434 

43.766 
45.130 
46.530 
48.001 
49.472 

52.380  50.956 
53.747  52.445 
55.124,53.965 
56.509j55.489 
57.898j57.022 

59.290i58.564 
60.68l!60.109 
62.069i61.685 
63.449:63.271 
64.82164.853 

66.390 
67.878 
69.345 
70.769 
72.158 

73.388 
74.574 
75.638 
76.737 
77.833 

78.889 
79.866 


72.697 
73.923 
75.120 
76.286 

77.418 

78.515 
79.572 
80.589  80.782 
81.574i81.664 
82.512:82.505 


83.406 
84.262 
85.078 
85.859 


83.320 
84.090 
84.829 
85.538 


86.585  86.193 
87.293  86.813 


87.904 
88.508 
89.064 
89.614 


87.444 
87.977 
88.546 
88.946 


Formula,    A^;  =  100^1  — (1  —  z;)(1  +  a»)|, 


*^67 


AMERICAN    LIFE   TABLE.      REVERSION    PAYABLE    AT    THE   END   OF    THE   YEAR    OF    DEATH, 
OF  WHICH   REVERSION    $100    IS    THE    PRESENT  VALUE. 


AGE. 

X. 


0 
1 
2 
3 

4 

5 
6 

7 
8 
9 

10 
11 
12 
13 
14 

15 
16 
17 
18 
19 

20 
21 
22 
23 
24 

25 
26 
27 
28 
29 

30 
31 
32 
33 
34 

35 
36 
37 
38 
39 

40 

41 
42 
43 

44 

45 
46 
47 
48 
49 


Interest  4  Per  Cent. 


Male. 


262  51 
357.79 
413.09 
446.57 
466.40 

478.54 
484.03 
484.73 
482.42 
477.21 

469.46 
459.71 
449.03 

437.98 
426.80 

415.94 
405.75 
396.40 

388.18 
381.26 

375.38 

369.85 
364.44 
359.01 
353.51 

347.98 
342.41 
336.80 
331.18 
325.53 

319.88 
314.21 

308.56 
302.90 

297.27 

291.65 
286.06 
280.50 
274.99 
269.53 

264.10 
258.75 
253.45 
248.23 
243.08 

238.00 
233.01 
228.10 
223.27 
218.56 


Female. 


278.68 
362.38 
416.16 
448.93 

469.48 

481.09 
478.28 
475.08 
471.79 
468.10 

464.99 
458.67 
450.76 
439.31 
426.37 

413.68 
403.24 
394.20 

387.76 
381.48 

375.53 

369.66 
364.05 
358.68 
354.10 

349.55 
344.97 
340.37 
335.58 
330.73 

325.79 
320.82 
315.86 
310.87 
305.00 

301.02 
296.30 
291.56 

286.83 
282.10 

277.35 
272.30 

267.08 
261.82 
256.48 

251.14 
245.77 
240.46 
235.17 
229.91 


290.15 
419.15 
502.13 
556.48 
591.23 

614.36 
626.76 
631.19 
630.28 
624.34 

613.72 
599.38 
583.40 
566.60 
549.69 

533.19 
517.89 
504.01 
492.08 

482.28 


5  Per  Cent. 


Male.  IPemale. 


310.76 
425.24 
506.10 
559.31 
595.24 

617.47 
615.27 
612.37 
609.42 
605.84 

601.54 
595.10 
584.01 
566.57 
546.51 

526.93 
511.17 

497.81 
488.83 
480. 12 

474.27  471.94 
466.83  463.84 
456.20 
448.93 
442.99 


459.64 
452.28 
444.88 

437.37 

429.77 
422.05 
414.39 
406.59 

398.77 
390.92 
383.04 
375.18 
367.31 

359.44 
351.62 
343.84 
336.10 
328.43 

320.84 
313.30 
305.88 
298.55 
291.34 

284.24 

277.26 
270.42 
263.71 
257.14 


437.06 
431.09 
425.06 
418.73 
412.27 

405.63 
398.93 
392.22 
385.48 

378.74 


6  Per  Cent. 


Male.     Female, 


312.72 
473.48 

585.82 
664.50 
718.03 

756.14 
778.69 
789.33 
791.83 
786.16 

772.92 
753.41 
731.21 
707.61 
683.67 

660.46 
639.02 
619.81 
603.54 
590.70 

580.55 
571.33 
562.37 
553.28 
543.95 

534.50 
524.88 
515.12 
505.23 
495.25 

485.13 
475.01 
464.77 
454.50 
444.25 


372.15  433.93 

365.78  423.68 


359.40 
352.99 
346.57 

340.14 
333.17 
325.91 
318.58 
311.10 

303.60  334.74 
296.06325.54 
288.59316.51 
281.16307.66 
273.76  299.01 


413.43 
403.26 
393.14 

383.11 
373.18 
363.37 
353.68 
344.14 


337.36 

482.09 
591.02 
668.23 
723.59 

760.34 
759.76 
758.32 
756.83 
754.43 

751.03 

744.27 
729.98 
705.32 
676.41 

648.26 
626.10 
607.68 
596.02 
584.69 

574.18 
563.79 
554.02 
544.84 
537.66 

530.53 
523.31 
516.02 
508.21 
500.20 

491.93 
485.36 
475.10 
466.59 
458.09 

449.76 
441.77 
433.76 
425.69 
417.59 

409.43 
400.43 
390.98 
381.37 
371.51 

361.60 
351.61 
341.69 
331.83 
321.99 


AGE. 

X. 


50 

51 

52, 

53 

54 

55 
56 
57 
58 
59 

60 
61 
62 
63 
64 

65 
66 
67 
68 
69 

70 
71 
72 
73 

74 

75 
76 

77 
78 
79 

80 
81 
82 
83 
84 

85 
86 
87 
88 
89 

90 
91 
92 
93 
94 

95 
96 
97 
98 
99 


4  Per  Cent. 


Male.  Female. 


213.93 
209.41 
204.97 
200.65 
196.44 


192. 
188. 
184. 
180. 

177. 

173. 
170. 
166. 
163, 
160. 


33 
33 
45 

67 
01 

45 
01 
68 
46 
36 

157.36 
154.47 
151.69 
149.02 
146.45 

143.99 
141.63 
139.36 
137.20 
135.13 

133.15 
131.27 
129.48 

127.77 
126.15 

124.61 
123.15 
121.76 
120.46 
119.22 

118.06 
116.96 
115.93 
114.95 
114.04 

113.19 
112.39 
111.64 
110.94 
110.30 

109.68 
109.15 
108.64 
108.17 
107.72 


224.69 
219.59 
214.54 
209.63 
204.85 


200. 
195. 
191. 
186. 
182. 

178. 
174. 
171. 
167. 
163. 

160.26 
156.99 
153.82 
150.80 
147.90 

145.12 
142.47 
139.88 
137.40 
135.03 

132.82 
130.77 
128.82 
126.99 
125.28 

123.79 
122.41 
121.19 
119.97 
118.79 

117.68 
116.67 
115.74 
114.87 
114.05 

113.28 
112.55 
111.87 
111.20 
110.65 

110.10 
109.55 
109.09 
108.61 
108.27 


5  Per  Cent. 


6  Per  Cent. 


Male.    Female.'   Male.    Female, 


250.72 
244.46 
238.34 
232.39 
226.60 


220. 
215. 
210. 
205. 
200. 

195. 
190. 
186. 
181. 

177. 

173.76 
169.94 
166.26 
162.73 
159.35 

156.12 
153.03 
150.08 
147.26 
144.58 

142.02 
139.59 
137.28 
135.08 
133.00 

131.03 
129.16 
128.40 
125.73 
124.16 

122.68 
121.30 
119.99 
118.76 
117.61 

116.54 
115.54 
114.58 


266.44 
259.29 
252.22 
245.36 

238.72 

232.26 
225.98 
219.88 
213.98 
208.31 

202.79 
197.46 
192.30 
187.21 
182.39 

177.79 
173.42 
169.21 
165.19 
161.36 

157.70 
154.21 
150.82 
147.57 
144.48 

141.62 
138.95 
136.44 
134.09 
131. 

129.98 
128.21 
126.67 
125.12 
123.61 

122.20 
120.92 
119.75 
118.65 
117.62 

116.64 
115.73 
114.87 


113.70114.06 
112.89113.33 

112.121112.64 
111.451111.95 
110.81'111.38 
110.221110.77 
109.65ill0.35 


290.58 
282.34 
274.33 
266.54 
258.98 


251. 
244. 
237. 
231. 
224. 

218. 
212. 
206. 
201. 
195. 

190.91 
186.06 
181.41 
176.96 

172.72 

168.66 
164.80 
161.11 
157.61 
154.27 

151.10 
148.09 
145.24 
142.54 
139.98 

137.56 
135.28 
133.12 
131.09 
129.17 

127.36 
125.67 
124.09 
122.59 
121.19 

119.90 
118.68 
117.54 
116.47 
115.49 

114.56 
113.76 
112.98 
112.28 
111.59 


312.25 
302.76 
293.38 
284.30 
275.53 

267.02 
258.77 
250.76 
243.05 
235.66 

228.49 
221.58 
214.92 
208.33 
202.13 

196.25 
190.68 
185.31 
180.22 
175.37 

170.75 
166.36 
162.11 
158.05 
154.19 

150.63 
147.32 
144.21 
141.30 
138.58 

136.26 
134.10 
132.21 
130.32 
128.48 

126.76 
125.21 
123.79 
122.45 
121.20 

120.02 
118.92 
117.88 
116.91 
116.02 

115.19 
114.36 
113.67 
112.94 
112.43 


FOBMULA, 


10000 


*268 


AMERICAN    LIFE    TABLE.      PRESENT  VALUE    OF  JOINT    LIFE    ANNUITIES. 
PAET  I RELATIVE   AGE   {x)  OF   EACH   SINGLE   LIFE. 

General  Rule.  Add  the  single  Relative  Ages  (x),  whether  of  Male  or  Female,  from  Part  I.  With 
their  Sum  and  the  Joint  Rate  of  Interest,  enter  Part  II.,  and  at  the  junction  (which  may  require  interpola- 
tion, page  298)  will  be  the  Present  Value  of  $1  per  annum. 

Note.  In  the  case  of  Two  Equal  Ages  of  Females,  Part  II.  may  be  entered  with  either  Age  in  Tears 
by  the  column  of  "Equal  Ages,"  and  by  the  actual  Rate  of  Interest. 


JotNT  Rate  of  Istebest  Per  Cent. 


For  tJie  Actual  Rate 

Tw#  Lives ... 
Three  Lives. . 

Four  Lives 

Five  Lives 

Six  Lives.  . . . 


3 

3 
3.920 
4.849 
5.785 
6.731 


3i 

3i 
4.425 
5.358 
6.299 
7.249 


4 

4 
4.929 
5.867 
6.812 


44 

^ 

5.434 
6.376 
7.326 

8.285 


5 

5 

5.938 
6.885 
7.839 
8.803 


6 

6 

6.947 
7.903 

8.867 
9.839 


7       Per  Cent. 

7 

7.956 

8.920 

9.894 

10.875 


Example. 
.37  +  .99  =  1.36. 


Interest   5   per  cent.     Age  of  Male  26,  of  Female  39  years.     Sum   of  Relative 
By  Part  II.,  the  Present  Value  of  $1  per  annum  during  joint  life  is  $12,092. 


Explanation.  The  formulas  below  result  from  further  Equalizations  from  page  259  text.  The 
tabular  Ages  {x)  depend  on  the  theoretic  formula  for  V ,  pages*256— 7,  by  which,  annuities  were  computed 
even  below  age  0,  merely  to  furnish  Relative  Ages  for  equal  annuities  of  the  Male  or  the  Female  Life 
Table.  Under  the  age  7,  the  Relative  Ages  for  two-life  annuities  are  assumed  to  be  the  same  as  for  equal 
annuities  at  older  ages.     The  columns  m.  d.  are  monthly  differences. 


EELATIVEAGE^^a;'). 

EELATIVE  AGE  (x). 

EELATIVE  AGE  (x). 

AGE  X. 
Years. 

LQiEX. 
Years. 

\      / 

AGE  a:. 
Years. 

1 

Male. 

Female. 

Male. 

m.  d. 

Female. 

m.  d. 

Male. 

m.  d. 

Female. 

m.  d. 

0 

3.89 

3.44 

30 

0.54 

0.42 

0.50 

0.33 

60 

8.33 

6.58 

7.24 

6.33 

1 

0.86 

0.79 

31 

.59 

.50 

.54 

.33 

61 

9.12 

7.17 

8.00 

7.00 

2 

.22 

.22 

32 

.65 

.50 

.58 

.33 

62 

9.98 

8.17 

8.84 

7.92 

3 

.12 

.10 

33 

.71 

.50 

.62 

.50 

63 

10.96 

8.50 

9.79 

8.83 

4 

+  .01 

+  .05 

34 

.77 

.67 

.68 

.42 

64 

11.98 

9.75 

10.85 

9.42 

5 

-.04 

-.03 

35 

0.85 

0.67 

0.73 

0.50 

65 

13.15 

10.5 

11.98 

10.7 

6 

-.05 

-.04 

36 

.93 

.75 

.79 

.50 

66 

14.41 

11.3 

13.26 

11.7 

7 

-.05 

-.04 

37 

1.02 

.83 

.85 

.58 

67 

15.76 

12.7 

14.67 

12.9 

8 

-.05 

-.03 

38 

1.12 

.92 

.92 

.58 

68 

17.29 

13.8 

16.22 

14.4 

9 

-.05 

-.03 

39 

1.23 

.92 

.99 

.67 

69 

18.95 

15.0 

17.95 

16.0 

10 

-.04 

-.02 

40 

1.34 

1.08 

1.07 

0.75 

70 

20.75 

16.5 

19.87 

18.2 

11 

-.02 

-.02 

41 

1.47 

1.17 

1.16 

.83 

71 

22.73 

18.3 

22.06 

19.3 

12 

+  .03 

+  .03 

42 

1.61 

1.25 

1.26 

1.00 

72 

24.93 

19.6 

24.37 

22.1 

13 

.06 

.06 

43 

1.76 

1.42 

1.38 

1.08 

73 

27.28 

22.0 

27.02 

25.0 

14 

.07 

.07 

44 

1.93 

1.58 

1.51 

1.25 

74 

29.92 

23.6 

30.02 

27.0 

15 

0.10 

0.11 

45 

2.12 

1.58 

1.66 

1.33 

75 

32.75 

26.2 

33.26 

30.0 

16 

.11 

.13 

46 

2.31  1.92 

1.82 

1.58 

76 

35.90  28.7 

36.83 

32.6 

17 

.15 

.17 

47 

2.54  {2.00 

2.01 

'1.67 

77 

39.34 

31.4 

40.77 

35.8 

18 

.17 

.18 

48 

2.78 

2.25 

2.21 

1.83 

78 

43.11 

34.2 

45.07 

39.3 

19 

.20 

.20 

49 

3.05 

2.42 

2.43 

2.08 

79 

47.21 

37.8 

49.79 

39.4 

20 

0.22 

0.21 

50 

3.34 

2.67 

2.68 

2.33 

80 

51.75 

41.3 

54.52 

42.3 

21 

.24 

.24 

51 

3.66 

2.92 

2.96 

2.58 

81 

56.71 

45.1 

59.60 

42.7 

22 

.26 

.27  1 

52 

4.01 

3.25 

3.27 

2.83 

82 

62.12 

49.2 

64.72 

48.7 

23 

.28 

.30  j 

53 

4.40 

3.42 

3.61 

3.17 

83 

68.03;  54.3 

70.56 

55.4 

24 

.31 

.32 

54 

4.81 

3.83 

3.99 

3.42 

84 

74.54 

59.8 

77.21 

60.2 

25 

0.34 

0.34 

55 

5.27 

4.33 

4.40 

3.83 

85 

81.72 

65.3 

84.44 

62.3 

26 

.37 

.37 

56 

5.79 

4.42 

4.86 

4.25 

86 

89.56 

70.1 

91.92 

65.3 

27 

.41 

.40 

57 

6.32 

5.00 

5.37 

4.75 

87 

97.97 

79.3 

99.75 

72.6 

28 

.45 

.43 

58 

6.94 

5.50 

5.94 

5.08 

88 

107.49 

86.8 

108.46 

78.8 

29 

.49 

.46 

59 

7.60 

6.08 

6.55 

5.75 

89 

117.91 

117.91 

Formula  for  m  Lives  :    Joint  Kate  {i)  =  —  100  + 100  -f-  vs""-^. 
Kelative  Age  {x)  =  1000  Log  — .     Here  jtJa;  =  the  probability,  and  s  =  0.9.91145. 


♦269 


AMERICAN  LIFE  TABLE.      PRESENT  VALUE  OF  JOINT  LIFE  ANNUITIES. 

PAET   n.— PRESENT  VALUE   (a)  OF   $1  PER  ANNUM,  PAYABLE  AT  THE  END  OF  EACH 

YEAR  DURING  THE  JOINT  CONTINUANCE  OF  ALL  THE  LIVES. 


tors  0)  "^(JD 


6.88 

1.58 

0.44 

.20 

+  .10 

-.06 
-.08 
-.08 
.06 
-.06 

-.04 

-.04 

+.06 

.12 

.14 

0.22 
.26 
.34 
.36 
,40 

0.42 
.48 
.54 
.60 
.64 

0.68 
.74 
.80 
.86 


0 
1 
2 
3 
4 

5 
6 

7 
8 
9 

10 

11 
12 
13 
14 

15 
16 
17 
18 
19 

20 
21 
22 
23 

24 

25 
26 
27 
28 


3 
Per  Ct. 


.92  29 


1.00 
1.08 
1.16 
1.24 
1.36 

1.46 
1.58 
1.70 
1.84 
1.98 

2.14 
2.32 
2.52 
2.76 
3.02  44 


30 
31 
32 
33 
34 

35 
36 
37 
38 
39 

40 

41 
42 
43 


3.32 
3.64 
4.02 
4.42 
4.86 


12.576 
16.285 
18.042 
18.953 
19.482 

19.776 
19.740 
19.695 
19.648 
19.640 

19.527 
19.432 
19.269 
19.007 
18.690 

18.363 
18.086 
17.798 
17.674 
17.508 

17.348 
17.187 
17.032 
16.883 
16.761 

16.638 
16.512 
16.384 
16.245 
16.100 

15.948 
15.792 
15.632 
15.467 
15.299 

15.132 

14.968 
14.801 
14.629 
14.453 

14.272 
14.066 
13.843 
13.608 
13.359 


4 
Per  Ct. 


45 
46 
47 
48 
49 


10.656 
13.787 
15.279 
16.061 
16.524 

16.794 
16.783 
16.766 
16.748 
16.723 

16.691 
16.634 
16.519 
16.318 
16.069 

15.809 
15.591 
15.400 
15.275 
15.151 

15.032 
14.912 

14.797 
14.687 
14.601 

14.514 
14.425 
14.334 
14.234 
14.129 

14.017 
13.902 
13.783 
13.661 
13.536 

13.411 
13.290 
13.165 
13.037 
12.905 

12.769 
12.610 
12.435 
12.250 
12.052 


13.100 
12.828 
12.549 
12.259 
11.958 


0 
Per  Ct. 


9.211 
11.906 
13.192 
13.873 
14.282 

14.527 
14.531 
14.530 
14.529 
14.523 

14.512 
14.479 
14.395 
14.237 
14.035 

13.822 
13.646 
13.492 
13.396 
13.300 

13.209 
13.117 
13.029 
12.945 


Per  Ct; 


8.096 
10.451 
11.576 
12.175 
12.540 

12.763 
12.775 

12.783 
12.792 

12.798 

12.799 
12.782 
12.721 
12.592 
12.425 

12.247 
12.100 
11.973 
11.896 
11.820 

11.749 
11.676 
11.606 
11.541 
12.88311.495 

12.82011.449 


7 
Per  Ct. 


11.844 
11.623 
11.396 
11.158 
10.908 


12.756 
12.690 
12.616 
12.539 

12.455 
12.369 
12.279 
12.187 
12.092 

11.998 
11.907 
11.813 
11.716 
11.617 

11.513 
11.390 
11.252 
11.105 
10.945 

10.776 
10.596 
10.409 
10.212 
10.004 


11.401 
11.353 
11.297 
11.239 

11.175 
11.109 
11.040 
10.969 
10.896 

10.824 
10.755 
10.684 
10.610 
10.534 

10.455 
10.358 
10.249 
10.131 
10.001 


7.213 

9.299 

10.296 

10.829 

11.156 

11.360 
11.376 
11.389 
11.404 
11.417 

11.426 
11.419 
11.374 
11.268 
11.126 

10.974 
10.850 
10.742 
10.680 
10.618 

10.560 
10.500 
10.444 
10.392 
10.357 

10.322 
10.286 
10.250 
10.207 
10.162 

10.113 

10.061 

10.008 

9.952 

9.895 

9.838 
9.785 
9.731 
9.675 
9.616 

9.556 
9.479 
9.391 
9.295 
9.189 


9.863 
9.714 
9.559 
9.394 
9.219 


9.075 
8.952 
8.822 
8.683 
8.535 


o  >  c^ 


5.36 
5.92 
6.54 
7.22 

7.98 

8.80 

9.72 
10.74 
11.88 
13.10 

14.48 
16.00 
17.68 
19.58 
21.70 

23.96  65 


50 
51 
52 
53 
54 

55 
56 
57 
58 
59 

60 
61 
62 
63 
64 


26.52 
29.34 
32.44 
35.90 

39.74 
44.12 
48.74 
54.04 
60.04 

66.52 
73.86 
81.54 
90.14 
99.58 

109.04 
119.20 
129.44 
141.12 
154.42 

168.88 
183.84 
199.50 
216.92 
235.82 

255.88 
277.88 
301.14 
327.30 
353.90 

383.42 
416.02 
448.28 
490.76 


3 
Per  Ct. 


66 
67 
68 
69 

70 
71 
72 
73 

74 

75 
76 

77 
78 
79 

80 
81 
82 
83 
84 

85 
86 
87 
88 
89 

90 
91 
92 
93 
94 

95 
96 
97 
98 
99 


4 
Per  Ct. 


5 
PerCt. 


11.648 
11.333 
11.008 
10.681 
10.351 

10.019 
9.683 
9.343 
9.003 
8.665 

8.323 

7.981 
7.638 
7.282 
6.937 

6.598 
6.268 
5.938 
5.615 
5.299 

4.989 
4.686 
4.382 

4.082 
3.789 

3.513 
3.253 
3.003 
2.765 
2.536 

2.346 
2.167 
2.018 
1.863 

1.708 


1.562 
1.431 
1.312 
1.201 
1.097 

0.998 
0.906 
0.820 
0.739 
0.666 

0.600 
0.530 
0.476 
0.415 
0.385 


6 
PerCt. 


10.649 

10.385 

10.110 

9.832 

9.551 

9.266 
8.976 
8.681 
8.385 
8.088 

7.787 
7.484 
7.179 
6.860 
6.550 

6.243 
5.944 
5.643 
5.348 

5.057 

4.771 
4.491 
4.208 
3.927 
3.641 

3.392 
3.146 
2.908 

2.682 
2.464 

2.282 
2.111 
1.968 
1.819 
1.670 


9.786 
9.563 
9.329 
9.091 
8.850 

8.603 
8.351 
8.094 
7.834 

7.573 

7.307 
7.038 
6.765 
6.478 


7 
Per  Ct 


9.035 

8.845 
8.645 
8.440 
8.231 

8.017 
7.797 
7.572 
7.343 
7.112 

6.875 
6.635 
6.390 
6.131 


8.378 
8.215 
8.042 
7.865 
7.684 


6.198  5.877 


1.528 
1.401 
1.286 
1.178 

1.077 

0.980 
0.891 
0.807 
0.727 
0.656 

0.591 
0.522 
0.470 
0.410 
0.381 


5.920 
5.647 
5.372 
5.101 
4.834 

4.569 
4.309 
4.045 
3.782 
3.523 

3.278 
3.045 
2.819 
2.604 
2.395 

2.221 
2.057 
1.920 
1.776 
1.632 

1 
1 


495 
373 
1.261 
1.156 
1.058 

0.963 
0.876 
0.794 
0.716 
0.646 

0.583 
0.515 
0.464 
0.404 
0.375 


5.625 
5.375 
123 

4.874 
4.627 

4.382 
4.140 
3.893 
3.646 
3.402 

3.170 
2.950 
2.735 
2.529 
2.329 

2.163 
2.005 
1.874 
1.736 

1.597 

1.464 
1.345 
1.237 
1.135 
1.039 

0.947 
0.862 
0.782 
0.705 
0.637 

0.574 
0.508 
0.457 
0.399 


7.497 
7.304 
7.105 
6.902 
6.697 

6.486 
6.270 
6.050 
5.815 
5.584 

5.354 
5.126 
4.894 
4.664 
4.436 

4.208 
3.982 
3.751 
3.519 

3.289 

3.069 
2.860 
2.656 
2.459 
2.267 

2.108 
1.956 
1.830 
1.697 
1.562 

1.434 
1.319 
1.214 
1.114 
1.021 

0.931 
0.848 
0.770 
0.695 
0.628 

0.566 
0.502 
0.452 
0.396 


0.3720.370 


Formula,    ajxc  — 


Da 


♦270 


AMERICAN  FEMALE  LIFE  TABLE.     PRESENT  VALUE  OF  WIDOW'S  TX)WER  IN  AN  ESTATE 
WORTH  $100,  ACCORDING  TO  A  GIVEN  RATE  OF  INTEREST. 

Example.  A  widow  whose  age  is  39  is  entitled  to  Dower  in  an  Estate  worth  ^7,200,  at  5  per  cent, 
interest.  Opposite  age  39  is  23.475,  to  be  multiplied  by  72  (the  number  of  hundreds  in  7,200) ;  the  product 
$1,690.20  is  the  present  value  of  the  Dower. 

By  the  laws  of  most  of  tlie  States,  on  the  death  of  the  husband,  the  widow  is  entitled  to  "  the  life  use  of 
one-third  of  the  real  estate,"  of  which^he  present  value  is  given  by  this  Table.  In  some  States,  where  the 
Dower,  instead  of  one-third,  is  one-half  of  the  life  use,  multiply  the  present  result  by  3  and  divide  the  product 
by  2.  For  greater  accuracy,  the  present  Table  is  based  on  "  complete  annuities  "  of  the  Female  Life  Table, 
continuing  to  the  day  of  death.     For  page  *255,  line  12,  take  |  of  the  6,  to  be  the  5  per  cent.  Dower. 


AGE. 

3              4 

5 

6 

7 

A&E. 

3 

4 

5 

6 

7 

X. 

Per  Cent.  Per  Cent. 

Per  Cent. 

Per  Cent 

Per  Cent. 

X. 

50 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

5 

23.840    26.266 

27.800 

28.818 

29.525 

15.257 

18.201 

20.510 

22.338 

23.800 

6 

23.773 

26.225 

27.780 

28.813 

29.534 

51 

14.926 

17.850 

20.156 

21.993 

23.471 

7 

23.699 

26.177 

27.754 

28.806 

29.538 

52 

14.586 

17.486 

19.787 

21.630 

23.121 

8 

23.622 

26.127 

27.727 

28.797 

29.543 

53 

14.241 

17.114 

19.408 

21.257 

22.760 

9 

23.539 

26.070 

27.694 

28.782 

29.544 

54 

13.892 

16.736 

19.021 

20.873 

22.386 

10 

23.449 

26.006 

27.653 

28.762 

29.539 

55 

13.538 

16.350 

18.623 

20.476 

21.998 

11 

23.339 

25.921 

27.592 

28.720 

29.514 

56 

13.179 

15.956 

18.214 

20.065 

21.594 

12 

23.188 

25.791 

27.483 

28.630 

29.439 

57 

12.814 

15.553 

17.794 

19.642 

21.176 

13 

22.977 

25.594 

27.303 

28.465 

29.288 

58 

12.447 

15.145 

17.366 

19.208  1  20.745 

14 

22.733 

25.359 

27.082 

28.258 

29.092 

59 

12.078 

14.733 

16.931 

18.764   20.303 

15 

22.482 

25.115 

26.849 

28.037 

28.882 

60 

11.703 

14.312 

16.485 

18.307 

19.845 

16 

22.259 

24.902 

26.649 

27.850 

28.705 

61 

11.327 

13.886 

16.031 

17.839 

19.372 

17 

22.055 

24.708 

26.470 

27.683 

28.550 

62 

10.946 

13.454 

15.567 

17.358 

18.886 

18 

21.896 

24.565 

26.344 

27.573 

28.452 

63 

10.556 

13.006 

15.083 

16.853 

18.371 

19 

21.736 

24.421 

26.217 

27.461 

28.353 

64 

10.170 

12.561 

14.600 

16.348 

17.854 

20 

21.578 

24.280 

26.094 

27.354 

28.259 

65 

9.786 

12.118 

14.116 

15.839 

17.331 

21 

21.418 

24.136 

25.968 

27.244 

28.161 

66 

9.406 

11.676 

13.632 

15.327 

16.803 

22 

21.261 

23.994 

25.844 

27.136 

28.068 

67 

9.025 

11.230 

13.141 

14.806 

16.262 

23 

21.104 

23.854 

25.723 

27.032 

27.977 

68 

8.648 

10.787 

12.651 

14.282 

15.717 

24 

20.963 

23.732 

25.620 

26.948 

27.908 

69 

8.274 

10.345 

12.326 

13.756 

15.166 

25 

20.820 

23.606 

25.516 

26.862 

27.837 

70 

7.904 

9.905 

11.-668 

12.226 

14.610 

26 

20.672 

23/477 

25.408 

26.773 

27.764 

71 

7.536 

9.468 

11.177 

12.696 

14.051 

27 

20.521 

23.344 

25.296 

26.680 

27.688 

72 

7.170 

9.027 

10.680 

12.155 

13.477 

28 

20.361 

23.202 

25.174 

26.578 

27.601 

73 

6.806 

8.588 

10.181 

11.610 

12.897 

29 

20.196 

23.053 

25.046 

26.469 

27.512 

74 

6.448 

8.154 

9.686 

11.067 

12.315 

30 

20.024 

22.897 

24.910 

26.354 

27.414 

75 

6.104 

7.735 

9.207 

10.539 

11.749 

31 

19.847 

22.736 

24.769 

26.233 

27.311 

76 

5.774 

7.333 

8.745 

10.028 

11.198 

32 

19.666 

22.569 

24.622 

26.107 

27.203 

77 

5.454 

6.939 

8.291 

9.525 

10.652 

33 

19.480 

22.396 

24.470 

25.975 

27.091 

78 

5.146 

6.560 

7.852 

9.036 

10.123 

34 

19.289 

22.219 

24.312 

25.838 

26.973 

79 

4.849 

6.193 

7.426 

8.559 

9.603 

35 

19.096 

22.039 

24.152 

25.700 

26.854 

80 

4.587 

5.869 

7.048 

8.137 

9.143 

36 

18.902 

21.858 

23.993 

25.562 

26.737 

81 

4.3^6 

5.558 

6.685 

7.729 

8.698 

37 

18.704 

21.672 

23.827 

25.418 

26.615 

82 

4.112 

5.279 

6.360 

7.364 

8.298 

38 

18.500 

21.480 

23.654 

25.268 

26.486 

83 

3.884 

4.994 

6.026 

6.987 

7.884 

39 

18.291 

21.281 

23.475 

25.112 

26.352 

84 

3.658 

4.711 

5.693 

6.611 

7.470 

40 

18.075 

21.075 

23.288 

24.948 

26.211 

85 

3.443 

4.441 

5.374 

6.248 

7.069 

41 

17.841 

20.847 

23.078 

24.759 

26.045 

86 

3.245 

4.191 

5.079 

5.913 

6.698 

42 

17.594 

20.603 

22.850 

24.552 

25.859 

87 

3.061 

3.958 

4.802 

5.598 

6.349 

43 

17.337 

20.348 

22.609 

24.331 

25.660 

88 

2.884 

3.735 

4.537 

5.295 

6.012 

44 

17.068 

20.077 

22.351 

24.092 

25.442 

89 

'2.717 

3.523 

4.285 

5.007 

5.691 

45 

16.790 

19.795 

22.080 

23.839 

25.210 

90 

2.556 

3.319 

4.041 

4.727 

5.378 

46 

16.501 

19.499 

21.793 

23.569 

24.960 

91 

2.405 

3.126 

3.811 

4.462 

5.083 

47 

16.204 

19.194 

21.494 

23.286 

24.696 

92 

2.261 

2.942 

3.591 

4.209 

4.799 

48 

15.898 

18.876 

21.181 

22.987 

24.416 

93 

2.124 

2.759 

3.380 

3.965 

4.525 

49     15.582 

18.545 

20.853 

22.670 

24.117 

94 

1.998 

2.605 

3.185 

3.740 

4.272 

FoJRMULA,     Dower  on  100  = 

f          Or-T,^-: 

V 

I 

UNlVc, 

.  \ 

UNIVERSITY  OF  CALIFORNIA  LIBRARY 
BERKELEY 

Return  to  desk  from  which  borrowed. 
This  book  is  DUE  on  the  last  date  stamped  below. 


SENT  ON  ILL 

SEP  0  9  ]m 

U.  C.  BERKELEY 

LD  21-95»n-ll,'50(2877sl6)476 


YE  n?6l4 


/ 


!V\  e-e  c 


f  I 


